AN ABSTRACT OF THE THESIS OF
Ratih E. Lusianti for the degree of Master of Science in Chemical Engineering
presented on August 31, 2010.
Title: Removal of Cryoprotectant with the Use of a Microseparation Device.
Abstract approved:_________________________________________________________________
Adam Z. Higgins
Cryoprotectants (CPAs) such as glycerol and dimethyl sulfoxide (DMSO) are
commonly used during cryopreservation of cell based therapeutics. Although
these additives are beneficial during freezing, it is often desirable to remove
them before infusion into a patient. Currently, the most common method for
CPA removal is by centrifugation. This method is time consuming, labor
intensive, and can also lead to significant cell losses. In this study, we
investigate the possible use of a microseparation device for removal of CPAs
from red blood cell suspensions. A mathematical model was developed to
predict the CPA removal performance of the device and cell volume changes
during the process. Experiments to ascertain the permeability properties of
several different types of membranes of interest were conducted using the
device. The resulting experimental values were then incorporated into the
model to make CPA removal predictions. To assess the accuracy of the model
predictions, glycerol removal experiments from solutions without red blood
cells were carried out. Through comparison of the experimental data and the
model predictions, it was found that the model could accurately predict CPA
removal for membranes with sufficiently small pores where mass transfer is
dominated by diffusion; but in membranes with larger pores where mass
transfer is dominated by pressure driven flow, the model predicted values
that are lower than what was obtained through experiments. The reason for
this effect is the pressure discrepancy that was found between the pressure
drop recorded during the experiment and the model predicted pressure drop.
The model predicted pressure drop assumes ideal fluid flow condition
whereas the actual conditions during the experiment indicates the presence
of air bubbles trapped inside the channels, obstructing the flow of fluid and
possibly altering the surface area available for mass transfer. Parametric
studies using model simulations on the CPA removal performance of the
membranes with smaller pores were conducted. Through parametric studies,
CPA removal trends and cell volume changes during the process using the
membranes of interest were better understood. The information gained from
this study is useful for designing the next prototype of the microseparation
device as well as for developing an optimal CPA removal protocol for red
blood cell suspensions.
Copyright by Ratih E. Lusianti
August 31, 2010
All Rights Reserved
Removal of Cryoprotectant with the Use of a Microseparation Device
by
Ratih E. Lusianti
A THESIS
Submitted to
Oregon State University
In partial fulfillment of
the requirements for the
degree of
Master of Science
Presented August 31, 2010
Commencement June 2011
Master of Science thesis of Ratih E. Lusianti presented on August 31, 2010.
APPROVED:
_________________________________________________________________________________________
Major Professor, representing Chemical Engineering
_________________________________________________________________________________________
Head of the Department of Chemical, Biological, and Environmental
Engineering
_________________________________________________________________________________________
Dean of the Graduate School
I understand that my thesis will become part of the permanent collection of
Oregon State University libraries. My signature below authorizes release of
my thesis to any reader upon request.
_________________________________________________________________________________________
Ratih E. Lusianti, Author
ACKNOWLEDGEMENTS
I would like to thank Dr. Adam Higgins for being a great advisor through this
entire process, my lab mates and friends for assisting me in completing this
work, and Kevin and Layla for keeping me sane and making sure I didnt’t go
off the deep end.
TABLE OF CONTENTS
Page
1 Introduction
1
2 Background
4
2.1 Cryopreservation ………………………………………………………
4
2.2 Cryoprotectant Removal ...………………………………………….
7
2.2.1 Centrifugation ...…………………………………………………
7
2.2.2 Hollow Fiber Dialysis ...………………………………………
9
2.2.3 Microfluidic Devices ………………………………………….
11
2.3 Membranes ……………………………………………………………….
14
2.3.1 Gambro AN69-ST ………………………………………………
16
2.3.2 Millipore ISOPORE …………………………………………….
16
2.4 Cryoprotectants ………………………….……………………………..
17
3 Mathematical Model
18
3.1 Cell Membrane Transport ………………………………………….
20
3.2 Synthetic Membrane Transport …………………………………
21
3.3 Volume Balances ………………………………………………………
22
3.4 Solute Balances ………………………………………………………...
24
3.5 Pressure Drop …………………………………………………………..
25
3.6 Model Programming …………………………………………………
26
4 Experimental Setup
28
4.1 Microseparation Device ………………………………………….….
28
4.1.1 Microseparation Device Assembly ……………….….….
29
4.2 Hydraulic Permeability Experiment ………………………..….
31
4.2.1 Experimental Apparatus …………………………………….
31
TABLE OF CONTENTS (Continued)
Page
4.2.2 Experimental Procedure …………………………………….
32
4.2.3 Analytical Method …………………………………………….
33
4.3 Diffusive Permeability Experiment …………………………….
35
4.3.1 Experimental Apparatus …………………………………….
35
4.3.2 Experimental Procedure …………………………………….
36
4.3.3 Analytical Method ………………………………………………
37
4.4 Model Validation Experiment ………………………………………
39
4.4.1 Experimental Apparatus ………………………………………
39
4.4.2 Experimental Procedure ………………………………………
39
4.4.3 Analytical Methods ………………………………………………
40
5 Results and Discussion
42
5.1 Hydraulic Permeability Expriments ……………………………..
42
5.1.1 Gambro AN69-ST ………………………………………………..
42
5.1.2 Millipore ISOPORE HTTP …………………………………….
47
5.1.3 Millipore ISOPORE TMTP ……………………………………
52
5.2 Diffusive Permeability Experiments……………………………..
57
5.2.1 Gambro AN69-ST ………………………………………………..
57
5.2.2 Millipore ISOPORE HTTP …………………………………….
59
5.2.3 Millipore ISOPORE TMTP ……………………………………
60
5.3 Model Validation Experiments ……….……………………………
61
5.4 Parametric Studies ………………………………………………………
73
6 Conclusions
81
6.1 Hydraulic Permeability ………………………………………………..
81
6.2 Diffusive Permeability …………………………………………………
82
6.3 Model Validation …………………………………………………………
83
TABLE OF CONTENTS (Continued)
Page
6.4 Parametric Studies ………………………………………………………
84
6.5 Future Work ……………………………………………………………….
85
Bibliography
125
LIST OF APPENDICES
Appendix
Page
A Nomenclature ……………………………………………………………………………
87
B Derivation of Differential Equations …………………………...………………
90
C Protocol for Microseparation Device Assembly …………………..………
101
D Protocol for Hydraulic Permeability Experiment ………………...………
103
E Protocol for Diffusive Permeability Experiment ………………….………
106
F Protocol for Model Validation Experiment …………………...……………..
109
G Pressure Calibration Curve …………………………………………...……………
112
H Concentration Calibration Curve ……………………………………...………… 114
I Hydraulic Permeability Experimental Data ………………………………….. 115
I.1
Gambro AN69-ST …………………………………………………….. 115
I.2
Millipore ISOPORE HTTP …………………………………………
I.3
Millipore ISOPORE TMTP ………………………………………… 117
116
J Diffusive Permeability Experimental Data …………………………………… 118
J.1
Gambro AN69-ST …………………………………………………….. 118
J.2
Millipore ISOPORE HTTP …………………………………………. 118
J.3
Millipore ISOPORE TMTP ………………………………………… 119
K Model Validation Experiment ………………………………………………….….. 120
K.1
Gambro AN69-ST …………………………………………………….. 120
K.2
Millipore ISOPORE HTTP …………………………………………. 120
K.3
Millipore ISOPORE TMTP ………………………………………… 120
L Simulation Data …………………………………………………………………………. 121
L.1
Gambro AN69 …………………………………………………………. 121
L.2
Millipore ISOPORE HTTP …………………………………………
L.3
Millipore ISOPORE TMTP ………………………………………… 122
L.4
Parametric Studies …………………………………………………… 122
121
LIST OF FIGURES
Figure
3.1
Page
Diagram of the differential volume in microseparation
device ………………………………………………………………………………
19
Boundary conditions at x=0 and x=L. The unknown variables
at x=0 and the target values at x=L are boxed ……………………..
27
4.1
Single sheet of lamina embossed with microchannels …………
28
4.2
Assembled view of the microseparation device …………………..
30
4.3
Exploded view of the microseparation device …………………….
30
4.4
Experimental apparatus of the hydraulic permeability
experiment ……………………………………………………………………….
32
Experimental apparatus of the diffusive permeability
experiment ……………………………………………………………………….
36
4.6
Experimental apparatus of the model validation experiment .
39
5.1
Hydraulic permeability of AN69 to DI water...................................
43
5.2
Hydraulic permeability of AN69 to 10% w/v glycerol
solution .……………………..……………………………………....……………..
44
Hydraulic permeability of AN69 to 40% w/v glycerol
solution ……………………………………………………………………………..
44
Hydraulic permeability of AN69 to glycerol solutions of
different viscosities ……………………………………………………………
46
Hydraulic permeability of AN69 to glycerol solutions of
different viscosities compared to theoretical projections ….....
47
5.6
Hydraulic permeability of ISOHTTP DI water……………………….
48
5.7
Hydraulic permeability of ISOHTTP to 10% w/v glycerol
solution .……………………..………………………….…………………………..
49
3.2
4.5
5.3
5.4
5.5
LIST OF FIGURES (Continued)
Figure
5.8
Page
Hydraulic permeability of ISOHTTP to 40% w/v glycerol
solution ………………………………………………………………………..……
49
5.9
Hydraulic permeability of ISOHTTP to glycerol solutions of
different viscosities ……………………………………………………………. 50
5.10
Hydraulic permeability of ISOHTTP to glycerol solutions of
different viscosities compared to theoretical projections …….. 51
5.11
Hydraulic permeability of ISOTMTP to DI water ………………….
53
5.12
Hydraulic permeability of ISOTMTP to 10% w/v glycerol
solution ……………………………………………………………………………..
53
Hydraulic permeability of ISOTMTP to 40% w/v glycerol
solution ……………………………………………………………………………..
54
Hydraulic permeability of ISOTMTP to glycerol solutions of
different viscosities ……………………………………………………………
55
Hydraulic permeability of ISOTMTP to glycerol solutions of
different viscosities compared to theoretical projections …….
56
Diffusive permeability of AN69 to 10% w/v glycerol solution
for flow rates ranging from 0.1 to 1 ml/min ………………………..
58
Diffusive permeability of ISOHTTP to 10% w/v glycerol
solution for flow rates ranging from 0.1 to 1 ml/min …………..
60
Diffusive permeability of ISOTMTP to 10% w/v glycerol
solution for flow rates ranging from 0.1 to 1 ml/min …………..
61
Model prediction comparison for urea removal to Tuhy’s
model and experimental data using AN69 ………………………….
63
Comparison between model validation experimental data
and model predictions for membrane AN69 using the
experimental Lp value for 10% w/v solution ………………………
65
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
LIST OF FIGURES (Continued)
Figure
5.21
5.22
5.23
5.24
Page
Comparison between model validation experimental data
and model predictions for membrane ISOHTTP using the
experimental Lp value for 10% w/v solution ………………………
66
Comparison between model validation experimental data
and model predictions for membrane ISOTMTP using the
experimental Lp value for 10% w/v solution ………………………
66
Comparison of experimental data and model predictions
of glycerol removal using different hydraulic permeability
values for the ISOHTTP membrane …………………………………….
67
Comparison of experimental data and model predictions
of glycerol removal using different hydraulic permeability
values for the ISOTMTP membrane …………………………………….
68
5.25
Effect of flow rate on the fractional removal of glycerol from
red blood cells suspended in 10% w/v glycerol solution
using AN69 ………………………………………………………………………... 74
5.26
Effect of flow rate on the fractional removal of glycerol from
red blood cells suspended in 10% w/v glycerol solution
using ISOHTTP ……………………………………………………...…………… 75
5.27
Effect of dialyzer length on the fractional removal of glycerol
from red blood cells suspended in 10% w/v glycerol
solution using AN69 …………………………………………………………... 77
5.28
Effect of dialyzer length on the fractional removal of glycerol
from red blood cells suspended in 10% w/v glycerol
solution using ISOHTTP ……………………………………………………… 77
5.29
The change in concentration of the extracellular solution
stream with respect to microchannel length for AN69 and
ISOHTTP ……………………………………………………………………………. 79
5.30
The relative cell volume change with respect to microchannel
length for AN69 and ISOHTTP …………………………………………….. 79
LIST OF TABLES
Table
Page
2.1
Membrane properties for comparison ………………………………… 17
5.1
Comparison of pressure drops obtained from experiment
and from model predictions for validation experiment using
the AN69 membrane ………………………………………………………….. 69
5.2
Comparison of pressure drops obtained from experiment
and from model predictions for validation experiment using
the ISOHTTP membrane ……………………………………………………... 70
5.3
Comparison of pressure drops obtained from experiment
and from model predictions for validation experiment using
the ISOTMTP membrane …………………………………………………….. 70
6.1
Hydraulic permeability values in m/Pa-s for the three
membranes tested using three solutions of varying glycerol
concentrations …………………………………………………………………… 82
6.2
Average diffusive permeability values for the three
membranes tested for a flow rate range from 0.1 ml/min to
1 ml/min ……………………………………………………………………………. 83
6.3
Linear approximation of Ps as a function of flow rate for the
three membranes tested …………………………………………………….. 83
LIST OF APPENDIX FIGURES
Figure
Page
B.1
Diagram of the system with coordinates ………………………………. 90
B.2
Concentration profile inside a permeable membrane ……………. 92
B.3
Cell volume content …………………………………………………………….. 97
LIST OF APPENDIX TABLES
Table
Page
A.1
Nomenclature …………………………………………………………………...
90
G.1
Pressure calibration curve for transducer 1 ………………………..
112
G.2
Pressure calibration curve for transducer 2 ………………………..
112
G.3
Pressure calibration curve for transducer 3 ………………………..
113
G.4
Pressure calibration curve for transducer 4 ………………………..
113
H.1
Concentration calibration curve ……………………….………………..
114
I.1
Experimental data for hydraulic permeability of AN69 to DI
water. Average of 3 sets ……………………………………………………..
115
I.2
Experimental data for hydraulic permeability of AN69 to 10 %
w/v glycerol. Average of 3 sets ………………………………………….. 115
I.3
Experimental data for hydraulic permeability of AN69 to 40 %
w/v glycerol. Average of 3 sets ………………………………………….. 115
I.4
Experimental data for hydraulic permeability of ISOHTTP to DI
water. Average of 3 sets …………………………………………………….. 116
I.5
Experimental data for hydraulic permeability of ISOHTTP to
10% w/v glycerol. Average of 3 sets …………………..……………….
116
Experimental data for hydraulic permeability of ISOTMTP to
40% w/v glycerol. Average of 3 sets …………………………………..
116
I.6
I.7
Experimental data for hydraulic permeability of ISOTMTP to DI
water. Average of 3 sets …………………………………………………….. 117
I.8
Experimental data for hydraulic permeability of ISOTMTP to
10% w/v glycerol. Average of 3 sets …………………..……………….
117
Experimental data for hydraulic permeability of ISOTMTP to
40% w/v glycerol. Average of 3 sets …………………………………..
117
I.9
LIST OF APPENDIX TABLES (Continued)
Table
J.1
J.2
J.3
K.1
K.2
K.3
L.1
L.2
L.3
L.4
L.5
Page
Experimental data for diffusive permeability of AN69 to 10%
w/v glycerol solution for flow rate range between 0.1 to 1.0
ml/min …………………………………………………………………………….
118
Experimental data for diffusive permeability of ISOHTTP to
10 % w/v glycerol solution for flow rate range between 0.1
to 1.0 ml/min ………………………………………………………………….
118
Experimental data for diffusive permeability of ISOTMTP to
10 % w/v glycerol solution for flow rate range between 0.1
to 1.0 ml/min …………………………………………………………………..
119
Experimental data for model validation experiment using
AN69 ……………………………………………………………………………….
120
Experimental data for model validation experiment using
ISOHTTP ………………………………………………………………………….
120
Experimental data for model validation experiment using
ISOTMTP ………………………………………………………………………….
120
Simulation data for model validation experiment using
AN69 and Ps and Lp obtained from experiment …………………
121
Simulation data for model validation experiment using
ISOHTTP and Ps and Lp obtained from experiment
(Lp = 1.03e-8 m/Pa-s) …………………………………………………........
121
Simulation data for model validation experiment using
ISOHTTP and Lp value from theoretical projection
(Lp = 1.70e-8 m/Pa-s) ………………………………………………………
121
Simulation data for model validation experiment using
ISOTMTP and Ps and Lp obtained from experiment
(Lp = 2.03e-8 m/Pa-s) ………………………………………………………..
122
Simulation data for model validation experiment using
ISOTMTP and Lp value from theoretical projection
(Lp = 3.74e-8 m/Pa-s) ………………………………………………………..
122
LIST OF APPENDIX TABLES (Continued)
Table
L.6
L.7
L.8
Page
Simulation data for parametric study varying flow rate using
AN69 and permeability parameters from experiment …………
122
Simulation data for parametric study varying flow rate using
ISOHTTP and permeability parameters from experiment …….
123
Simulation data for parametric study varying channel length
using AN69, permeability parameters from experiment and a
flow rate of 0.4 ml/min ………………………………………………………
123
L.9
Simulation data for parametric study varying channel length
using ISOHTTP, permeability parameters from experiment and
a flow rate of 0.4 ml/min ………………………………………………….... 123
L.10
Simulation data for extracellular solution concentration and
relative cell volume change as a function of microchannel
length for AN69 …………………………………………………………………
124
Simulation data for extracellular solution concentration and
relative cell volume change as a function of microchannel
length for ISOHTTP ……………………………………………………………
124
L.11
DEDICATION
I dedicate this to my family: Bapak, Ibu, and my little sister ‘Pupy’.
1
Removal of Cryoprotectant with the Use of a Microseparation Device
Chapter 1 – Introduction
Cell therapy is a form of medical treatment that aims to replace, repair or
enhance the biological function of damaged tissue or organs by transplanting
or transfusing isolated living cells into the body [1]. With the growing
popularity of cell therapy in the medical field, the demand of cell therapy
products for treatment is projected to increase into the future.
Cryopreservation plays an essential part in enabling the increase of the
production of cell therpeutics because it allows for long term storage.
Hematopoietic cells are amongst the most common types of cells to be
cryopreserved with products ranging from cryopreserved bone marrow to
frozen red blood cells for transfusion [2]. Cryopreserved cells are frozen in a
solution that contains cryoprotective agents (CPA) to protect it from freezing
injury. Before cryopreserved cell therapy products can be used on patients,
the CPA needs to be removed to avoid adverse health effects. This study
specifically focuses on the CPA removal process in previously frozen red
blood cells.
Most of the blood products that are stocked in blood banks nowadays
are in the form or conventional whole red blood cells (CW-RBC) preserved
through refrigeration. Although the shelf life of blood products can be
2
immensely lengthened by cryopreservation, CW-RBC is viewed as a more
practical form of blood products because the process of removing the CPA
from thawed FS-RBC is arduous. The current standard method of CPA
removal from FS-RBC through centrifugation is inadequate because it is time
consuming, labor intensive, cost ineffective, and causes significant cell loss. In
this study, a method of CPA removal using a microfluidic device consisting of
two lamina plates embossed with parallel arrays of microchannels separated
by a porous membrane is explored.
There are four major goals for this project: (1) to develop a
mathematical model that accurately predicts the mass transfer process inside
the microseparation device, (2) to ascertain the permeability properties of
several different types of membrane that will be used to remove CPA from a
suspension of red blood cells, (3) to characterize the removal performance of
the microseparation device by running simulations using the membrane
permeability properties measured in experiments and verifying the model
predictions with experimental data, and (4) to perform several model
simulations to investigate the effect of changing different parameters on the
CPA removal capabilities of the device. All experiments in this study were
carried out using glycerol solutions of different concentration without red
blood cells. The effects of CPA removal on the red blood cells were studied by
conducting simulations of the mathematical model. This project serves as a
3
foundational study to gain insight on how CPA removal from red blood cells
suspension using a microseparation device can be optimized.
4
Chapter 2 – Background
2.1 Cryopreservation
In 1949, C. Polge, A.U. Smith, and A.S. Parks discovered that a sample of fowl
spermatozoa survived freezing to -70oC when it was frozen in a solution of
glycerol [3]. Although accidental, the discovery is what paved the way for an
essential technique in cryobiology known today as cryopreservation.
Cryopreservation is defined as a technique of maintaining biological samples
at cryogenic temperatures (-196oC), to effectively bring all chemical,
biological, and physical activity to a halt [4]. Recent advances in tissue
engineering and cell therapy have enabled the commercial use of biological
products. One major setback in increasing production and distribution is the
lack of an efficient method in which to preserve and store biological products.
Biological products that are simply preserved through refrigeration have a
limited shelf life. Because all metabolic activity in the cellular level is stopped,
biological samples that are cryopreserved have significantly longer shelf lives
compared to samples that are preserved through refrigeration. For example,
blood cryopreserved in 40% w/v glycerol solution has an FDA approved shelf
life of 10 years [5]; significantly longer compared to the shelf life of
refrigerated conventional whole red blood cells (CW-RBC) of 21 days [6].
Longer product shelf life will enable distributors to maintain a large supply of
biological products to ensure a steady supply to patients in need. In a nutshell,
5
it seems like cryopreservation is the answer that biological product
manufacturers have been waiting for.
The cryopreservation process entails the freezing of biological cells in
an aqueous solution from +37oC down to -196oC, and thawing the frozen
sample back to +37oC. It is important that high cell viability is maintained
through the entire freeze-thaw process to ensure a high survival rate in vivo
once the product is transfused into patients [7]. Once subzero temperature is
reached during the freezing process, the water content in the aqueous
solution will favor the solid state and begin to form ice crystals. Ice crystal
formation in the aqueous solution causes freezing injury which may damage
or even cause cell fatality [4]. To avoid freezing injury, cryoprotective agents
(CPA) such as glycerol and dimethyl sulfoxide (DMSO) are routinely added to
the aqueous solution to protect cells during the cryopreservation process. The
addition of CPA reduces the formation of ice crystals and any consequent
damages to the cell membrane [7]. If enough CPA is added, ice formation can
be suppressed entirely and the aqueous solution would instead form a
vitreous, glassy state [7]. Although effective in suppressing ice formation, high
CPA concentration in the aqueous solution causes cell toxicity; which would
also damage and possibly cause cell death [7]. The right balance of solvent
and CPA in the aqueous solution is important in maintaining high cell viability
during the cryopreservation process. The development of an optimal protocol
6
for the freeze and thaw process is crucial to the success of cryopreservation
[8].
Aside from freezing and thawing, CPA removal from the cryopreserved
product is equally important. The necessity of complete removal of CPA is
dependent on what CPA was used during the freezing process. Glycerol is a
common compound that is found in the body; hence, cryopreserved products
with small amounts of glycerol can be used on a patient with relatively low
health risks. DMSO, however, is less commonly found in the body should be
removed completely to avoid any adverse health effects. Studies have linked
DMSO to adverse health effects in patients who received treatments using
cryopreserved cell products [9, 10, 11, 12]. It was revealed that the adverse
health effects became less serious with decreasing amounts of DMSO left in
the cell product [2]. Hence, to avoid any health risks, it is preferable to wash
out as much CPA as possible from cryopreserved samples.
Hematopoietic cells have become the type of cells most commonly
cryopreserved for medical therapy [2]. In 1951, Mollison and Sloviter
discovered that human red blood cells can be frozen, thawed, washed, and
transfused into a patient with high in vivo survival rate (85-90%) [13]. With
this discovery, it was thought that frozen red blood cells (FS-RBC) would be
the answer to all problems associated with the CW-RBC products. Problems
such as short shelf life, seasonal shortages, and difficulty in meeting high
7
demands in a time of war or other catastrophic events would be mitigated if
blood banks are able to stockpile FS-RBC [14]. Upon further investigation, it
was discovered that the move from CW-RBC to FS-RBC proves to have a few
more deterrents than originally thought. One such deterrent is the CPA
washing process of thawed FS-RBC. The process of removing CPA from
thawed FS-RBC is time consuming, labor intensive, and costly. Because of
these issues, FS-RBC only account for a small percentage of the the blood
supply kept by blood banks and organizations. The military uses FS-RBC as a
part of their blood supply and blood banks store FS-RBC products of rare
blood types that are not commonly donated [14]. There is a need for a new
CPA removal technology to make the switch from CW-RBC to FS-RBC a reality.
2.2 Cryoprotant Removal
Several methods are available for removing the CPA from thawed FS-RBC.
Although only centrifugation is used commercially, other methods have
shown promise in CPA removal. The pros and cons of each method are
discussed in the following subsections.
2.2.1 Centrifugation
The centrifugal removal of CPA from thawed FS-RBC employs the use of cell
washers like the ones manufactured by Haemonetics and COBE. CPA removal
8
using the centrifugation method was first commercially done using a
manually operated, batch process cell washers like the Haemonetics 115
[15]. The blood washing process using the Haemonetics 115 is a complicated
process that requires multiple batch steps to decrease the glycerol
concentration. The batch step entails adding a solution of lower osmolality,
centrifuging the blood, removing the supernatant from the RBC, and
resuspending the RBC in a solution with an even lower osmolality. These
steps are done multiple times until enough glycerol is removed from the RBC
suspension [16]. The blood washing process must be done in steps of
decreasing osmolality in order to avoid osmotic damage from excessive
shrinking and swelling. Although the blood washed meet the criteria for
transfusion, this procedure is far from ideal [15]. Due to the manual nature of
the Haemonetics 115, the blood washing process is labor intensive and time
consuming (45 minutes per unit of blood), requiring trained operators to
properly wash thawed FS-RBC [15]. Furthermore, the Haemonetics 115
features a rotating seal which exposes the system to the atmosphere and thus
increase the risk of contamination [15]. Because the Haemonetics 115 is an
open system, the blood washed using the unit must be used within 24 hours
[15, 16].
Due to the disadvantages of the Haemonetics 115 cell washer, an
improved unit called the ACP 215 was created. Unlike its predecessor, the
9
ACP 215 is automated and features a closed system to minimize the risk of
contamination [17]. Organizations like the United States Armed Services
Blood Program employs the use of this equipment in conjunction with a
washing protocol [18] developed by the Naval Blood Research Laboratory to
remove CPA from thawed FS-RBC in 40% glycerol [19]. The cell washing
process using the ACP 215 still entails the addition of solution in decreasing
osmolality to decrease the glycerol concentration; however, since everything
is programmed internally, it reduces the level of complexity associated with
the blood washing operation. Because it’s a closed system, thawed FS-RBC
washed with the ACP 215 unit has a shelf life of 14 days, significantly longer
than blood units washed using the Haemonetics 115 [19]. Although its
automated and atmospherically sealed, the blood washing process using the
ACP 215 is still time consuming (55 minutes per unit of blood) and causes loss
of up to 13% of the RBC [19].
2.2.2 Hollow-Fiber Dialysis
Currently the standard of care in removing toxins from the blood of patients
with renal disease, hollow fiber dialysis has shown promise for effectively
removing CPA from thawed FS-RBC. A common hollow-fiber module is similar
to a shell and tube heat exchanger with thousands of hollow fibers encased in
a polymer shell. Blood is flowed inside the hollow fibers and the wash
10
solution is flowed in the shell side within the polymer casing in a counter
current configuration. Several studies to investigate the performance of
hollow fiber dialyzers in removing CPA from blood product have been
conducted. Ding et al developed a model to simulate the CPA removal
capabilities of a hollow fiber module. Based on simulations, they found that
this method can decrease the maximal swelling volume of the RBC and
washing time when compared to the centrifugation method [20, 21].
Wickramashinge et al carried out experiments using thawed FS-RBC,
platelets, and peripheral blood hematopoietic progenitor cells and found that
all blood products were successfully washed using a hollow fiber module to
transfusion standards in 30 minutes or less [15, 22]. Arnaud et al
demonstrated that the 95% of the DMSO content in a suspension of platelets
were successfully removed in one pass through a polysynthane hollow fiber
dialyzer [23].
There are also several disadvantages associated with CPA removal
using a hollow fiber dialyzer like flow maldistribution and volumetric flow
rate restrictions [24]. Flow maldistribution in hollow fiber modules is mainly
caused by non uniform packing of the hollow fibers inside the polymer shell,
which cause stagnant regions in wash fluid outside of the hollow fibers [24].
Because hollow-fiber dialyzers were originally designed for kidney dialysis, it
requires a high operational volumetric flow rate making it less ideal for the
11
processing of cell-based therapeutics with small volume doses like umbilical
cord blood or bone marrow stem cells. The required high volumetric flow rate
inside the device could also incur excessive shear stress on the red blood cells,
causing hemolysis and reducing the amount of viable cells in the end product
[24]. In addition to flow maldistribution and flow rate restrictions, hollow
fiber dialyzers also require a large amount of washing solution or dialysate
during operation. Most hollow fiber dialyzers use a 3:5 blood to dialysate flow
rate, resulting in a 60% greater dialysate volume than blood volume
processed [24]. The large requirement of dialysate fluid reduces the economic
feasibility of this strategy.
2.2.3 Microfluidic Devices
Microfluidic devices feature a large surface area to volume ratio that
intensifies mass and heat transfer processes by decreasing the path length for
diffusion [24]. Over the years, microfluidic systems have been used in a
variety of biological applications. One such application is the use of
microfluidics system in manipulating cells and other biological samples by
exploiting the microscale transport phenomena [25]. Song et al developed a
microfluidic device that consists of a single long and narrow channel with
three inlet ports and one outlet port [25]. This device was used to load and
remove CPA from cell suspensions in a gradual manner. For CPA removal, the
cell suspension is injected into the device through the center port while
12
phosphate-buffered saline (PBS) solution is injected into the other two ports
to the left and right. Cell suspensions with CPA loaded and removed using this
method exhibited a 25% increase in viability compared to conventional
loading and removal methods [25]. However, because this method combines
the cell stream and the wash stream with no downstream separation process,
the CPA from the cell suspension was not actually removed but merely
diluted. Because this process increases the final volume of the cell suspension,
the end product is less ideal for transfusion into patients.
Mata et al developed a microfluidics device that flows the cell stream
parallel to the wash stream, and allows diffusion of CPA to take place between
the two streams through diffusion. This method was reported to be able to
conclusively demonstrate the effective removal of DMSO while maintaining a
high (90% and above) cell recovery [26, 27]. Although this device was
successful in removing the CPA content, some cells were still lost in the
process due to the lack of a barrier that separates the cell stream from the
wash stream. The absence of a clear partition in this device also prevents the
ability to control the cell density of the end product due to intermixing
between the cell and the wash stream. Because the two streams are not
separated, this device relies on diffusional mass transfer and is unable to take
advantage of pressure-driven convective flow between the two streams.
Furthermore, the absence of a barrier in this device limits the flow
13
configuration to only co-current, a less effective flow configuration for mass
transfer.
In this study, a microseparation unit consisting of a porous membrane
sandwiched between two polymer laminas embossed with parallel arrays of
microchannels was used. The polymer laminas consist of 26 microchannels,
each microchannel being 200 m wide, 100 m deep, and 56 mm long. The
removal process is continous and gradual where a CPA-rich cell stream is
pumped on one side of the membrane and a CPA-free wash stream is pumped
on the other side in a counter current configuration. The concentration and
pressure gradient between the two streams induces glycerol transport
through the membrane. The removal of CPA using this microseparation
device has multiple potential advantages over the commercial centrifugation
method as well as other methods previously discussed. The process of
removing CPA from a cell-laden stream using the microseparation device is
one continuous process instead of a multistep procedure associated with
centrifugation, making it potentially less labor intensive and time consuming
than the centrifugation method. The microscale size of the device also makes
it more suitable to handle the processing of smaller volume cell-based
therapeutics in compared to hollow-fiber dialyzer. Moreover, because the
fluid path is defined and controlled in the microchannels, the possibility of
having flow maldistribution and dead volumes within the device is reduced.
14
Precisely controlling the fluid path inside the device also eliminates
requirement of the high volumetric flow rate and large amount of wash
solution when compared to hollow-fiber dialyzer. The presence of a clear
partition between the cell-laden stream and the wash stream enables
operation in a counter-current configuration, taking advantage of pressuredriven convective flow instead of just diffusion, and potentially recovering
100% of the cells, assuming no cell lysis during the process.
2.3 Membranes
Biocompatibility is an important factor when choosing a membrane for
biological applications. Upon comparing membrane materials, it was found
through previous studies that synthetic membranes are less prone to cause
adverse inflammatory reaction in hemodialysis patients when compared to
cellulosic membranes [28, 29]. Furthermore, synthetic membranes typically
have larger pores, allowing higher water flux and better ultrafiltration
capacity compared to cellulose based membranes [28]. For these reasons, all
the membranes that were chosen for this study were synthetic based.
Aside from biocompatibility, membrane thickness is one of two
important factors to take into consideration in order to maximize mass
transfer between the CPA-rich stream and the wash stream. For this
15
application, a thin membrane is desired for a several reasons: (1) a thin
membrane has less resistance to mass transfer compared to a thick
membrane because the molecule has to diffuse through a shorter length [30],
and (2) thick membranes has the potential to sag into the microchannels
causing channel blockage. One membrane that proved to be unsuitable for
this application due to its thickness is the PALL Supor-800 membrane. The
Supor-800 membrane is a biocompatible membrane with a pore diameter and
membrane thickness of 0.45 and 140 microns, respectively [31]. The
thickness of the membrane itself was more than the microchannel height;
upon assembly, it was found that the membrane sagged completely into the
microchannels, effectively blocking fluid flow.
The second factor to take into consideration when choosing a
membrane to maximize mass transfer is the average pore size. Larger pore
size will allow solutes to pass through more easily; however, pores that are
too large may also allow the cells to pass through to the wash stream, which is
undesirable. It is known that membranes with a nominal pore diameter of 0.8
to 1 microns allow the passage of intact red blood cells [32]. Hence, the ideal
membrane for removal of CPA from red blood cells suspension should have
an average pore large enough to allow maximum mass transfer between the
two streams, but small enough to ensure that all the red blood cells are
contained in the cell-laden stream.
16
2.3.1 Gambro AN69-ST
The AN69-ST membrane is a highly biocompatible polyacrylonitrile
ultrafiltration membrane that is commonly used in hemodialysis. It is a wet
stored membrane with a smooth luminal surface and an average pore size of
4 nm [33]. The membrane is relatively thin, with an average thickness of 21
microns.
2.3.2 Millipore ISOPORE
Two types of ISOPORE membranes were tested in this study: ISOPORE HTTP
(ISOHTTP) and ISOPORE TMTP (ISOTMTP). Both ISOPORE membranes are
dry stored, microfiltration membranes made of polycarbonate using the same
method of production. The only distinguishing difference that set the two
membranes apart is the average pore size; the ISOHTTP has an average pore
size of 0.4 microns whereas the ISOTMTP has a much larger average pore size
of 5 microns [34]. Both ISOPORE membranes have an average thickness of 721 microns [34]. Only the HTTP model is suitable for the application of CPA
removal from red blood cells suspensions. The large pores of the ISOTMTP
membrane is expected to allow passage of red blood cell through to the wash
stream causing unwanted cell loss. The ISOTMTP membrane may be still be
useful in removing CPA from suspensions of larger cells, like human oocytes
with an approximate size of 100 microns. According to manufacturer’s
specification, the ISOTMTP membrane is suitable for bioassay and cytology
17
applications. However, the biocompatibility of the ISOHTTP membrane is
unknown. To the author’s knowledge, no publications exist in which the
ISOHTTP membrane was used in a biological application. A table summarizing
the properties of all the membranes is presented in table 2.1.
Membrane
Material
Storage
Thickness
(m)
AN69-ST
Polyacrilonitrile
Wet
21
ISOPORE HTTP
Polycarbonate
Dry
7-21
ISOPORE TMTP Polycarbonate
Dry
7-21
Table 2.1: Membrane properties for comparison
Pore Size
(m)
0.004
0.4
5
2.4 Cryoprotectants
CPAs are generally divided into two categories: permeating CPAs like glycerol
and DMSO, and non-permeating CPAs like polyvinyl pyrrolidone [4]. Red
blood cells are typically frozen in either 20% or 40 % w/v glycerol solution
[19] whereas umbilical cord blood and bone marrow are typically frozen in
10% w/v DMSO solution [35]. Because this study focuses on CPA removal
from FS-RBC, glycerol was used exclusively in all experiments. The hydraulic
permeability experiments were done with three solutions with varying
glycerol concentrations: DI water, 10% w/v glycerol and 40% glycerol. The
diffusive permeability and model validation experiments were done using
10% w/v glycerol solution and DI water. All solutions used in the experiments
did not contain red blood cells.
18
Chapter 3 – Mathematical Model
The goal of this model is to accurately predict the CPA removal capabilities of
the microseparation device by simulating the mass transfer that occurs
between the cell laden, glycerol rich stream and the wash stream. Being able
to accurately predict the mass transfer and CPA removal performance is
crucial in developing an optimal CPA removal protocol. The flow and mass
transfer in the cell stream, extracellular solution stream, and wash stream
were modeled using volume and solute balances whereas the mass transfer
through the cell and the synthetic membrane were modeled using the twoparameter (2P) and the Kedem-Katchalsky (KK) formulation, respectively.
Similar modeling strategies have been utilized to simulate the CPA removal
capabilities in a variety of separation devices. Ding et al modeled the flow
distribution and mass transfer process inside a hollow fiber module using the
conservation equations coupled with the KK formulation [20]. Tuhy modeled
the mass transfer of urea using the same microseparation device using the
conservation equations coupled with Darcy’s law in the absence of cells [24].
A diagram showing the differential volume for modeling in the
microseparation device is shown in figure 3.1.
19
Figure 3.1: Diagram of the differential volume in microseparation device
For the model, the system was divided into three separate streams; a
stream consisting of the cells exclusively, a stream of extracellular solution
suspending the cells, and a wash stream. The cell and the extracellular
solution flow on the top side of the membrane whereas the wash stream flows
on the bottom side as shown in the diagram. There are four fluxes that
describe the membrane transport: Jw,c is the water flux through the cell
membrane, Js,c is the solute flux through the cell membrane; Jv is the solution
flux through the synthetic membrane; and Js is the solute flux through the
synthetic membrane. The velocity of the streams was assumed to be constant
and uniform, with no variation in the y or z direction. The uniform velocity
assumption allows spatial uniformity of the concentration and pressure in the
y and z direction. The mass transfer that occurs in the system was assumed to
only occur from the cells to the extracellular solution, and from the
20
extracellular solution through the membrane and onto the wash stream.
Additional general assumptions that were also taken are: rectangular uniform
channels, laminar flow, constant molar volume, constant temperature and no
reaction within the system.
3.1 Cell Membrane Transport
Mass transfer across a membrane can be determined using numerous
formalisms. Such formalisms include a one-parameter (solute permeability)
model, a two-parameter model (water and solute permeability), and a threeparameter model or better known as the KK formalism which adds a solutesolvent interaction term () in addition to the water and solute permeability
[36]. The introduction of a third parameter, , significantly increases the
complexity of the KK formalism compared to the first two. In a study done by
Kleinhans, it was determined that the addition of  is often unnecessary and
the 2P model describes the transport process as well as the more complicated
KK formalism for biological membranes [36]. The 2P model written in terms
of the cell membrane permeabilities is
J w,c  Lp ,c RT (Cc  Cs ,c  C1  Cs ,1 )
J s ,c  Ps,c (C1  Cc )
(3.1)
(3.2)
21
where Jw,c is the cell water flux; Js,c, the cell solute flux; Lp,c, the water
permeability of the cell membrane; R, the universal gas constant; T, the
temperature; Cc, the CPA concentration of the cell stream; Cs,c, the salt
concentration of the cell stream; C1, the CPA concentration of the extracellular
solution stream; Cs,1, the salt concentration of the extracellular solution
stream; and Ps,c, the solute permeability of the cell membrane.
3.2 Synthetic Membrane Transport
The analysis of the mass transfer across the synthetic membrane is done
using the three-parameter KK formalism. Recent publications have shown
that glycerol can pass through hemodialyzer membranes easily and
completely, thus making the value of  equal to zero [37]. Because this study
exclusively used glycerol as a CPA, the solute-solvent coefficient was set to
zero in the KK formalism. The KK formalism written in terms of the
membrane permeabilities is
Jv  Lp (P1 P2 )
(3.3)
Js  Cm Jv  Ps (C1  C2 )
(3.4)
where Jv is the volumetric solution flux; Js, the molar solute flux; P1, the
pressure of the top stream, which includes the cells and the extracellular
22
solution; P2, the pressure of the wash stream; Lp, the membrane hydraulic
permeability; Ps, the membrane diffusive permeability; C1 and C2, the CPA
concentration of the extracellular solution stream and wash stream,
respectively. Cm is the mean intramembrane concentration derived using the
local equation for the solute flux within the membrane [38, 39]. For detailed
derivation of Cm, refer to appendix B.
3.3 Volume Balances
Because the model assumes constant molar volume for glycerol and water,
the flux equations from the 2P and KK formalism were used to derive
differential equations that describe the volumetric flow rate change in each
stream as a function of the channel x-coordinate. The volume balance on the
cell stream is particularly important because it relates to the shrinking and
swelling of the individual cells as they are exposed to a hypotonic or
hypertonic solution. Cell shrinking and swelling tolerances plays an important
role in CPA addition and removal because excessive shrinking and swelling
could cause significant damage or death to the cells. The volume balance
differentials written in terms of the flux equations from the 2P and the KK
formalism are
23
dQc
A n
 ( J s,c  vg  J w,c )  c c  (W  H )
dx
Q1  Qc
(3.5)
A n
dQ1
 ( J s ,c  vg  J w,c )  c c  (W  H )  J v W
dx
Q1  Qc
(3.6)
dQ2
  J v W
dx
(3.7)
where the first, second, and third differential describe the volumetric flow
rate change with respect to the x-coordinate for the cell stream, extracellular
solution stream, and wash stream, respectively. Qc is the volumetric flow rate
of the cell stream; Q1, the volumetric flow rate of the extracellular solution
stream; Q2, the volumetric flow rate of the wash stream; H, the microchannel
height; W, the microchannel width; vg, molar volume of glycerol; Ac, the cell
membrane surface area of a single cell; and
nc
, the number of cells that pass
Ac  nc
through the differential x per time. The term Q1  Qc was derived as a
substitution for the original term Atotal, which describes the total surface area
of all the cells contained in the differential volume. The term Atotal included a
cell volume variable, a variable that is not constant. During the process, the
cell volume is not a constant variable since the cells will either shrink or swell
during inside the device. Hence, to simplify solving the differential equation,
the cell volume term was substituted in terms of flow rate and other constant
24
variables that are known. The detailed derivation of the substitution along
with the derivation of the volume balances are presented in appendix B.
3.4 Solute Balances
Similar to the volume balances, a set of differential equations used to describe
the change in solute concentrations with respect to the channel length was
also derived. The solute balances written in terms of solute fluxes through the
cell and synthetic membranes are

dCc
Ac  nc
d (Qc ) 
1

 (W  H )  Cc
 ( J s , c  vg ) 

dx (Qc  Qb ) 
Q1  Qc
dx 
(3.8)
A n
dC1
1 
dQ 
  ( J s ,c  vg )  c c  (W  H )  J s  W  C1 1 
dx
Q1 
Q1  Qc
dx 
(3.9)
dC2
1

dx
Q2
dQ2 

 J s  W  C2 dx 
(3.10)
where the first, second, and third differential describe the solute
concentration change with respect to the channel length for the cell stream,
suspension solution stream, and wash stream, respectively. Detailed
derivations of the solute balances are presented in appendix B.
25
3.5 Pressure Drop
Differential equations to describe the pressure drop within the
microseparation device were derived using the pressure drop equation for a
rectangular channel [40]. The pressure drop differential equations written in
terms of the stream flow rates are
dP1

dx
dP2

dx
Q1  Qc

H
64   
3 
(W  H ) 1
 W  tanh 
 
4  1  3
5
H
2

W






(3.11)
Q2

H
64   
3 
(W  H ) 1
 W  tanh 
 
2  3
5
H
2

W






(3.12)
The first differential describes the pressure change with respect to channel
length for the top stream which includes the cell and the suspension solution
stream, whereas the second differential describes the pressure change with
respect to channel length for the wash stream 1 and 2 are the viscosity of the
top and bottom streams, respectively.
26
3.6 Model Programming
Eight coupled differential equations were derived to describe the mass
transfer process inside the microseparation device. These governing
differential equations were programmed into MATLAB to be solved
simultaneously using Ode45, a built in function in MATLAB that is capable of
solving coupled differential equations given the boundary conditions at x=0.
Because the device is set to run in a counter current configuration, the
boundary conditions at x=0 are only known for the concentration and flow
rate of the cell stream and the suspension solution stream as well as the
pressure for the wash stream. The diagram shown in figure 3.2 illustrates the
unknown variables at x=0. To solve the differential equation, initial guesses
for the unknown variables at x=0 were set and the fminsearch function was
used to iteratively revise the initial guesses until the model predicted value
matches the known target value at x=L. This solution strategy is similar to the
shooting method to solve boundary-value problems and have been used in
other studies to find heat transfer parameters in a counter-current heat
exchanger [41, 42].
27
Figure 3.2: Boundary conditions at x=0 and x=L. The unknown variables at
x=0 and the target values at x=L are boxed.
The mathematical model enables the user to input different
parameters for the mass transfer process that is going to be simulated; like
the cell and synthetic membrane permeabilities, the type and concentration of
CPA, the cell volume fraction in the stop stream, and the flow rates of the top
and bottom stream. Although this model was originally designed for a specific
microseparation unit, the user can also change the number and the
dimensions of the microchannels to simulate the removal performance of a
theoretical microseparation device. This is especially useful for parametric
studies and as a design tool for the next generation of microseparation device.
28
Chapter 4 – Experimental Setup
4.1 Microseparation Device
The microchannel separation device that was used during this study features
two laminas embossed with parallel arrays of microchannels separated by a
porous membrane. A steel casing was used to facilitate alignment and to
create a compression seal between the two laminas. The lamina was
produced by the Microproducts Breakthrough Institute by hot embossing into
a thin polysulfone polymer sheet using a computer numerical controlled
(CNC) machine. Each lamina has of 26 microchannels that are each 56 mm
long, 200 microns wide, and 100 microns deep. A picture of the lamina used
in the separation device is presented in figure 4.1.
Figure 4.1. Single sheet of lamina embossed with microchannels
29
4.1.1 Microseparation Device Assembly
Three different membranes were used in this study: Gambro AN69
ultrafiltration membrane, Millipore ISOPORE HTTP microfiltration
membrane, and Millipore ISOPORE TMTP microfiltration membrane. The
microseparation unit was assembled just prior to testing to avoid any damage
to the membrane caused by drying. Two laminas were thoroughly rinsed with
water prior to assembly. A piece of membrane was placed in between the
lamina, with the microchannels side facing the membrane. The excess
membrane was then trimmed off and the alignment pins were placed to
ensure proper alignment in the steel casing. The lamina was then placed on
the bottom steel casing before placing the top casing on. The bolts were then
inserted in place and tightened by hand, before finally using a torquemeter to
tighten each bolt to 80 cN-m. A detailed protocol of the microseparation
device assembly is presented in appendix C. Figure 4.2 and 4.3 show the
assembled and exploded view of the device, respectively.
30
Figure 4.2: Assembled view of the microseparation device
Figure 4.3: Exploded view of the microseparation device
31
4.2 Hydraulic Permeability Experiment
4.2.1 Experimental Apparatus
The experimental apparatus consists of the microseparation unit, two syringe
pumps (NE-1010, New Era Pump System), two 60 ml syringe (309653, BD),
four pressure transducers (Deltran I, Utah Medical), eight pieces of 15 cm
intravenous (IV) tubing (2C6228, Baxter), one stopwatch, and one serological
pipette tip. Depending on which membrane is being tested, a 1 ml (53283704, VWR), 5 ml (53283-706, VWR), or 10 ml disposable serological pipette
tip (53283-708, VWR) may be used. Pressure transducers were connected to
the inlet and outlet ports of the microseparation unit by IV tubing. The
pressure signals read by the transducers were recorded using a data
acquisition card (USB-6210, National Instruments) and the Measurement and
Automation Explorer software. Syringes were connected to the pressure
transducers and then to the inlet ports of the microseparation unit in a cocurrent configuration. The fluid exiting the top stream is flowed into a waste
container while the volume of the fluid that exits the bottom stream is
measured by attaching the serological pipette to the outlet tubing of the
bottom stream. A detailed diagram showing the experimental apparatus is
shown in figure 4.4.
32
Figure 4.4: Experimental apparatus for the hydraulic permeability experiment
4.2.2 Experimental Procedure
The microseparation device was assembled with the membrane to be tested
and connected to the experimental apparatus. Two 60-ml syringes were filled
with DI water and connected to the setup to rinse the membrane and
microchannels. Approximately 10 ml of DI water was allowed to pass through
the top and bottom side of separation unit at a flow rate of 1 ml/min. After
rinsing the channels and the membrane, the syringes containing the DI water
was switched with syringes containing the solution to be tested. Another 10
ml of solution was allowed to pass through each side of the separation unit
before the syringe pump connected to the bottom stream is turned off and the
outlet tube of the bottom stream is fitted onto the serological pipette.
33
Depending on which membrane is being tested, a 1 ml, 5 ml, or 10 ml
disposable serological pipette tip may be used. An additional 10 ml of solution
was allowed to pass through the top stream of the microseparation unit
before sampling was commenced to ensure that the system has come to
steady state. For the AN69 membrane, a sampling time of 10 minutes was
selected. The volume level on the pipette was recorded right before the
stopwatch was started and right after it was stopped to measure the flux of
solution that crosses the membrane. The ISOPORE membranes have a much
higher solution flux rate than the AN69 membranes. Hence, it was not
possible to carry out the same procedure to measure out the flux. Instead of
selecting a sampling time, the flux was measured by the time it took for 1 ml
of solution to cross the membrane. The pressure readings (in mV) from all
four pressure transducers were also noted while sampling. This experiment
was done with five different feed flow rates: 1, 0.8, 0.6, 0.4, and 0.2 ml/min,
and triplicate samples were collected for each flow rate. Detailed protocol for
the hydraulic permeability experiment is presented in appendix D.
4.2.2 Analytical Method
The results of the experiment were analyzed using the solution flux equation
from the KK formalism shown in equation 3.3. This method was inspired by
the work done by Liao to find membrane permeability properties in hollow
fiber dialyzers [37]. The solution flux expression can be written in terms of
34
filtrate volume collected per time and rearranged to solve for the hydraulic
permeability
Lp 
V
t
Ax ( P1  P2 )
(4.1)
where Ax is the membrane surface area available for mass transfer and the
quantity (P1-P2) is the average transmembrane pressure between the top and
bottom stream. The average transmembrane pressure was calculated with the
equation
P
P
( P1  P2 )   1,inlet 1,outlet
2

  P2,inlet  P2,outlet 


2
 

(4.2)
where P1,inlet is the pressure reading at the inlet of the top stream; P1,outlet is
the pressure reading at the outlet of the top stream; P2,inlet is the pressure
reading at the inlet of the bottom stream; and P2,outlet is the pressure reading
at the outlet of the bottom stream. Because the flow rate of solution into the
bottom stream is stopped to measure the filtrate volume, the average
pressure of the bottom stream is approximately at atmospheric.
The filtrate volume collected during the selected sampling time was obtained
from experiments and the total area available for mass transfer can be
calculated from the microchannel geometry. The readings from the pressure
transducers (in mV) were converted to pressure units (Pa) using a calibration
35
curve (presented in appendix G). The pressure measurements from the inlet
and outlet of the top and bottom stream were then averaged to obtain the
average transmembrane pressure.
4.3 Diffusive Permeability Experiment
4.3.1 Experimental Apparatus
The experimental apparatus for the diffusive permeability consists of the
microseparation unit, two syringe pumps (NE-1010, New Era Pump System),
two 60-ml syringes (309653, BD), four pressure transducers (Deltran I, Utah
Medical), eight pieces of 15 cm intravenous (IV) tubing (2C6228, Baxter), one
stopwatch, and six 15-ml centrifuge tubes (89039-664,VWR) per flow rate
tested. Pressure transducers were connected to the inlet and outlet ports of
the microseparation unit by IV tubing. The pressure signals read by the
transducers were recorded using a data acquisition card (USB-6210, National
Instruments) and the Measurement and Automation Explorer software.
Syringes were connected to the pressure transducers and then to the inlet
ports of the microseparation unit in a co-current configuration. The outlet
tubing from each stream was placed in a waste container until the system is
ready for sampling. A detailed diagram showing the experimental apparatus
is shown in figure 4.5.
36
Figure 4.5: Experimental apparatus of the diffusive permeability experiment
4.3.2 Experimental Procedure
The microseparation device was assembled with the membrane to be tested
and connected to the experimental apparatus. Two 60-ml syringes were filled
with DI water and connected to the inlet ports of the microseparation unit to
rinse the membrane and microchannels. Approximately 10 ml of DI water was
allowed to pass through both streams of the separation unit at a flow rate of 1
ml/min. After rinsing the channels and the membrane, the syringe containing
the DI water to the bottom stream was refilled and the syringe connected to
the top stream was emptied and refilled a 10% w/v glycerol solution. The
same flow rate for the top and bottom streams were selected and the syringe
pumps holding both syringes were started simultaneously. By watching the
37
pressure readings, the flow rate to the bottom stream was adjusted so that
the pressure drop between the top and bottom stream was approximately
zero. After mitigating any pressure driving force between the two streams,
the system is allowed to run until 10 ml of solution has passed through both
sides of the microseparation unit before samples were collected to ensure
that the system has come to steady state. Seven flow rates were tested for this
experiment: 1, 0.8, 0.6, 0.4, 0.3, 0.2, and 0.1 ml/min, and samples from each
flow rate were collected in triplicates for each stream. Detailed protocol for
this experiment is appended in appendix E.
4.3.3 Analytical Method
The results of the experiment were analyzed using the solute flux equation
from the KK formalism presented in equation 3.4. The development of this
method was based off of the work done by Liao to assert the membrane
permeability properties in a hollow fiber dialyzer [37]. By mitigating the
pressure gradient between the top and bottom stream, the equation is
reduced to
Js  Ps (C1  C2 )
(4.3)
where C1 and C2 are the CPA concentration of the top and bottom stream,

respectively. The solute flux can be written as a mass balance of the amount of
CPA that enters and leaves the top stream
38
Q1,0C1,0  Q1, L C1, L
Amembrane
 Ps (C1  C2 )
(4.4)
where Q1,0 and C1,0 are the flow rate and concentration of the top stream at the
inlet, Q1,L and C1,L are the flow rate and concentration of the top stream at the
outlet, and A is the membrane surface area that is available for mass transfer.
If we assume that the solution in the channel is well mixed, no diffusion
boundary layer effects, steady state, constant diffusive permeability, and that
the rate of change in concentration in both streams are proportional to the
concentration difference, we can write the concentration difference in terms
of a logarithmic mean of the solute concentration of the top and bottom
stream. The diffusive permeability can then be solved with rearrangement of
equation 4.5.
Q1,0C1,0  Q1,L C1,L
 PsClm
Amembrane
(4.5)
The concentration of the 10% w/v stock solution as well as the

concentrations of the samples obtained from experiments were measured in
mOsm/kg water using an osmometer (3300, Advanced) and then converted
to a unit of mol/m3 using a calibration curve presented in appendix H. The
inlet flow rate of the top stream was determined from the syringe pump and
the outlet flow rate of the bottom stream was determined through mass
balances.
39
4.4 Model Validation Experiment
4.4.1 Experimental Apparatus
The experimental apparatus for the model validation experiment was the
same as for the diffusive permeability experiment except that the two streams
were set to flow counter-current of one another. A detailed diagram showing
the experimental apparatus is shown in figure 4.6.
Figure 4.6: Experimental apparatus of the model validation experiment
4.4.2 Experimental Procedure
The microseparation device was assembled with the membrane to be tested
and connected to the experimental apparatus. Two 60-ml syringes were filled
40
with DI water and connected to the inlet ports of the microseparation unit to
rinse the membrane and microchannels. Approximately 10 ml of DI water was
allowed to pass through both sides of the separation unit at a flow rate of 1
ml/min. After rinsing the channels and the membrane, the syringes
containing the DI water to the bottom stream was refilled and the syringe
connected to the top stream was emptied and refilled with a 10% w/v
glycerol solution. The same flow rate is selected for the top and bottom
stream, and the system is allowed to run until 10 ml of solution has passed
the separation unit to ensure that the system has come to steady state before
sampling was commenced. Five flow rates were tested for this experiment: 1,
0.8, 0.6, 0.4, 0.2 ml/min, and samples from each flow rate were collected in
triplicates for each stream. Detailed protocol for this experiment is presented
in appendix F.
4.4.3 Analytical Method
The variable of interest for the mass transfer experiment is the fractional
glycerol removal from the top stream. The fractional removal was calculated
using the following equation
C Q 
% Re moval  1   1.L 1, L 
C Q 
 1,o 1,o 
(4.6)
41
where C1 and Q1 are the CPA concentration and flow rate of the top stream.
The subscript o and L denotes conditions at the inlet and outlet, respectively.
The concentration of the stock 10% w/v solution and the samples were
measured in mOsm/kg water using an osmometer (3300, Advanced) and then
converted to mol/m3 using a calibration curve presented in appendix H. The
inlet flow rate of the top stream was determined from the syringe pump and
the outlet flow rate of the bottom stream was determined through mass
balances.
42
Chapter 5 – Results and Discussion
5.1 Hydraulic Permeability Experiments
The hydraulic permeability experiments were done using three different
solutions, all without red blood cells: DI water, 10% w/v, and 40% w/v
glycerol. Three sets of experiments were done for each membrane. In each
set, a piece of membrane was assembled onto the microseparation device and
five different flow rates were tested: 1, 0.8, 0.6, 0.4, and 0.2 ml/min. After one
set is completed, the microseparation device was taken apart and a new
membrane is assembled into the unit to begin the next set. Each time the
microseparation device is assembled, different amounts of air bubbles get
trapped within the channels, reducing the surface area available for mass
transfer. In addition to trapped air bubbles, membrane sagging and channel
blocking may also contribute to differences in available mass transfer area
per set. Due to these factors, the experiments were done in triplicate sets for
each type of membrane to obtain an average value of the hydraulic
permeability.
5.1.1 Gambro AN69-ST
The hydraulic permeability of a membrane is a property that determines how
much solution is allowed to pass through for a given amount of exerted
pressure. The amount of transmembrane pressure exerted is proportional to
43
the amount of solution that is allowed to pass through. In this experiment, five
different flow rates was flowed in the top stream of the microseparation
device to obtain the amount of solution that passes through the membrane
given a certain transmembrane pressure drop. The Lp value for each flow rate
in a set was calculated using eq 4.1. Then, all Lp values from a set was
averaged to obtain a set averaged Lp value. The set averaged Lp value from the
three sets of experiments were then averaged again to obtain the averaged Lp
value of the membrane. Figure 5.1, 5.2, and 5.3 presents the results for the
hydraulic permeability experiment using the AN69 membrane and DI water,
10% w/w glycerol, and 40% w/v glycerol, respectively.
1.6E-10
1.4E-10
Average Lp = 7.55e-11 m/Pa-s
V/t (m3/s)
1.2E-10
1.0E-10
8.0E-11
6.0E-11
1st Set
4.0E-11
2nd Set
2.0E-11
3rd Set
Average
0.0E+00
0.00
0.50
1.00
Ax(P1-P2) (m2-Pa)
1.50
Figure 5.1: Hydraulic permeability of AN69 to DI water.
44
1.6E-10
1.4E-10
Average Lp = 7.27e-11 m/Pa-s
V/t (m3/s)
1.2E-10
1.0E-10
8.0E-11
1st Set
6.0E-11
2nd set
4.0E-11
3rd Set
2.0E-11
Average
0.0E+00
0.00
0.50
1.00
Ax(P1-P2) (m2-Pa)
1.50
2.00
Figure 5.2: Hydraulic permeability of AN69 10% w/v glycerol solution.
1.6E-10
1.4E-10
Average Lp = 2.78e-11 m/Pa-s
V/t (m3/s)
1.2E-10
1.0E-10
8.0E-11
6.0E-11
1st Set
4.0E-11
2nd set
3rd Set
2.0E-11
Average
0.0E+00
0.00
1.00
2.00
Ax(P1-P2)
3.00
4.00
5.00
(m2-Pa)
Figure 5.3: Hydraulic permeability of AN69 to 40% w/v glycerol solution.
The value of the hydraulic permeability of a membrane is dependent
on the viscosity of the solution that passes through. According to Darcy’s law,
the flux of fluid through a porous media is proportional to the exerted
45
pressure drop and inversely proportional to the solution viscosity and the
thickness of the porous media, written as
Jv 

(P  P )
L 1 2
(5.1)
where Jv is the solution flux; , the permeability of the medium; , the solution
viscosity; L, the thickness of the porous media; and (P1-P2) is the
transmembrane pressure drop. The term L in Darcy’s law is equal to the
membrane’s hydraulic permeability; indicating that the hydraulic
permeability value should decrease with increasing solution viscosity and
membrane thickness. Figure 5.4 shows that a decreasing trend is apparent
when comparing the membrane hydraulic permeability versus the solution
viscosity.
46
9.E-11
= 0.903e-4 Pa-s
8.E-11
= 1.17e-3 Pa-s
Lp (m/s-Pa)
7.E-11
6.E-11
5.E-11
4.E-11
3.E-11
2.E-11
= 3.22e-3 Pa-s
1.E-11
0.E+00
0
0.1
0.2
% Glycerol
0.3
0.4
Figure 5.4: Hydraulic permeability of AN69 to glycerol solutions of different
viscosities.
The viscosities of the solutions tested are 0.903e-3, 1.17e-3, and 3.22e3 Pa-s for DI water, 10% w/v glycerol, and 40%w/v glycerol, respectively.
Based on the viscosity differences and Darcy’s law, the hydraulic permeability
of 10% w/v, and 40% w/v glycerol should approximately be 20% and 80%
less than the value for DI water, respectively. Assuming that the hydraulic
permeability value for the 40% w/v glycerol solution is the most accurate
based on the standard error, a theoretical projection of what the hydraulic
permeability should be according to Darcy’s law for DI water and 10% w/v
glycerol can be calculated. A theoretical projection of what the hydraulic
permeability should be for 10% w/v and 40%w/v solution can also be
calculated using the manufacturer’s reported Lp value for DI water of 7.03e11 m/Pa-s . Figure 5.5 presents the hydraulic permeability data from
47
experiments plotted with the theoretical projections using Darcy’s law based
on Lp values of the 40% w/v solution and manufacturer’s DI water value.
From the figure it can be seen that the hydraulic permeability values obtained
from the experiments fall in the range of the theoretical values projected
using Darcy’s law.
1.4E-10
Experimental Data
1.2E-10
Theoretical from 40% w/v Lp value
Lp (m/s-Pa)
1.0E-10
Theoretical from manufacturer's
value
8.0E-11
6.0E-11
4.0E-11
2.0E-11
0.0E+00
0
0.1
0.2
0.3
0.4
% Glycerol
Figure 5.5: Hydraulic permeability of AN69 to glycerol solutions of different
viscosities compared to theoretical projections
5.1.2 Millipore ISOPORE HTTP
The hydraulic permeability experiment using the ISOHTTP membrane was
done in the exact same fashion as the experiment for the AN69 membrane.
Three sets of experiments were done, testing the same range of flow rates per
set. Because the ISOHTTP membrane has an average pore size that is 100
48
times larger than the AN69, the filtrate volume collected during the
experiment was much larger than the filtrate volume of the AN69-ST
membrane. The larger solution flux made it slightly more difficult to maintain
a steady and distinct transmembrane pressure during the experiment
compared to the AN69 membrane for solutions with low or no glycerol
content. Figure 5.6, 5.7, and 5.8 presents the results for the hydraulic
permeability of DI water, 10% w/w glycerol, and 40% w/v glycerol,
respectively.
9.0E-09
8.0E-09
Average Lp = 1.40e-8 m/Pa-s
V/t (m3/s)
7.0E-09
6.0E-09
5.0E-09
4.0E-09
3.0E-09
1st Set
2nd Set
3rd Set
Average
2.0E-09
1.0E-09
0.0E+00
0.00
0.20
0.40
0.60
0.80
Ax(P1-P2) (m2-Pa)
Figure 5.6: Hydraulic permeability of ISOHTTP to DI water.
49
8.0E-09
Average Lp = 1.03e-8 m/Pa-s
7.0E-09
V/t (m3/s)
6.0E-09
5.0E-09
4.0E-09
3.0E-09
1st Set
2.0E-09
2nd set
1.0E-09
3rd Set
Average
0.0E+00
0.00
0.20
0.40
0.60
Ax(P1-P2)
0.80
(m2-Pa)
Figure 5.7: Hydraulic permeability of ISOHTTP to 10% w/v glycerol solution.
7.0E-09
Average Lp = 6.18e-9 m/Pa-s
6.0E-09
V/t (m3/s)
5.0E-09
4.0E-09
3.0E-09
1st Set
2.0E-09
2nd Set
3rd Set
1.0E-09
Average
0.0E+00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
Ax(P1-P2) (m2-Pa)
Figure 5.8: Hydraulic permeability of ISOHTTP to 40% w/v glycerol solution.
As is the case with the AN69 membrane, the average hydraulic
permeability of the ISOHTTP membrane was expected to decrease with
50
increasing viscosity. The average membrane hydraulic permeability to
solutions of different glycerol concentrations is presented in figure 5.10.
1.6E-08
= 0.903e-3 Pa-s
1.4E-08
Lp (m/s-Pa)
1.2E-08
= 1.17e-3 Pa-s
1.0E-08
8.0E-09
6.0E-09
= 3.22e-3 Pa-s
4.0E-09
2.0E-09
0.0E+00
0
0.1
0.2
0.3
0.4
% Glycerol
Figure 5.9: The hydraulic permeability of the ISOHTTP to glycerol solutions of
different viscosities.
From the figure it can be seen that the hydraulic permeability of
ISOHTTP does decrease with increasing viscosity. For comparison purposes, a
theoretical projection according to Darcy’s law for what the hydraulic
permeability value should be for DI water and 10% w/v glycerol was
calculated based on the value for 40% w/v glycerol solution. Figure 5.11
presents the experimental data plotted with the theoretical projection using
Darcy’s Law. From the figure it can be seen that the decreasing trend of the
experimental data is more gradual than what is predicted by the theoretical
projection. The discrepancies may be attributed to the difficulties in
51
measuring the transmembrane pressure during the experiment for the
solutions with low or no glycerol content. Millipore reports a hydraulic
permeability range between 2.42e-8 to 1.93e-7 m/Pa-s for the ISOHTTP
membrane [34]. The lower value of this range is in good agreement with the
theoretical projected value for DI water. The accuracy of the measurements
for the DI water and the 10% w/v glycerol experiments may be improved by
testing higher flow rates, which would result in a more steady and distinct
transmembrane pressure.
4.00E-08
Experimental Data
3.50E-08
Lp (m/s-Pa)
3.00E-08
Theoretical projection
using 40%w/v Lp value
2.50E-08
Theoretical projection
using Millipore lower
range value
2.00E-08
1.50E-08
1.00E-08
5.00E-09
0.00E+00
0
0.1
0.2
0.3
0.4
% Glycerol
Figure 5.10: Hydraulic permeability of ISOTMTP to solutions of different
viscosities compared to theoretical projections.
52
5.1.3 Millipore ISOPORE TMTP
The hydraulic experiment for the ISOTMTP membrane was done in the same
manner as the previous membranes, testing the same range of flow rates per
set of experiment. The average pore size of the ISOTMTP membrane is much
larger than first two membranes; one thousand times larger than the pores of
the AN69 membranes and approximately ten times larger than the average
pore of the ISOHTTP membrane. Due to the much larger pore size, the
resulting filtrate volume for the ISOTMPT membrane was significantly larger
than previous membranes for a given transmembrane pressure. The high
solution flux across the membrane made it extremely difficult to create a
steady and distinct transmembrane pressure difference for solutions with no
and low glycerol contents. A more steady and distinct transmembrane
pressure was able to be maintained for the 40% w/v glycerol solution due to
its high viscosity. Figure 5.11, 5.12, and 5.13 presents the results for the
hydraulic permeability experiment using the ISOTMTP membrane and DI
water, 10% w/w glycerol, and 40% w/v glycerol, respectively.
53
1.2E-08
Average Lp = 1.35e-8 m/Pa-s
V/t (m3/s)
1.0E-08
8.0E-09
6.0E-09
4.0E-09
1st Set
2nd set
3rd Set
Average
2.0E-09
0.0E+00
0.00
0.20
0.40
Ax(P1-P2)
0.60
(m2-Pa)
Figure 5.11: Hydraulic permeability of the ISOTMTP to DI water
1.4E-08
Average Lp = 2.03e-8 m/Pa-s
1.2E-08
V/t (m3/s)
1.0E-08
8.0E-09
6.0E-09
1st Set
2nd Set
3rd Set
Average
4.0E-09
2.0E-09
0.0E+00
0.00
0.10
0.20
0.30 0.40 0.50
Ax(P1-P2) (m2-Pa)
0.60
0.70
0.80
Figure 5.12: Hydraulic permeability of the ISOTMTP to 10% w/v glycerol
solution.
54
1.2E-08
Average Lp = 1.36e-8 m/Pa-s
1.0E-08
V/t (m3/s)
8.0E-09
6.0E-09
1st set
4.0E-09
2nd set
2.0E-09
3rd Set
Average
0.0E+00
0.00
0.20
0.40
0.60
0.80
Ax(P1-P2) (m2-Pa)
Figure 5.13: Hydraulic permeability of the ISOTMTP to 40%w/v glycerol
solution.
Even with a much larger average pore size, the hydraulic permeability
of the membrane should still decrease with increasing viscosity. By looking
the data presented in figure 5.14, it can be seen that the plot of average
membrane Lp versus the glycerol concentration does not follow the expected
trend. The amount of scatter and the large degree of uncertainty indicated by
the error bars in figure 5.14 signify that the values for the hydraulic
permeability of DI water and 10% w/v glycerol solution to the membrane are
less accurate than the hydraulic permeability of the 40% w/v glycerol
solution. Using the Lp value for 40% w/v glycerol solution, a theoretical
projection of what the Lp values should be for DI water and 10% w/v glycerol
55
solution was calculated. The comparison of the experimental data and the
theoretical projection is presented in figure 5.15.
2.5E-08
= 1.17e-3 Pa-s
Lp (m/s-Pa)
2.0E-08
1.5E-08
= 0.903e-3 Pa-s
= 3.22e-3 Pa-s
1.0E-08
5.0E-09
0.0E+00
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
% Glycerol
Figure 5.14: Hydraulic permeability of ISOTMTP to solutions of different
viscosities.
56
6.E-08
Experimental Data
Lp (m/s-Pa)
5.E-08
Theoretical Relationship
4.E-08
3.E-08
2.E-08
1.E-08
0.E+00
0
0.1
0.2
0.3
0.4
% Glycerol
Figure 5.15. Hydraulic permeability of ISOTMTP to solutions of different
viscosities compared to theoretical projection
Figure 5.15 illustrates a large discrepancy between the projected
theoretical value and the actual experimental measurements. Millipore
reported a single value of 6.05e-7 m/Pa-s instead of a range for the hydraulic
permeability of ISOTMTP to DI water [34]. The manufacturer’s reported
hydraulic permeability is an order of magnitude larger than the value
obtained from experiments. Although the degree of certainty of the value
reported by Millipore is unknown, with the amount of discrepancy from
comparison to the theoretical projection, it can be deduced that the design of
the hydraulic permeability experiment is unsuitable for the ISOTMTP
membrane. The accuracy of the measurements for the ISOTMTP membrane
may be improved by revising the design of the experiment in terms of the
flow rates used. A much higher flow rate range compared to the range tested
57
for the AN69 experiment should be used to maintain a steady and distinct
transmembrane pressure.
5.2 Diffusive Permeability Experiments
The diffusive permeability experiments were done with 10% w/v glycerol
solution without red blood cells and DI water flowing co-currently. Like the
hydraulic permeability experiments, the diffusive permeability experiments
were also done in triplicates to obtain an average value for each membrane.
Each set of experiments was done using seven different flow rates: 1, 0.8, 0.6,
0.4, 0.3, 0.2, and 0.1 ml/min.
5.2.1 Gambro AN69-ST
The diffusive permeability at each flow rate is calculated using the solute flux
equation from the KK formulation. By assuming steady state, well mixed, no
boundary layer effects, and constant diffusive permeability, the flux term in
equation 4.3 can be rewritten as a mass balance of glycerol between the inlet
and outlet of the channels and the concentration gradient term can be
rewritten in terms of a logarithmic mean. The Ps value of the membrane at
each of the flow rates tested was calculated and then averaged over the three
sets of experiments. The averaged diffusive permeability for the range of the
flow rates tested for membrane AN69 is presented in figure 5.16.
58
7.E-06
6.E-06
Ps (m/s)
5.E-06
4.E-06
Ps = 2.96E-06(Q) + 3.44E-06
R² = 9.38E-01
3.E-06
2.E-06
1.E-06
0.E+00
0
0.2
0.4
0.6
Flow Rate (ml/min)
0.8
1
Figure 5.16: Diffusive permeability of AN69 to 10% w/v glycerol solution for
flow rates ranging from 1 to 0.1 ml/min
The diffusive permeability in this experiment is analogous to the
overall mass transfer coefficient, which depends on the resistance to mass
transfer of the membrane, as well as the mass transfer resistances in the fluid
on either side of the membrane [30]. In the range of flow rates tested, it can
be seen that Ps slightly decreases with decreasing flow rate. This effect is
attributed to the boundary layer resistance present in the glycerol and wash
stream. Resistance to mass transfer in the fluid can be minimized through
perfect mixing or agitation of the fluid [43]. In the microchannels, the extent
of mixing in the fluid decreases with decreasing flow rate; hence, for lower
flow rates, the resistance to mass transfer for the fluid is increased,
decreasing the apparent value of the diffusive permeability. In the range of
flow rates tested, the relationship of the diffusive permeability to the flow
59
rate can be adequately approximated with a simple linear relationship. The
experimental data was fitted with a linear approximation to obtain an
expression for diffusive permeability as a function of flow rate that could be
easily incorporated into the mathematical model.
5.2.2 Millipore ISOPORE HTTP
Due to its small size, glycerol molecules can diffuse through
membranes with nanoscale pores completely and easily [37]. With this
information, it is expected that pore size will not have much of an effect in the
diffusive permeability value of the ISOHTTP membrane when compared to
the AN69 membrane despite its pores being one hundred times larger. The
averaged diffusive permeability for the range of the flow rates tested for
membrane ISOHTTP is presented in figure 5.17. From the figure it can be
seen that the diffusive permeability also decreases with decreasing flow rate
as expected. The experimental for the ISOHTTP data was also approximated
with a linear relationship to facilitate incorporation into the mathematical
model.
60
1.E-05
1.E-05
Ps (m/s)
1.E-05
8.E-06
Ps = 8.16E-06(Q) + 4.88E-06
R² = 0.991
6.E-06
4.E-06
2.E-06
0.E+00
0
0.2
0.4
0.6
0.8
1
1.2
Flow Rate (ml/min)
Figure 5.17: Diffusive permeability of ISOHTTP to 10% w/v glycerol solution
for flow rates ranging from 1 to 0.1 ml/min
5.2.3 Millipore ISOPORE TMTP
The averaged diffusive permeability for the range of the flow rates
tested for membrane ISOTMTP is presented in figure 5.18. The result of this
experiment further confirms that average membrane pore size does not affect
diffusive permeability. The average pore size of ISOTMTP is approximately
one thousand times larger than the average pore size of the AN69 membrane,
yet the diffusive permeability values of the two membranes are comparable.
The slightly higher range of values that was observed in the ISOPORE
membrane result may be attributed to other things; such as difference in pore
density which would cause a difference in surface area available for mass
transfer or a slight effect of pressure driven flow. For the Ps experiments, the
61
transmembrane pressure was minimized by adjusting the flow rate of the
bottom stream; however, a slight transmembrane pressure difference is
inevitable, causing slight pressure driven flow through the membrane. Similar
to the diffusive permeability trend for the AN69 and the ISOHTTP membrane,
the change in diffusive permeability for the ISOTMTP membrane was
approximated with a linear relationship to facilitate incorporation into the
mathematical model.
2.5E-05
Ps (m/s)
2.0E-05
1.5E-05
1.0E-05
Ps = 1.74E-05(Q) + 2.19E-06
R² = 0.974
5.0E-06
0.0E+00
0
0.2
0.4
0.6
0.8
Flow Rate (ml/min)
1
1.2
Figure 5.18: Diffusive permeability of ISOTMPT to 10% w/v glycerol solution
for flow rates ranging from 1 to 0.1 ml/min
5.3 Model Validation Experiments
The main purpose of the model validation experiment is to produce data that
can be compared to the predictions of the mathematical model. Comparison
62
of the data from the model validation experiment to the results of the
mathematical model simulation will be able to determine the accuracy of the
model. The ability to predict removal rate along with parametric studies on
the microseparation unit is crucial in developing the most optimal CPA
removal protocol, as well as in designing the prototype of the next generation
of the device.
Before the model validation experiments were carried out, several
preliminary tests was done to ensure the model was working properly. The
first test done was by setting the cell permeability values Lp,c and Ps,c to zero.
The model prediction showed that there was no mass transfer between the
cell and the extracellular solution stream, which is what was expected. The
second test done was to set the solution flux through the synthetic membrane
to zero. By making the solution flux equal to zero, it is expected that there
would be no mass exchange between the top and the bottom stream, making
the flow rates constant. Upon analyzing the flow rates of both the top and
bottom stream, it was confirmed that it remained constant, indicating no mass
transfer across the synthetic membrane. The last test performed to ensure the
model was working properly was to compare the model predictions to the
predictions of a different model that was developed for the same
microseparation device. Tuhy developed a model to characterize the mass
transfer of urea in the same microseparation device in a study about
63
microdialysis [24]. The model developed by Tuhy is different from the model
developed for this study in that it uses Navier-Stokes equation to describe the
flow in the microchannels and that it does not include the presence of cells in
the top stream. Figure 5.19 presents the model’s removal prediction of urea
compared to the removal predictions of Tuhy’s model and experimental
fractional removal data using the AN69 membrane.
70%
Model Prediction
Fractional Removal (%)
60%
Tuhy's model prediction
50%
Tuhy's experimental data
40%
30%
20%
10%
0%
0
1
2
3
4
Mean Velocity (m/s)
5
6
Figure 5.19: Model prediction comparison for urea removal to Tuhy’s model
and experimental data using AN69
Figure 5.19 shows that the model prediction developed for this study
is in good agreement with Tuhy’s model prediction and experimental data.
Good agreement between the two model predictions indicates that the
simplification assumption of plug flow inside the microchannel is adequate to
describe the mass transfer in the device. This test along with the other
64
preliminary test affirms that the model can properly predict the removal rate
of solutes given the right membrane permeability values.
The model validation experiment measures the fractional removal of
the solute from the CPA rich stream. The fractional removal is dependent on
the fluid flow rate inside the channels. If two solutions of different
concentrations separated by a porous membrane were allowed to come to
equilibrium, the concentration in both compartments would eventually be
equal if infinite time is allowed. Moreover, for counter-current flow mass
transfer in the device, a theoretical 100% removal would be attained given
infinite residence time and channel length. Hence, slower flow rates are
expected to have a higher CPA fractional removal compared to higher flow
rates due to the longer residence time inside the microseparation device. Five
different flow rates were done per set of experiments: 1, 0.8, 0.6, 0.4, and 0.2
ml/min. Like the other experiments, the model validation experiments were
done in triplicates to get an average fractional removal. The results from the
model validation experiments were compared to the values obtained from
simulation. Although the model simulates glycerol removal in a countercurrent configuration, it incorporates parameters that were obtained from the
Lp and Ps experiments, which were both obtained in experiments using cocurrent configuration. Because the experiments were done without red blood
cells, the model was also set to have no red blood cells in the glycerol rich
65
stream. The comparison of the validation experiments data and the model
predictions for the membranes AN69, ISOHTTP, and ISOTMTP are presented
in figures 5.20, 5.21, and 5.22, respectively.
Fractional Removal (%)
30%
Experimental Data
Model Prediction
25%
20%
15%
10%
5%
0%
0
0.2
0.4
0.6
0.8
1
1.2
Flow Rate (ml/min)
Figure 5.20: Comparison between model validation experimental data and
model predictions for membrane AN69 using the experimental Lp value for
10% w/v solution
66
100%
Experimental Data
Fractional Removal (%)
90%
Model Prediction
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
0.2
0.4
0.6
0.8
1
1.2
Flow Rate (ml/min)
Figure 5.21: Comparison between model validation experimental data and
model predictions for membrane ISOHTTP using the experimental Lp value
for 10%w/v solution.
100%
Fractional Removal (%)
90%
80%
70%
60%
50%
40%
30%
20%
Experimental Data
10%
Model Prediction
0%
0
0.2
0.4
0.6
0.8
1
1.2
Flow Rate (ml/min)
Figure 5.22: Comparison between model validation experimental data and
model predictions for membrane ISOTMTP using the experimental Lp value
for 10%w/v solution.
67
From the figures it can be seen that the agreement between the model
prediction to the experimental data decreases with increasing pore size; the
fit of the model to the experimental data is best for the AN69 data, then the
ISOHTTP data, and the least for the ISOTMTP data. Recalling the Lp
experimental results and how there were discrepancies for both the ISOPORE
membranes, simulations were carried out using the theoretical Lp value
projected using Darcy’s Law based on the Lp value for 40% w/v glycerol
solution. Figure 5.23 and 5.24 presents the model prediction with the
theoretically projected Lp values for the ISOHTTP and the ISOTMTP
membrane, respectively.
100%
Experimental Data
Fractional Removal (%)
90%
Prediction using experimental Lp for 10% w/v
glycerol
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
0.2
0.4
0.6
0.8
Flow Rate (ml/min)
1
1.2
Figure 5.23: Comparison of experimental data and model predictions of
glycerol removal using different hydraulic permeability values for the
ISOHTTP membrane
68
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Fractional Removal (%)
Experimental
Data
Prediction using
experimental Lp
for 10% w/v
glycerol
Prediction using
theoretical Lp for
10% w/v glycerol
0
0.5
1
1.5
Flow Rate (ml/min)
Figure 5.24: Comparison of experimental data and model predictions of
glycerol removal different hydraulic permeability values for the ISOTMTP
membrane
From the figures it can be seen that the fit for the ISOHTTP membrane
is improved by using the theoretically projected value of Lp for 10% w/v
glycerol solution. The model prediction for the ISOTMTP membrane,
however, still does not adequately agree with the experimental data after
using the theoretically projected Lp value. This indicates the presence of some
other unknown effect inside the microseparation device.
Upon further investigation, it was discovered that the predicted
pressure drop in the microchannels does not match the pressure drop
recorded during experiments. The recorded pressure drops during
experiments were much higher than the predicted pressure drops for all
69
three membranes. Tables 5.1, 5.2, and 5.3 lists the pressure drop recorded
during the experiments and the predicted pressure drop from the model
simulation for the AN69, ISOHTTP, and ISOTMTP membrane, respectively.
The experimentalP1 and P2 are the pressure drops between the inlet
pressure transducer and outlet pressure transducer of the top and bottom
stream, respectively. In the experimental apparatus the pressure transducers
are connected by 15 cm IV tubing to the microseparation device. Hence, the
P1 and P2 that was recorded during the experiment is not truly the pressure
drop from the inlet and outlet of the microchannels; it includes the 15 cm IV
tubing connectors, and the header regions of the lamina. The predicted P1
and P2 exclusively represents the pressure drop from the inlet and outlet of
the top and bottom microchannels.
Flow Rate
Experimental
Predicted
Experimental
Predicted
(ml/min)
P1 (Pa)
P1 (Pa)
P2 (Pa)
P2 (Pa)
1
25802
3707
17813
2850
0.8
20722
2961
13141
2285
0.6
15659
2216
9928
1720
0.4
10596
1471
6424
1155
0.2
5235
727
3212
587
Table 5.1: Comparison of pressure drops obtained from experiment and from
model predictions for validation experiment using the AN69 membrane.
70
Flow Rate
Experimental
Predicted
Experimental
Predicted
(ml/min)
P1 (Pa)
P1 (Pa)
P2 (Pa)
P2 (Pa)
1
9636
3285
10137
2699
0.8
7469
2625
7512
2163
0.6
5384
1965
5468
1627
0.4
3895
1305
4008
1091
0.2
2108
646
2256
533
Table 5.2: Comparison of pressure drops obtained from experiment and from
model predictions for validation experiment using the ISOHTTP membrane.
Flow Rate
Experimental
Predicted
Experimental
Predicted
(ml/min)
P1 (Pa)
P1 (Pa)
P2 (Pa)
P2 (Pa)
1
11506
2984
12264
2546
0.8
10403
2387
10804
2038
0.6
7723
1789
7592
1530
0.4
5638
1191
5548
1022
0.2
3255
594
3212
513
Table 5.3: Comparison of pressure drops obtained from experiment and from
model predictions for validation experiment using the ISOTMTP membrane.
Although the pressure drops recorded during experiments represent
slightly different conditions, it does not explain the large pressure difference
seen in all membranes. Several different tests were performed to ascertain
what is attributing to the pressure drop discrepancies. The pressure
transducers were calibrated twice to ensure that they were not defective. The
calibration results from both tests were similar, indicating that the pressure
transducers worked properly during the experiments. Another possible cause
for the pressure discrepancy is membrane sagging or swelling, reducing the
channel height on both side of the microseparation device. Simulations were
carried out, decreasing the channel height until the predicted pressure drop
71
matched the experimental pressure drop. It was found that the channel height
in the mathematical model had to be reduced to half, from 100 microns to
about 50 microns, for the pressure drop to match. It is unlikely that the
membrane would sag or swell so much into the channels considering all
membranes used in this study are only about 20 microns thick. The last
theory as to what could be causing the pressure discrepancy is the presence
of trapped air bubbles inside the channels. The model predicts the pressure
drops of the top and bottom stream assuming ideal conditions; that there is
nothing that would obstruct the flow of fluid from the entrance of the channel
to the outlet. Most of the air bubbles that get trapped within the channels
were probably introduced during assembly of the device. Great care was
taken to not introduce excessive air bubbles while assembling and connecting
the device into the apparatus; however, it is virtually impossible to
completely eliminate air bubbles from the system even after flushing the
channels with the solution for an extended period of time. Because the
channels are microscale, the tiniest amount of air bubble is capable of
adhering into the channel walls, obstructing the flow of fluid. There are
several ways that air bubbles could obstruct the flow of fluid: (1) the air
bubbles may stick to the channel walls, effectively reducing the channel width
and height that is clear for flow, (2) large enough air bubbles may adhere to
the walls and cause complete blockage of whole channels, reducing the
amount of operating channels, (3) air bubbles could be trapped in the header
72
region of the lamina, blocking whole regions of channel for fluid flow, and (4)
a combination of all three possible ways. Because of the physical nature of
the device, with the lamina encased in a metal housing, visual observation of
how the air bubbles obstruct fluid flow in the device is not possible. A new
method of non-visual observation of the air bubbles is necessary to modify
the mathematical model to account for non-ideal situations inside the device
to make better predictions of the CPA removal. If bubbles were successfully
eliminated from inside the device creating conditions that are close to ideal,
the experimental data may better agree with the model prediction.
Although model validation experiments for all membranes show
discrepancies between the experimentally recorded pressure drop and the
model predicted pressure drop, the model provided predictions that were in
good agreement with experimental data for the membranes with small pores.
This effect is most probably attributed to the diffusion dominated mass
transfer when membranes with small pores are used. Because the mass
transfer process is dominated by diffusion, the pressure discrepancy between
the experiment and the model prediction has less of an effect. For membranes
with small enough pores like the AN69, the pressure discrepancy has almost
no effect in the fractional removal, as evident by the good agreement between
the model prediction and the experimental data. The mass transfer through
membranes with large pores however, is mostly dominated by pressure
73
driven flow. This is why from the comparison of the model prediction to the
experimental data, the effect of the pressure discrepancy is more evident in
membranes with larger pores. As the dominating factor in the mass transfer
process shifts from diffusion to pressure driven, the discrepancy between the
model prediction to the experimental data becomes more apparent. However,
since the use of membrane with large average pore size like ISOTMTP is
unsuitable for CPA removal from red blood cell suspensions, this matter is of
less importance for the scope of this study.
5.4 Parametric Study on Mathematical Model
Parametric studies were conducted to gain insight on the effects of several
parameters on the CPA removal performance for the membranes of interest.
Although all experiments in this study were done in the absence of cells, the
parametric studies conducted incorporated cells into the simulations, which
account for about 40% of the volume of the top stream for red blood cell
suspensions. From the model validation experiment, it is known that the
fractional removal of CPA increases with decreasing flow rate. The simulation
of the mathematical model for the parametric studies used membrane
permeaility properties that were found through experiments. Figure 5.25 and
5.26 shows the effect of flow rate in the CPA removal of a stream that is 40%
74
red blood cells by volume suspended in a 10% w/v glycerol solution using the
AN69 and ISOHTTP membranes, respectively
45%
Extracellular Solution
Stream
Fractional Removal (%)
40%
35%
Cell Stream
30%
25%
20%
15%
10%
5%
0%
0
0.2
0.4
0.6
0.8
1
1.2
Flow Rate (ml/min)
Figure 5.25: Effect of flow rate on the fractional removal of glycerol from red
blood cells suspended in 10% w/v glycerol solution using AN69
75
Fractional Removal (%)
80%
70%
Extracellular
Solution Stream
60%
Cell Stream
50%
40%
30%
20%
10%
0%
0
0.2
0.4
0.6
0.8
1
1.2
Flow Rate (ml/min)
Figure 5.26: Effect of flow rate on the fractional removal of glycerol from red
blood cells suspended in 10% w/v glycerol solution using ISOHTTP
Both figures 5.25 and 5.26 show that the removal rate of glycerol from
the extracellular solution is much greater than the rate of removal from the
cells. This is due to the cell membrane’s permeability properties being much
smaller than the permeability properties of the synthetic membrane. The
water and solute permeability of red blood cell membranes is about 1.6e-12
m/Pa-s and 4.2e-8 m/s, respectively [44]; much smaller when compared to
the hydraulic and diffusive permeability of both the AN69 and ISOHTTP
membranes. Because glycerol is more rapidly removed from the extracellular
solution stream, the CPA concentration of the cell stream and the extracellular
solution stream will not be at equilibrium upon exiting the microseparation
device. Mass transfer between the extracellular solution stream and the cell
76
stream will continue outside of the device until the CPA concentrations in the
two streams come to equilibrium.
In addition to decreasing flow rate, increasing the microchannel length
would also increase the CPA fractional removal. The relationship between
channel length and CPA removal is useful in designing the next generation
prototype of microseparation device. Figure 5.27 and 5.28 shows the effect of
channel length in the CPA removal of a stream that is 40% red blood cells by
volume suspended in a 10% w/v glycerol solution using the AN69 and
ISOHTTP membranes, respectively, using a fluid flow rate of 0.4 m/min. From
the figures it can be seen that doubling the channel length will also double the
CPA fractional removal. This is an important factor to consider in the design
of the future microseparation device prototype.
77
Fractional Removal (%)
70%
60%
Extracellular
Solution Stream
50%
Cell Stream
40%
30%
20%
10%
0%
0
50
100
150
200
Channel Length (mm)
Figure 5.27: Effect of dialyzer length on the fractional removal of glycerol
from red blood cells suspended in 10% w/v glycerol solution using AN69
100%
Extracellular
Solution Stream
Fractional Removal (%)
90%
80%
Cell Stream
70%
60%
50%
40%
30%
20%
10%
0%
40
60
80
Channel Length (mm)
100
120
Figure 5.28: Effect of dialyzer length on the fractional removal of glycerol
from red blood cells suspended in 10% w/v glycerol solution using ISOHTTP
78
As mentioned in earlier chapters, an important factor to consider while
removing CPA from a cell suspension stream is the cell volume changes that
occur during the process. It must be ensured that through the entire process
that the cells are not subjected to extreme changes in concentration as to
cause excessive shrinking or swelling. Through simulations, the change in
concentration of the extracellular solution as well as the cell volume changes
as a function of microchannel length may be examined for the
microseparation device with the use of any given membrane, solution, or flow
rate. Figure 5.30 and 5.31 presents the concentration change in the
extracellular solution stream and the relative cell volume change as a function
of distance from microchannel inlet for membranes of interest, respectively.
The relative cell volume was calculated by taking the cell volume at x and
dividing it by the isotonic cell volume to obtain a normalized cell volume. Both
figures were simulated using the permeability parameters obtained in
experiments with a fluid flow rate of 0.4 ml/min.
79
Extracellular Concentration (M)
1.2
AN69
1
ISOHTTP
0.8
0.6
0.4
0.2
0
0
20
40
60
80
100
Distance from inlet (mm)
Figure 5.29: The change in concentration of the extracellular solution stream
with respect to microchannel length for AN69 and ISOHTTP
Relative Cell Volume Change
2.00
1.80
1.60
1.40
1.20
AN69
1.00
ISOHTTP
0.80
0
20
40
60
80
100
Distance from inlet (mm)
Figure 5.30: The relative cell volume change with respect to microchannel
length for AN69 and ISOHTTP
80
From both figures it can be seen that the removal process with the
AN69 membrane is more gradual, whereas removal with the ISOHTTP
membrane is more abrupt. The ISOHTTP membrane removes more CPA, but
subjects the cells to more rapid concentration changes. From figure 5.29, it
was deduced that by doubling the channel length the CPA is almost
completely removed by using the ISOHTTP membrane. However, from figure
5.31 it can also be seen that doubling the channel length causes the cells to
swell to almost twice its isotonic volume. A channel length that maximizes
CPA removal without risking lysing of the cells due to excessive swelling
should be chosen for the future prototype of the device. Studying trends and
approximations through parametric studies of the mathematical model is a
way to gain insight to enable the design of the most optimal microseparation
device and protocol for removal of CPA from red blood cells suspension.
81
Chapter 6 – Conclusions
6.1 Hydraulic Permeability
Hydraulic permeability values for three membranes using three solutions of
different glycerol concentrations were found. The results of the AN69 and the
ISOHTTP membrane followed the expected trend with respect to solution
viscosity, with a relatively low standard error. Unlike the AN69 and the
ISOHTTP membrane, the result for the ISOTMTP did not follow the expected
trend and had a relatively high level of uncertainty as indicated by the
standard error. This is due to the ISOTMTP membrane having a much larger
pore size compared to the other two membranes which caused it to be
difficult to maintain a steady transmembrane pressure between the two
streams. Using higher flow rates with the ISOTMTP membrane may help
achieve a more steady transmembrane pressure and may possibly improve
experimental results. It was also determined that pore size has a large effect
on hydraulic permeability. The hydraulic permeability values obtained for the
membrane AN69 were about three orders of magnitude smaller than those
found for the ISOPORE membranes. Table 6.1 summarizes the hydraulic
permeability values obtained from experiments for the three membranes
with the three solutions used.
82
Solution
Membrane
10% w/v
DI Water
Glycerol
AN69-ST
(7.55±0.27)e-11
(7.27±0.17)e-11
ISOPORE TMTP
(1.35±0.12)e-8
(2.03±0.17)e-8
ISOPORE HTTP
(13.7±0.94)e-9
(10.3±0.66)e-9
Table 6.1: Hydraulic permeability values in m/Pa-s for the
40% w/v
Glycerol
(2.78±0.12)e-11
(1.38±0.03)e-8
(6.18±0.27)e-9
three membranes
tested using three solutions of varying glycerol concentrations.
6.2 Diffusive Permeability
The diffusive permeability to glycerol solution was found through
experiments for three different membranes. The experimental results for all
three membranes indicated that the apparent diffusive permeability increases
with increasing fluid flow inside the channels. This dependency is due to the
resistance to mass transfer in the fluid boundary. The effects of fluid
boundary may be reduced with adequate mixing. Since the level of mixing
decreases with decreasing flow rate, the resistance to mass transfer from the
fluid boundary increases, causing the diffusive permeability values to be
lower. If the flow rate was increased to the point where the fluid inside the
channels were perfectly mixed, the diffusive permeability will become
constant; because at that point the only resistance to mass transfer will be
attributed to the membrane itself. The relationship between the diffusive
permeability and the flow rate for all three membranes wes able to be
approximated with a linear model with relatively high coefficient of
determination (R2) values to facilitate incorporation into the mathematical
83
model. Table 6.2 and 6.3 summarizes the average Ps values per flow rate
tested and the linear approximation, respectively.
AN69
Membrane
ISOHTTP
ISOTMTP
0.1
(3.35±0.11)e-6
(5.31±0.62)e-6
(2.67±0.14)e-6
0.2
(4.09±0.10)e-6
(6.46±0.16)e-6
(6.26±1.45)e-6
0.3
(4.43±0.32)e-6
(7.54±0.12)e-6
(7.46±1.27)e-6
0.4
(4.81±0.32)e-6
(8.37±0.17)e-6
(10.8±1.22)e-6
0.6
(5.49±0.27)e-6
(10.1±0.59)e-6
(12.1±0.04)e-6
0.8
(5.90±0.30)e-6
(11.3±0.08)e-6
(15.6±1.53)e-6
Flow rate
(ml/min)
1
(6.09±0.21)e-6
(12.8±0.25)e-6
(19.7±1.42)e-6
Table 6.2: Average diffusive permeability values for the three membranes
tested for a flow rate range from 0.1 ml/min to 1 ml/min.
Membrane
Linear Expression
R2
AN69
Ps = 2.96E-06(Q) + 3.44E-06
0.94
ISOHTTP
Ps = 8.16E-06(Q) + 4.88E-06
0.99
ISOTMTP
Ps = 1.74E-05(Q) + 2.19E-06
0.97
Table 6.3: Linear approximation of Ps as a function of flow rate for the three
membranes tested
6.3 Model Validation
CPA removal experiments were carried out to validate the results of the
model prediction. The model validation experiments were done with three
different membranes using a 10% w/v glycerol and DI water as the fluids in
the top and bottom streams, respectively. The results of the experiments were
84
compared to model simulations using membrane permeability values
obtained from previous experiments. It was found that the model prediction
and the experimental values were in good agreement for the AN69 and
ISOHTTP membrane. Upon further investigation it was found that the
pressure drops recorded during the experiments were much higher than the
values predicted by the model. This indicated that the fluid flow is obstructed
inside the channels, most likely by air bubbles. The effect of trapped air
bubbles inside the channel was more apparent in the ISOTMTP membrane.
This is because the larger pores in the ISOTMTP membrane allowed a higher
flux of fluid through the membrane, making the mass transfer process inside
the microseparation device largely controlled by convective pressure driven
flow. In membranes with smaller pores where the mass transfer is dominated
by diffusion, the effect of the pressure discrepancy is less apparent. To get the
model prediction to agree with the experimental data, the trapped air bubbles
must be eliminated from inside the microchannels when using membranes
with large pores.
6.4. Parametric Studies
Several parametric studies on the removal rate of CPA using the
membrane of interest were done. The CPA fractional removal increases with
decreasing fluid flow rate and increasing microchannel length. It was also
found that the CPA fractional removal can be doubled by doubling the channel
85
length. This information is useful for designing future prototypes of
microseparation device. By examining the extracellular concentration change
and the relative cell volume change it was determined that the ISOHTTP
membrane removes more CPA but subjects the red blood cells to a more
abrupt concentration change. However, even with a more abrupt
concentration change, the resulting relative cell volume change is still within
tolerable limits for the microseparation unit that was tested.
6.5 Future Work
With the results of this study it has been shown that using the
microseparation device to remove CPA from a red blood cell suspension is
feasible. The immediate next step that must be taken is to develop a method
to eliminate or minimize air bubbles trapped inside the channels so that
usage of the model to predict CPA removal is not only limited to membranes
with a sufficiently small average pore size. Elimination of trapped air bubbles
will also improve membrane permeability experimental results. Flushing the
device using high flow rates prior to experiments may help force the air
bubbles out. Once the presence of air bubbles inside the channels is
successfully mitigated, experiments to attain the membrane permeability
values of the membranes using different CPAs like DMSO may be done.
Experiments using a solution that actually contain red blood cells as opposed
to just glycerol solution should be conducted. Further investigation should be
86
performed to attain the ultimate goal of this work; to eventually be able to
develop an efficient process to remove CPA from previously frozen blood
suspensions using a microseparation device.
87
Appendix A – Nomenclature
Variable
Description
Jw,c
Volumetric water flux through the cell membrane.
Units
 m3 / s 
 2 
 m 
Js,c
Molar solute flux through the cell membrane.
 mol / s 


2
 m 
Jv
Volumetric solution flux through the synthetic membrane.
Js
Molar solute flux through the synthetic membrane.
 m3 / s 
 2 
 m 
 mol / s 


2
 m 
 m 


 Pa  s 
 m 


 Pa  s 
m
 
 s
m
 
 s
m
 
 s
 
Lp,c
Water permeability of cell membrane.
Lp
Hydraulic permeability of synthetic membrane.
Ps,c
Solute permeability of cell membrane.
Ps
Diffusive permeability of synthetic membrane.
Pd
Local diffusive permeability in the synthetic membrane.

Reflection coefficient.
Cc
Solute concentration in the cell stream.
Cs,c
Salt concentration in the cell stream.
C1
Solute concentration in the extracellular solution stream.
Cs,1
Salt concentration in the extracellular solution stream.
C2
Solute concentration in the wash stream.
 mol 
 3 
 m 
 mol 
 3 
 m 
 mol 
 3 
 m 
 mol 
 3 
 m 
 mol 
 3 
 m 
88
 mol 
 3 
 m 
 mol 
 3 
 m 
 mol 
 3 
 m 
 mol 
 3 
 m 
Cm
Mean intramembrane solute concentration.
Qc
Flow rate of the cell stream.
Q1
Flow rate of the extracellular solution stream.
Q2
Flow rate of the wash stream.
Qb
Flow rate of the osmotically inactive particles in the cell
stream.
P1
 Pa 
P2
Pressure of the top stream, mix of the cell and the
extracellular solution.
Pressure of the wash stream.
u
Average velocity inside the microchannels.
m
 
 s
1
2
Viscosity of the top stream, mix of the cell and the
extracellular solution.
Viscosity of the wash stream.
W
Microchannel width.
H
Microchannel height.
L
Microchannel length.

Membrane thickness.
Ax
Ac
Membrane area available for mass transfer from a single
channel.
Total surface area of all the cells in the differential volume
x∙W∙H.
The surface area of a single cell.
Vc
The volume of a single cell.
Vb
Osmotically inactive volume within the cell.
vg
Molar volume of glycerol.
c
Cell volume fraction.
 m2 


 mol 
 
nc
The number of cells occupying the differential volume
x∙W∙H per time.
 cells 


 s 
Atotal
 m3 
 
 s 
 Pa 
 Pa  s 
 Pa  s 
m
m
m
m
m 
m 
m 
m 
m 
2
2
2
3
3
89
R
Universal gas constant.
T
Temperature.
Table A.1: Nomenclature
J




 mol  K 
K 
90
Appendix B - Derivation of Governing Differential Equations
A diagram of the system is shown in figure B.1
Figure B.1: Diagram of the system with coordinates
Assumptions:
-
Uniform velocity. No variation in x, y, or z direction.
-
Concentration and pressure are spatially uniform in the y-direction.
-
Steady state
-
No direct mass transfer between the cell stream and the wash stream
-
Glycerol is the only permeable solute. Salt is impermeable.
-
Constant molar volume
-
Constant temperature
-
No reaction
91
Refer to appendix (A) for detailed description of all variables used in this
derivation.
The flux equations through the cell membrane are defined as
Jw,c  Lp,c RT(Cc  Cs,c  C1  Cs,1)
Js,c  Ps,c (C1  Cc )
(B.1)
(B.2)
where Jw,c is the water flux; Js,c, the solute flux; Lp,c, the water permeability of
the cell membrane; R, the universal gas constant; T, the temperature; Cc, the
solute concentration of the cell stream; Cs,c, the salt concentration of the cell
stream; C1, the solute concentration of the extracellular solution stream; Cs,1,
the salt concentration of the extracellular solution stream; and Ps,c, the solute
permeability of the cell membrane.
The flux equations through the synthetic membrane are defined as
Jv  Lp (P1 P2)
(B.3)
Js  Cm Jv  Ps (C1  C2 )
(B.4)
where Jv is the volumetric solution flux; Js, the molar solute flux; P1, the
pressure of the top stream, which includes the cells and the extracellular
solution; P2, the pressure of the wash stream; Lp, the membrane hydraulic
diffusivity; Ps, the membrane diffusive permeability; and C2, the solute
concentration of the wash stream. Cm is the mean intramembrane solute
92
concentration derived using the local equation for the solute flux within the
membrane [Waniewski,Villarroel].
Consider the schematic figure of a possible concentration profile inside of a
permeable membrane presented in figure B.2.
Figure B.2: Concentration profile inside a permeable membrane
C1 and C2 are the solute concentration of the extracellular solution stream and
the wash stream, respectively; and  is the membrane thickness. The correct
description of fluxes within the membrane is expressed as
J s  Pd
dC
 J vC
dx
(B.5)
where Pd is the local diffusive permeability and C is the solute concentration
in an aqueous solution that is in equilibrium with the membrane at any point
93
x, between 0 and  [31]. At steady state, both Js and Jv are constant; hence,
equation B.5 may be integrated from 0 to  and solved for Js.
Pd dC
J
C s
J v dx
Jv

C2
C1
1
J
C s
Jv
dC 
Js

 C2  J
v
ln 
J
C  s
 1 J
v

Let
Ps 
Pd
Jv
(B.6)


0
dx
(B.7)

 J
 v
 Pd


(B.8)
Pd
 .
(B.9)
J 
C2 Jv  J s
 exp  v 
C1Jv  J s
 Ps 
(B.10)
J 
C2 Jv  J s  C1Jv  J s  exp  v 
 Ps 
J
J s exp  v
 Ps

 Jv
  J s   C1 J v  exp 

 Ps

  C2 J v





1

 J  C exp  J v   C 
Js 
  2 
v 1

 J v   
 Ps 

 exp    1 
P
 s 

(B.11)
(B.12)
(B.13)
94




1

 J  C exp  J v   C 
Js 
  2 
v 1

 J v   
 Ps 

 exp    1 
 Ps  





1

 J  C exp  J v   C   C J  P (C  C )
Js 
  2 
v 1
m v
s
1
2

Ps 
 J v   


exp

1

  
 Ps  

(B.14)
(B.15)
Rearrange equation (B.15) and solve for Cm.
J 
C2  C1 exp  v 
 Ps   Ps (C  C )
Cm 
2
1
Jv
 Jv 
1  exp  
 Ps 
I.
Volume Balances
i.
Volume Balance on Cell Stream
(B.16)
In – Out + Generation =Accumulation
Qc x  Qc
x x
 (J s,c  vg  J w,c ) Atotal  0
(B.17)
Atotal is the total cell membrane area of all the cells in the
differential volume and is defined as
Atotal 
Ac
 c (W  H  x)
Vc
(B.18)
95
where Ac is the membrane area of a single cell, Vc is the volume of a
single cell, c is the cell volume fraction in the suspension, and W
and H are the microchannel width and height, respectively.
Define c and Vc in terms of known stream flow rates
c 
Qc
Q1  Qc
(B.19)
Qc
nc
(B.20)
Vc 
where
nc
is the number of cells that passes through the differential
length x per time.
Rewrite Atotal in terms of flow rates and substitute it back into the
differential.
dQc
A n
 ( J s,c  vg  J w,c )  c c  (W  H )
dx
Q1  Qc
ii.
(B.21)
Volume Balance on Stream 1
In – Out + Generation =Accumulation
Q1 x  Q1 xx  (Js,c  vg  Jw,c )Atotal  Jv W x  0
Express Atotal in terms of flow rates of the cell and suspension
solution stream.
(B.22)
96
Q1 x  Q1 x x  ( J s ,c  vg  J w,c ) 
Ac  nc
 (W  H  x )  J v W  x  0
Q1  Qc
(B.23)
Q1 x  Q1 xx
x
 ( J s,c  vg  Jw,c ) 
Ac  nc
 (W  H )  Jv W  0
(B.24)
Q1  Qc
A n
dQ1
 ( J s ,c  vg  J w,c )  c c  (W  H )  J v W
dx
Q1  Qc
iii.
(B.25)
Volume Balance on Stream 2
In – Out + Generation =Accumulation
Q2
x x
 Q2 x  J v  W  x  0
Q2 xx  Q2 x
x
 J v W  0
dQ2
  J v W
dx
II.
Solute Balances
i.
Solute Balance on Cell Stream
(B.26)
(B.27)
(B.28)
Within a cell volume, there are osmotically inactive particles that
occupy volume but do not play a part in the mass transfer process.
Solutes within the cells are dissolved in the osmotically active part
of the cells, in the volume Vc-Vb.
97
Figure B.3: Cell volume content
The solute balance must take into account the osmotically inactive
part of the cell volume as well as the osmotically active. Hence, the
volumetric flow rate that is involved in the mass transfer process is
(Qc-Qb), where Qb is the volumetric flow rate of the osmotically
inactive particles within the cell.
In – Out + Generation =Accumulation
[(Qc  Qb )  Cc ] x  [(Qc  Qb )  Cc ] xx  ( J s ,c  vg ) 
Ac  nc
 (W  H  x)  0
Q1  Qc
(B.29)
[(Qc  Qb )  Cc ] x  [(Qc  Qb )  Cc ] x x
x
 ( J s , c  vg ) 
Ac  nc
 (W  H )  0
Q1  Qc
(B.30)
d [(Qc  Qb )  Cc ]
A n
 ( J s ,c  vg )  c c  (W  H )
dx
Q1  Qc
Cc
d (Qc  Qb )
dC
A n
 (Qc  Qb ) c  (Js,c  vg )  c c  (W  H )
dx
dx
Q1  Qc
(B.31)
(B.32)
The flow rate of the osmotically inactive part of the cell is constant,
and hence the derivative of it is zero.
98
dQc
dC
A n
 (Qc  Qb ) c  ( J s,c  vg )  c c  (W  H )
dx
dx
Q1  Qc
(B.33)

dCc
Ac  nc
dQc 
1

 (W  H )  Cc
 ( J s ,c  vg ) 

dx (Qc  Qb ) 
Q1  Qc
dx 
(B.34)
Cc
ii.
Solute Balance on Stream 1
In – Out + Generation =Accumulation
(Q1  C1 ) x  (Q1  C1 ) xx  ( J s ,c  vg ) 
Ac  nc
 (W  H  x)  J s W  x  0
Q1  Qc
(B.35)
(Q1  C1) x  (Q1  C1) xx
x
 (Js,c  vg ) 
Ac  nc
 (W  H)  Js W  0
Q1  Qc
(B.36)
A n
d (Q1  C1 )
 ( J s ,c  vg )  c c  (W  H )  J s W
dx
Q1  Qc
(B.37)
A n
dQ1
dC
 Q1 1  ( J s,c  vg )  c c  (W  H )  J s W
dx
dx
Q1  Qc
(B.38)
A n
dC1
1 
dQ 
  ( J s ,c  vg )  c c  (W  H )  J s  W  C1 1 
dx
Q1 
Q1  Qc
dx 
(B.39)
C1
iii.
Solute Balance on Stream 2
In – Out + Generation =Accumulation
Q2  C2
Q2  C2
x x
 Q2  C2 x  J s W  x  0
x x
 Q2  C2
x
x
 J s W  0
(B.40)
(B.41)
99
C2
d (Q2  C2 )
  J s W
dx
(B.42)
dQ2
dC
 Q2 2  J s W
dx
dx
(B.43)
dC2
1

dx
Q2
III.
dQ2 

 J s  W  C2 dx 
(B.44)
Pressures
The differential equation that describes the pressure in the top and
bottom stream was derived from a pressure drop equation in a
rectangular channel [Bahrami, 2007].
P  c2  1 64  
 
u
 5 tanh

  L 3 
2   
where
c
(B.45)
H
W
c
, b ,   .
2
2
b
(B.46,47,48)
i.
Pressure of Top Stream
u
P  c2
L
H
P  2 
u
L 
2
 
 1 64  
 3   5 tanh 2   


H
 1 64   W 

  tanh  
 
5
H
3
2 

 W  

H 
H
64   




Q1  Qc dP1  2  1
 W  tanh  
 

Ax
dx 1  3
5
H
2 

 W  
(B.49)
(B.50)
2
(B.51)
100

H
64  

Q1  Qc dP1 H
1
W
 

(W  H ) dx 4  1  3
5

2
dP1

dx
ii.


 tanh

 

 H 
2 
 W  
Q1  Qc

H
64   
3 
(W  H ) 1
 W  tanh 
 
4  1  3
5
H
2

W
(B.52)






(B.53)
Pressure of Bottom Stream

H 
H
64   




Q2 dP2  2  1
 W  tanh  
 

Ax dx 2  3
5
H
2 

 W  
2

H
64  

Q2
dP H
1
W
 
 2
(W  H ) dx 4  2  3
5

2
dP2

dx


 tanh

 

 H 
2 
 W  
Q2

H
64   
3 
(W  H ) 1
 W  tanh 
 
2  3
5
H
2

W






(B.54)
(B.55)
(B.56)
101
Appendix C - Protocol for Microseparation Device Assembly
1. Prepare the metal housing for the lamina plates by loosening and
removing the bolts to expose the inside. Make sure the gaskets on the inlet
and outlet ports are in place.
2. Select 2 lamina plates and note which ones they are on lab notebook. Also
note the assembly position of the plates, which plate is on top and which is
on the bottom.
3. Dispense a small amount of DI water to wet the microchannels on both
lamina plates. Run fingers across the channels to ensure channels are wet
to reduce the chance of trapped bubbles once the device is assembled.
4. Cut a piece of membrane. If the membrane is dry-stored, wet the
membrane using DI water before placing it between the lamina plates. If
the membrane is stored in glycerol, it may be directly placed in between
the lamina plates. Place the alignment pins to secure the plates once the
membrane is sandwiched. Trim any excess membrane off the lamina
plates.
5. Insert the coupled lamina plates into the metal housing. Assemble the
metal housing so that lamina plates are encased.
6. Place the bolts in place and screw them in by hand.
7. Using a torquemeter, screw the bolts in to 80 cN-m. Once a bolt is screwed
in with the proper amount of torque, screw the bolt that is directly
102
opposite of it. Tightening bolts in opposition helps distribute even
pressure on the device.
103
Appendix D - Protocol for Hydraulic Permeability Experiment
1. Prepare solution for experiment (see solution making protocol). Solution
with the same concentration should be flowed through the top and bottom
stream of the microdialyzer for this experiment.
2. Assemble the microdialyzer with the membrane to be tested sandwiched
between the two laminas (see microdialyzer assembly protocol).
3. If using a membrane that is stored in glycerol, Load two 60 ml syringes
with DI water and attach it to the apparatus co-currently. Place the
syringes on syringe pumps and set the syringe pump flowrates to 1
ml/min. Activate the syringe pump and flush out the glycerol in the
membrane with DI water for about 10 minutes. If using a membrane that
is stored dry, this step may be skipped.
4. Fill two 60 ml syringes with the solution that is to be used for the
experiment and attach it to the apparatus, co-currently. Place the loaded
syringes on the syringe pumps.
5. Turn the computer on and once computer is booted, click on Measurement
& Automation explore. Once the program has loaded, click on my VI logger
task IV.
6. Select an operating flow rate and set both syringe pumps to the selected
flow rate. Activate the syringe pump and allow 10 ml of solution to pass
104
through the microdialyzer to assure the channels are filled with the
solution to be tested.
7. After 10 ml of solution has passed, stop the syringe pump to the bottom
stream and leave the syringe pump to the top stream on. Once the syringe
pump to the bottom stream is turned off, click on the ‘Run Task’ button on
the top left corner of the data acquisition program interface.
8. Find the color that corresponds to each transducer on the program and
note it on the lab notebook. Find the corresponding color by gently
tapping each transducer.
9. Allow the system to come to steady state by waiting for 20 minutes before
sampling.
10. Once the system has come to steady state, collect the volume of water that
drips out from the bottom stream for a certain collection time. Be sure the
outlet stream is level with the apparatus. Take three samples. Note the
collected volume, collection time, and pressure readings (in mV) from of
all four transducers in lab notebook.
11. Repeat experiment for a different flow rate.
12. Once experiments are done, stop the pumps and replace the solution
syringes with syringes filled with DI water and flush the system out for
approximately 10 minutes.
13. Disassemble the apparatus and take out the lamina plates from the metal
housing. Discard the used membrane and place the lamina plates in their
105
storage vials. Rinse the metal housing with DI water and dry with
kimwipes.
106
Appendix E - Protocol for Diffusive Permeability Experiment
1. Prepare solution for experiment (see soluton making protocol). The top
stream should have CPA solution running through while the bottom
stream should have pure water running through for the diffusive
permeability experiment.
2. Assemble the microdialyzer with the membrane to be tested sandwiched
between the two laminas (see microdialyzer assembly protocol).
3. If using a membrane that is stored in glycerol, Load two 60 ml syringes
with DI water and attach it to the apparatus co-currently. Place the
syringes on syringe pumps and set the syringe pump flowrates to 1
ml/min. Activate the syringe pump and flush out the glycerol in the
membrane with DI water for about 10 minutes. If using a membrane that
is stored dry, this step may be skipped.
4. Fill two 60 ml syringes with the solution that is to be used (CPA solution
for the top stream and pure water for the bottom stream) for the
experiment and attach it to the apparatus, co currently. Set the syringes on
syringe pumps to dispense the solution into the microdialyzer.
5. Select an operating flow rate for the syringe pump feeding solution to the
top stream and a similar flow rate for the syringe pump feeding solution to
the bottom stream.
107
6. Start both syringe pumps simultaneously. Click the ‘Run Task’ button on
the top left corner of the data acquisition program and watch for the
pressure to equilibrate.
7. Once the pressure is steady, adjust the flow rate of the bottom stream so
that the pressure drop for the top and bottom stream is equal.
8. Once the pressure drop difference is mitigated, allow the system to come
to steady state. Steady state is usually achieved after allowing 10 ml of
solution to pass through the microdialyzer.
9. While waiting for the system to come to steady state, prepare the sample
vials. Three samples each from the bottom and top stream will need to be
collected. Prepare 6 sample vials labeled appropriately. Weigh the vials
and note their empty weights on lab notebook.
10. Once steady state is reached, take samples from the top and bottom
stream. A sample collection time of 10 minutes is appropriate for flow
rates of 0.3 ml/min and higher. Slower flow rates need longer collection
time to ensure enough sample was collected. Repeat sampling process
twice to collect 3 pairs of samples total.
11. Once the samples are collected, weigh the vials again. Note the final vial
weights in lab notebook.
12. Repeat experiment for a different flow rate.
108
13. After the experiments are finished, stop the pumps and replace the CPA
syringe with a syringe filled with DI water and flush the system for
another 10 minutes.
14. Disassemble the apparatus and take out the lamina plates from the metal
housing. Discard the used membrane and place the lamina plates in their
storage vials. Rinse the metal housing with DI water and dry with
kimwipes.
109
Appendix F - Protocol for Model Validation Experiment
1. Assemble the microdialyzer with the membrane to be tested
sandwiched between the two laminas (see microdialyzer assembly
protocol).
2. Set up the apparatus, connecting the microdialyzer with the pressure
transducers and the tubing for syringe connection in a counter-current
configuration. Place waste receptacles on the end of the blood and
dialysate outlet tubes.
3. Turn on the power supply to the pressure transducers.
4. If the membrane used is stored in glycerol, load up two 60 mL syringes
with DI water and attach them with tubing to flow into the top and
bottom stream. Place the syringes on a syringe pump and set the
syringe pump on a flow rate of 1 ml/min. Start the syringe pump and
allow 10 ml of DI water to flow through the apparatus to flush the
glycerol from the membrane. Remove the syringes once the flushing
process is complete. If using a dry stored membrane, this step may be
skipped.
5. Load up one 60 mL syringe with CPA solution and another with DI
water. Attach the CPA solution syringe to flow into the top side of the
dialyzer and the DI water syringe to flow into the bottom side of the
dialyzer.
110
6. Select a flow rate on the syringe pump for the top and bottom stream.
7. Turn the computer on and once computer is booted, click on
Measurement & Automation explore. Once the program has loaded,
click on my VI logger task IV.
8. Once the data acquisition program on the computer is ready, activate
the syringe pumps. Once solution is flowing through the microdialyzer,
click on the ‘Run Task’ button on the top left of the computer program
interface.
9. Find the color that corresponds to each transducer on the program and
note it in the lab notebook. Find the corresponding color by gently
tapping each transducer.
10. Once each transducer is identified, select a flow rate and allow the
system to come to steady state before collecting samples. Steady state
should be achieved after allowing approximately 10-15 ml of solution
to pass through the microdialyzer.
11. While waiting for the system to come steady state, prepare the sample
vials. Three samples each from the bottom and top stream will need to
be collected. Prepare 6 sample vials labeled appropriately. Weigh the
vials and note their empty weights in lab notebook.
12. Once steady state is reached, take samples from the top and bottom
stream. A sample collection time of 10 minutes is appropriate for flow
rates of 0.3 ml/min and higher. Slower flow rates need longer
111
collection time to ensure enough sample was collected. Repeat
sampling process twice to collect 3 pairs of samples total from each
stream.
13. Once the samples are collected, weigh the vials again. Note the final
vial weights in lab notebook.
14. Repeat for a new flow rate.
15. After the experiments are finished, stop the pumps and replace the
CPA syringe with a syringe loaded with DI water and flush the system
for about 10 minutes.
16. Disassemble the apparatus and take out the lamina plates from the
metal housing. Discard the used membrane and place the lamina plates
in their storage vials. Rinse the metal housing with DI water and dry
with kimwipes.
112
Pressure (Pa)
Appendix G – Pressure Calibration Curve
109000
108000
107000
106000
105000
104000
103000
102000
101000
100000
P = 2,717,292.33(mV) + 98,344.77
R² = 1.00
0
0.001
0.002
0.003
0.004
Voltage (mV)
Pressure (Pa)
Figure G.1: Pressure calibration curve for transducer 1
109000
108000
107000
106000
105000
104000
103000
102000
101000
100000
P = 2,664,213.92(mV) + 98,790.98
R² = 1.00
0
0.001
0.002
0.003
Voltage (mV)
Figure G.2: Pressure calibration curve for transducer 2
0.004
Pressure (Pa)
113
109000
108000
107000
106000
105000
104000
103000
102000
101000
100000
P = 2,725,631.73(mV) + 99,017.22
R² = 1.00
0
0.001
0.002
0.003
0.004
Voltage (mV)
Figure G.3: Pressure calibration curve for transducer 3
109000
108000
Pressure (Pa)
107000
106000
105000
104000
103000
P= 2,678,197.24(mV)+ 98,780.36
R² = 1.00
102000
101000
100000
0
0.001
0.002
0.003
Voltage (mV)
Figure G.4: Pressure calibration curve for transducer 4
0.004
114
Appendix H – Concentratrion Calibration Curve
Glycerol Concentration (%w/v)
12
10
8
6
4
% w/v = 0.0079(mOsm/kg water) + 0.2011
R² = 0.99
2
0
-5
195
395
595
795
995
Osmolality (mOsm/kg water)
Figure H.1: Concentration Calibration Curve
1195
1395
115
Appendix I – Hydraulic Permeability Experimental Data
I.1 Gambro AN69-ST
Flow rate (ml/min)
Lp (m/Pa-s)
V/t (m3/s) A(P1-P2) (m2-Pa)
1.0
11.2e-11
1.49
7.68e-11
0.8
8.46e-11
1.12
7.57e-11
0.6
6.21e-11
0.84
7.53e-11
0.4
4.93e-11
0.60
8.18e-11
0.2
2.50e-11
0.36
6.18e-11
Table I.1: Experimental data for hydraulic permeability of AN69 to DI water.
Average of 3 sets.
Flow rate (ml/min)
Lp (m/Pa-s)
V/t (m3/s) A(P1-P2) (m2-Pa)
1.0
11.5e-11
1.71
6.72e-11
0.8
10.2e-11
1.40
7.29e-11
0.6
7.86e-11
1.10
7.16e-11
0.4
5.78e-11
0.80
7.36e-11
0.2
3.89e-11
0.49
7.82e-11
Table I.2: Experimental data for hydraulic permeability of AN69 to 10%
w/v glycerol. Average of 3 sets.
Flow rate (ml/min)
Lp (m/Pa-s)
V/t (m3/s) A(P1-P2) (m2-Pa)
1.0
12.3e-11
4.18
2.96e-11
0.8
9.63e-11
3.40
2.86e-11
0.6
7.18e-11
2.73
2.66e-11
0.4
5.06e-11
1.84
2.80e-11
0.2
2.86e-11
1.09
2.64e-11
Table I.3: Experimental data for hydraulic permeability of AN69 to 40%
w/v glycerol. Average of 3 sets.
116
I.2 Millipore ISOPORE HTTP
Flow rate (ml/min)
Lp (m/Pa-s)
V/t (m3/s) A(P1-P2) (m2-Pa)
1.0
6.78e-9
0.50
1.47e-8
0.8
5.04e-9
0.37
1.45e-8
0.6
3.42e-9
0.28
1.35e-8
0.4
2.05e-9
0.17
1.26e-8
0.2
0.73e-9
0.06
1.33e-8
Table I.4: Experimental data for hydraulic permeability of ISOHTTP to DI
water. Average of 3 sets.
Flow rate (ml/min)
Lp (m/Pa-s)
V/t (m3/s) A(P1-P2) (m2-Pa)
1.0
6.13e-9
0.66
1.02e-8
0.8
4.65e-9
0.46
1.02e-8
0.6
3.62e-9
0.36
1.03e-8
0.4
2.26e-9
0.22
1.12e-8
0.2
1.10e-9
0.10
1.03e-8
Table I.5: Experimental data for hydraulic permeability of ISOHTTP to 10%
w/v glycerol. Average of 3 sets.
Flow rate (ml/min)
Lp (m/Pa-s)
V/t (m3/s) A(P1-P2) (m2-Pa)
1.0
6.51e-9
0.92
7.10e-9
0.8
5.24e-9
0.76
6.93e-9
0.6
3.63e-9
0.55
6.58e-9
0.4
2.11e-9
0.36
5.88e-9
0.2
0.72e-9
0.16
4.42e-9
Table I.6: Experimental data for hydraulic permeability of ISOHTTP to 40%
w/v glycerol. Average of 3 sets.
117
I.3Millipore ISOPORE TMTP
Flow rate (ml/min)
Lp (m/Pa-s)
V/t (m3/s) A(P1-P2) (m2-Pa)
1.0
10.0e-9
0.59
1.73e-8
0.8
7.40e-9
0.48
1.55e-8
0.6
5.12e-9
0.40
1.28e-8
0.4
3.31e-9
0.30
1.16e-8
0.2
1.55e-9
0.18
1.04e-8
Table I.7: Experimental data for hydraulic permeability of ISOTMTP to DI
water. Average of 3 sets.
Flow rate (ml/min)
Lp (m/Pa-s)
V/t (m3/s) A(P1-P2) (m2-Pa)
1.0
11.8e-9
0.53
2.32e-8
0.8
9.11e-9
0.43
2.26e-8
0.6
6.78e-9
0.35
2.07e-8
0.4
4.18e-9
0.23
1.88e-8
0.2
1.78e-9
0.13
1.61e-8
Table I.8: Experimental data for hydraulic permeability of ISOTMTP to 10%
w/v glycerol. Average of 3 sets.
Flow rate (ml/min)
Lp (m/Pa-s)
V/t (m3/s) A(P1-P2) (m2-Pa)
1.0
11.5e-9
0.76
1.51e-8
0.8
9.42e-9
0.67
1.41e-8
0.6
7.11e-9
0.51
1.39e-8
0.4
4.54e-9
0.35
1.28e-8
0.2
2.19e-9
0.17
1.29e-8
Table I.9: Experimental data for hydraulic permeability of ISOHTTP to 40%
w/v glycerol. Average of 3 sets.
118
Appendix J- Diffusive Permeability Experimental Data
J.1 Gambro AN69-ST
Flow rate (ml/min)
Ps (m/s)
Standard Error
1.0
6.09e-6
2.09e-7
0.8
5.90e-6
3.10e-7
0.6
5.49e-6
2.68e-7
0.4
4.81e-6
3.21e-7
0.3
4.43e-6
3.66e-7
0.2
4.09e-6
1.01e-7
0.1
3.35e-6
1.14e-7
Table J.1: Experimental data for diffusive permeability of AN69 to 10% w/v
glycerol solution for flow rate range between 0.1 to 1.0 ml/min
J.2 Millipore ISOPORE HTTP
Flow rate (ml/min)
Ps (m/s)
Standard Error
1.0
12.8e-6
2.53-7
0.8
11.3e-6
0.80e-7
0.6
10.1e-6
5.88e-7
0.4
8.37e-6
1.67e-7
0.3
7.54e-6
1.25e-7
0.2
6.46e-6
1.60e-7
0.1
5.31e-6
6.27e-7
Table J.2: Experimental data for diffusive permeability of ISOHTTP to 10%
w/v glycerol solution for flow rate range between 0.1 to 1.0 ml/min
119
J.3 Millipore ISOPORE TMTP
Flow rate (ml/min)
Ps (m/s)
Standard Error
1.0
19.7e-6
1.42e-6
0.8
15.6e-6
1.53e-6
0.6
12.1e-6
0.40e-6
0.4
10.8e-6
1.22e-6
0.3
7.46e-6
1.27e-6
0.2
6.26e-6
1.45e-6
0.1
2.67e-6
0.14e-6
Table J.3: Experimental data for diffusive permeability of ISOTMTP to 10%
w/v glycerol solution for flow rate range between 0.1 to 1.0 ml/min
120
Appendix K- Model Validation Experimental Data
K.1 Gambro AN69-ST
Flow rate (ml/min)
Fractional Removal (%)
Standard Error
1.0
9.60
1.71e-3
0.8
10.83
2.85e-3
0.6
12.43
2.90e-3
0.4
14.67
4.10e-3
0.2
24.67
7.93e-3
Table K.1: Experimental data for model validation experiment using AN69
K.2 Millipore ISOPORE HTTP
Flow rate (ml/min)
Fractional Removal (%)
Standard Error
1.0
26.94
4.88e-3
0.8
31.92
4.03e-3
0.6
37.18
8.53e-3
0.4
42.61
1.11e-3
0.2
46.89
1.71e-3
Table K.2: Experimental data for model validation experiment using ISOHTTP
K.3 Millipore ISOPORE TMTP
Flow rate (ml/min)
Fractional Removal (%)
Standard Error
1.0
56.82
1.89e-2
0.8
64.64
1.99e-2
0.6
71.44
1.97e-2
0.4
76.14
3.19e-2
0.2
90.16
3.70e-2
Table K.3: Experimental data for model validation experiment using ISOTMTP
121
Appendix L – Simulation Data
L.1 Gambro AN69-ST
Flow rate (ml/min)
Fractional Removal (%)
Error
1.0
10.08
1.72e-19
0.8
11.28
4.96e-19
0.6
13.21
2.57e-19
0.4
16.83
3.47e-19
0.2
26.09
3.75e-19
Table L.1: Simulation data for model validation experiment using AN69 and
Ps and Lp obtained from experiment.
L.2 Millipore ISOPORE HTTP
Flow rate (ml/min)
Fractional Removal (%)
Error
1.0
25.92
5.21e-19
0.8
27.17
7.44e-19
0.6
29.20
1.19e-19
0.4
33.05
5.34e-19
0.2
42.68
6.03e-19
Table L.2: Simulation data for model validation experiment using ISOHTTP
and Ps and Lp obtained from experiment (Lp = 1.03e-8 m/Pa-s)
Flow rate (ml/min)
Fractional Removal (%)
Error
1.0
31.14
7.48e-19
0.8
32.22
2.47e-17
0.6
34.04
3.33e-19
0.4
37.51
1.89e-18
0.2
46.56
6.21e-19
Table L.3: Simulation data for model validation experiment using ISOHTTP
and Lp value from theoretical projection (Lp = 1.70e-8 m/Pa-s)
122
L.3 Millipore ISOPORE TMTP
Flow rate (ml/min)
Fractional Removal (%)
Error
1.0
39.11
2.63e-18
0.8
39.55
1.05e-18
0.6
40.27
1.77e-18
0.4
41.69
1.62e-18
0.2
45.67
1.56e-18
Table L.4: Simulation data for model validation experiment using ISOTMTP
and Ps and Lp obtained from experiment (Lp = 2.03e-8 m/Pa-s)
Flow rate (ml/min)
Fractional Removal (%)
Error
1.0
49.20
4.84e-18
0.8
49.55
2.53e-18
0.6
50.13
9.33e-19
0.4
52.40
7.21e-19
0.2
53.80
1.08e-18
Table L.5: Simulation data for model validation experiment using ISOTMTP
and Lp value from theoretical projection (Lp = 3.74e-8 m/Pa-s)
L.4 Parametric Studies
Extracellular
Cell Stream
Solution Stream
Error
Removal (%)
Removal (%)
1.0
16.48
2.71
2.49e-18
0.8
18.39
3.08
4.60e-19
0.6
21.46
3.73
2.57e-19
0.4
27.14
4.95
5.71e-18
0.2
41.17
8.41
2.35e-19
Table L.6: Simulation data for parametric study varying flow rate using AN69
Flow rate
(ml/min)
and permeability parameters from experiment.
123
Extracellular
Cell Stream
Solution Stream
Error
Removal (%)
Removal (%)
1.0
42.23
5.86
2.52e-19
0.8
44.16
6.43
3.06e-19
0.6
47.26
7.31
1.50e-18
0.4
53.00
8.95
2.70e-19
0.2
66.61
13.40
5.79e-19
Table L.7: Simulation data for parametric study varying flow rate using
Flow rate
(ml/min)
ISOHTTP and permeability parameters from experiment.
Extracellular
Cell Stream
Solution Stream
Error
Removal (%)
Removal (%)
50
24.74
4.45
1.62e-18
56
27.14
4.95
5.71e-19
70
32.38
6.09
2.78e-19
90
39.07
7.66
3.58e-18
110
44.96
9.16
8.80e-19
130
50.20
10.60
1.86e-18
150
54.86
12.02
1.96e-19
170
59.05
13.38
2.61e-19
Table L.8: Simulation data for parametric study varying channel length using
Microchannel
Length (mm)
AN69, permeability parameters from experiment and a flow rate of 0.4
ml/min
Extracellular
Cell Stream
Solution Stream
Error
Removal (%)
Removal (%)
50
47.59
7.85
9.05e-19
56
53.00
8.95
2.70e-19
70
65.20
11.74
2.56e-18
90
81.06
16.20
9.54e-19
110
94.12
21.41
1.91e-18
Table L.9: Simulation data for parametric study varying channel length using
Microchannel
Length (mm)
ISOHTTP, permeability parameters from experiment and a flow rate of 0.4
ml/min.
124
Distance
Cell Stream
Extracellular Solution
Relative Cell
from Inlet
Concentration
Stream Concentration (M)
Volume
(mm)
(M)
0.0
1.09
1.09
1.00
16.7
1.03
1.04
1.03
38.0
0.96
0.99
1.07
61.1
0.88
0.93
1.12
86.8
0.79
0.86
1.18
110.0
0.71
0.80
1.24
Table L.10: Simulation data for extracellular solution concentration and
relative cell volume change as a function of microchannel length for AN69
Distance
Cell Stream
Extracellular Solution
Relative Cell
from Inlet
Concentration
Stream Concentration (M)
Volume
(mm)
(M)
0.0
1.09
1.09
1.00
25.7
1.03
1.04
1.03
45.3
0.90
0.95
1.10
62.7
0.72
0.81
1.23
83.4
0.46
0.62
1.49
110.0
0.20
0.43
1.97
Table L.11: Simulation data for extracellular solution concentration and
relative cell volume change as a function of microchannel length for ISOHTTP
125
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