Final Project BE 309 Fall 1997
Intrinsic Viscosity of Horse RBC Suspensions
Group M6
Jennifer Russert
Derek Wong
Elizabeth Khaykin
Emily Rothman
Abstract
Intrinsic viscosity is a measure of the interaction of a colloidal particle with the
suspending solvent, where there are no interactions between those particles. The main
objective of this experiment is to determine the intrinsic viscosity of horse red blood cells
(RBCs) in phosphate buffered saline (PBS). This is done by calibrating low
concentrations and the testing them with a capillary viscometer at constant temperature of
30 C. The intrinsic viscosity of the red blood cells was found to be 0.0033  0.0024
mPa sec. This experiment outlines the development of the procedures and protocols for
measuring the intrinsic viscosity of horse RBCs and identifies the background literature
needed for future use as a standard lab experiment.
Background
Blood: a Colloidal Solution
Blood is made up of a suspension of particles in a solution of proteins and electrolytes
called plasma. It is a living tissue, which consists of many types of cells. In this
experiment we will be concerned primarily with the physical properties of blood, namely
its flow behavior.
Erythrocytes, leukocytes, and platelets are the main constituents of blood. The
erythrocytes or red blood cells (RBCs) are more than a thousand times more numerous
than the leukocytes or white blood cells (WBCs) and much larger than platelets. For this
reason the flow properties of blood mainly involve the RBCs. The concentration of RBCs
is expressed as the hematocrit, or the percent of RBCs in a sample of blood by volume.
Normally an adult human has a hematocrit of 40-45%. Less than that is considered
anemia, while more is polycythmia. The normal hematocrit of horses as suggested by
literature is around 37% (7).
Rheology is the branch of chemistry and material science that deals with the flow
properties of materials. Hemodynamics studies how blood flows in the body and how the
hemorheological properties influence flow rates, pressures, etc. The cardiovascular
system consists of a complex network of branched vessels, which form a closed loop.
Blood relies on its various properties to allow it to pass through tiny capillary
passageways and provide all the functions critical to life (8).
Rheological Properties
There are several interrelated factors that regulate the rheological properties of blood.
These include the extent of cellular aggregation, the deformability of RBC’s, the
composition of plasma, and even the concentration of RBC’s (hematocrit). It is this last
factor, hematocrit, that is tested to find the viscosity of red blood cells.
It has been found that many diseases involve changes in various rheological components.
For instance, it has been found that patients with myocardial infarction and arterial
thrombosis have blood viscosities at low rates of shear, which are elevated above normal
values. Patients with anemia or low hematocrit display a lowered value of blood
viscosity. On the opposite end, patients with polycythmia or high hematocrit display
higher values for viscosity.
Intrinsic viscosity is a property that polymer scientists are often concerned with. It can be
an indication of the size and shape of an isolated polymer molecule in a solvent so dilute
that there are no interactions between this molecule and any others other than those of the
solvent (3).
A normal red blood cell is round and moves through the smallest blood vessels quite
easily. But in people who have sickle-cell anemia, the blood cells break down. They lose
their round shape and take the form of a sickle-a farmer's implement. These sickled blood
cells get stuck in the small veins of the body, blocking other red blood cells from passing.
When the flow of blood to a part of the body is reduced, the oxygen supply to that part of
the body is cut off and cells begin to die.
Determination of Blood Viscosity
The intrinsic viscosity of RBC’s is a measure of the interaction of colloidal particles such
as RBC’s with the suspending solvent. When these are the dominant reactions, particleparticle interactions (e.g. those involving WBC’s or platelets) are negligible. To
determine intrinsic viscosity one must first measure the viscosity of RBC suspensions in
very dilute systems. Then one extrapolates a suitable function to infinite dilution. The
resulting value of intrinsic viscosity is theoretically related to properties of the particles in
the particular medium, which in this experiment is PBS.
Since the solutions are dilute, the measured viscosity will be only slightly greater than
that of the medium itself, so that very precise methods must be used to determine the
viscosity, and great attention must be paid to procedure, temperature control, etc. For our
lab the method of choice is the glass capillary viscometer, a very simple system but one
requiring careful lab procedures to obtain accurate results.
In order to find the viscosity of the RBC/PBS solutions, the viscosity of PBS alone has to
be determined. Using water as a standard, the viscosity of the PBS is found from the
ratio (2):
 PBS
d t
 PBS PBS
Equation-1
 water d water t water
where d represents the density,  the viscosity and t the time for the liquid to flow
through the viscometer from the top line of the capillary tube to the lower line. The
viscosity of the RBC/PBS samples is found in the same fashion (using water as a
standard). Armed with these viscosity values, specific viscosity, SP, for each sample of
RBC/PBS solution can be calculated using the following equation (2):
 sp 
 solution   solvent
 r  1
 solvent
Equation-2
where r is the ratio of the viscosity of the solution to that of solvent, solution/solvent. The
specific viscosity is the relative contribution of RBC to the viscosity of the solution.
When specific viscosity is divided by concentration, i.e. (sp/c), the resulting quantity
increases with concentration. This relationship is approximately linear, represented by
equation-3 (2):
 sp
c
 bc  [ ]
Equation-3
where b is a constant, or the slope. By plotting the quantity (sp/c) vs. the concentration
of the RBC in PBS the intrinsic viscosity [] can be extrapolated from the y-intercept of
the graph which is represented by equation-4 (2):
 sp
[ ]  lim (
c 0
c
)
Literature values for the intrinsic viscosity of human and horse blood can only be related
to the known value that can be found. This known value is the viscosity of water, to
which all horse red blood cell concentrations relate. The viscosity of water at 30 degrees
Celsius is 0.807mPAs (4).
Methods and Procedures
The procedures of this experiment can be split up into three sections: washing of the
RBCs and making of PBS solution, blood concentration and concentration calibration,
and viscosity measurements
Step one was to wash the red blood cells from the horse donor in order to separate them
from the blood plasma and achieve as close to a 100% concentration of the RBCs as
possible, also known as a 100% hematocrit. This was done by adding PBS buffer
solution to the horse blood then placing the blood in the centrifuge at a speed of 2500
RPM for 10 minutes. The plasma was then suctioned off from the surface of the blood.
This procedure was repeated 4 times, each time bringing the concentration closer to
100%. It was then done again at the beginning of each experimental period in case any
blood cells had died during the past week. The PBS solution that was used to wash the
cells and later to dilute to varying hematocrits was made using the chemicals in the
indicated amounts from Table 1 (1). The solution was mixed in a volumetric flask with
an error value of 0.60 mL.
PBS (Phosphate Buffered Saline)
Na2HPO4 (anhydrous)
2.30 g/L
NaH2PO4 (anhydrous)
0.46 g/L
NaCl
8.76 g/L
Table 1
The horse blood was then ready to be diluted into concentrations, which ranged from
0.25 - 3.0 %.
40 ml of each concentration was made using a 100-1000l micropipette and a graduated
cylinder. An amount of blood, amounts are specified in Table 2 for concentration range,
was pipetted into a 50mL graduated cylinder. In order to clean all traces of blood from
the micropipette tip, it was rinsed with PBS solution, which was then in turn added to the
graduated cylinder as well, filling it to 40mL. The concentrations that were created in
this manner are as follows
% Concentration
Vol. Blood (mL)
0.25
1.0
1.5
2.0
2.5
3.0
0.100
0.400
0.600
0.800
1.000
1.200
Vol. PBS and
Blood (mL)
40
40
40
40
40
40
Table 2
Though the concentrations were made with as much care as possible, it was necessary to
determine the exact concentrations the solutions turned out to be through a concentration
calibration. To do this a Spectrophotometer was used to measure the absorbance of the
concentration range. The absorbance was then related through regression to the exact
concentration value for each solution.
The trouble that arises with doing this is that the spectrophotometer is not able to read the
absorbance of a blood solution that is concentrated to the point were light is not allowed
to pass through it. This happens even at the low concentrations of 5%, 4%, or even at
2.5%. The method was still used, and it was found that a concentration of about 0.21%
hematocrit was the most concentrated sample that gave an absorbance value directly,
without dilution. The other solutions had to be diluted by a specified factor (shown later),
then placed into the spectrophotometer.
Several tubes of stock blood samples were given to us initially. These samples contained
all components of the blood: red blood cells, plasma, etc. The stock blood samples were
washed with PBS and centrifuged in order to remove the plasma component of the blood
(the supernatant) as much as possible, isolating red blood cells for our experiment.
However, there was still a small amount of plasma and other constituents present in the
isolated red-blood cells, therefore, the actual hematocrit of the read blood cells had to be
measured. A small amount of the red blood cells were placed in a capillary, and then
using microcapillary centrifuge the PBS was separated from the RBCs. After this
centrifugation step, the capillary was placed in the hematocrit reader, and the hematocrit
of the stock red blood cell sample was found to be 85.5%.
Hematocrit cannot be accurately measured with a hematocrit reader for the small
concentrations in our experimental range. Therefore, in order to accurately measure the
hematocrit of our samples during our experiment, a spectrophotometer and a calibration
curve of absorbance vs. hematocrit were used. The first concentration was made by
taking 7.5 L of the stock red blood cell (85.5%) and adding PBS to make 3000 L of
red blood cell solution. The hematocrit of this solution was 7.5 L / 3000 L x 85.5% =
0.21375%. The absorbance reading of this solution was recorded at 577 nm  1 nm, one
of the absorption peaks of oxygenated blood (BE 209 Final project -Absorbance of
Hemoglobin). This solution was then diluted serially, at half the original concentration
each time, and the absorbance reading for each concentration was recorded as listed:
Hematocrit (%)
Absorbance Reading
0.21
1.700
0.11
1.040
0.053
0.564
0.027
0.301
0.013
0.160
0.0067
0.072
Table 3
A second trial was done with another stock blood in the same fashion, and the calibration
is as follows:
Hematocrit (%)
0.14
0.068
0.034
0.017
0.0085
0.0042
Absorbance Reading
1.350
0.774
0.410
0.205
0.099
0.049
Table 4
Linear regression was applied to these two trials to obtain a calibration curve.
Graph 1
The slope and the intercept of the calibration curve were found to be 8.418  0.404 and
0.0726  0.0327 respectively. Knowing these values, hematocrit of the samples tested in
the experiment could be found by measuring the absorbance of the samples.
However, the concentrations of our samples ranged from approximately 0.25% to 3%
while the spectrophotometer was useful only up to 0.25% hematocrit. Therefore, our
samples had to be diluted as well. To increase accuracy, each sample of was diluted at
two different factors and the corresponding absorbance readings were taken. The results
are as follows:
Viscosity measure is the final procedure, which is carried out with a capillary viscometer.
The capillary viscometer was contained in a water bath to keep it at a constant
temperature of 30 degrees Celsius using a Haake D1 immersion heater/circulator. A
thermometer was also clamped to the water bath so that the constant temperature could be
further monitored. The heater/circulator was allowed to run at least 10 minutes before any
experiments were done.
Water and PBS were first tested, followed by samples of horse blood diluted to the various
concentrations with PBS. The lowest concentration was measured first. The sample was
dropped down the larger hole of the capillary viscometer (see Picture 1: tube G) and then
sucked through the other end with an auto-pipette. It was clamped to the water bath and
timed to see just how long the meniscus of the solution would take to fall from point C on
the tube to point E (Picture 1). This was repeated three times for every concentration with
different samples of blood. Then the viscometer was rinsed twice with the next higher
concentration and similar trials were performed.
Picture 1
The water bath not only kept the temperature of the sample constant as it was running
through the viscometer, but all of the samples were stored in the same water bath. This kept
them at the desired 30 degrees Celsius. Also, the samples were clamped within the water
bath making sure nothing bumped into the viscometer disturbing the sample while it was
being tested.
Equation 1, the viscosity ratio with respect to water requires the density of water, PBS,
and all tested con concentrations of blood to be known. The density of water at 30
degrees Celsius is known to be 0.99567 g/mL (4) and the PBS density at 30 degrees
Celsius was found to be 0.9974g/mL. This PBS density was found by tarring the weight
a dry 50mL volumetric flask on a scale reading to the thousandths, filling it with 30
degree PBS to exactly 50mL then weighing once more. The weight (49.873g) was
divided by the volume (50mL) and a density of 0.99746 g/mL was found. The density
for the blood concentrations were placed through the same procedure and were all found
to be the same, equal to the density of PBS, 0.99746g/mL.
Results
For the concentration calibration Graph 1 developed from the relation of the series
dilutions to their recorded absorbance. The equation of the regression line gives a
relationship between the absorbance and the percent hematocrit, which can be
extrapolated to determine the exact concentrations.
Graph 1
Table 5 gives the two dilutions of each sample, the absorbance read from the
spectrophotometer, the hematocrits found using the equation of the regression line from
Graph 1 described previously, and the average of the two dilution hematocrits. In most
cases the actual hematocrit is notably less than the targeted solution concentration, this
will be explained in the discussion.
Target
Dilution
Absorbance
Hematocrit %
Average %
Sample %
Factor
0.143235
0.25 Dilution I
0.5
0.698
0.148552
Dilution II
0.25
0.363
0.137919
0.647276
1 Dilution I
0.1
0.648
0.683363
Dilution II
0.05
0.330
0.611189
1.058901
1.5 Dilution I
0.1
0.985
1.083702
Dilution II
0.05
0.508
1.0341
1.329159
2 Dilution I
0.1
1.16
1.291593
Dilution II
0.05
0.648
1.366725
1.67604
2.5 Dilution I
0.1
1.44
1.624219
Dilution II
0.05
0.800
1.727862
2.395781
3.0 Dilution I
0.05
1.055
2.333716
Dilution II
0.025
0.590
2.457846
Table 5
With known concentrations, viscosity measurements commenced with greater
confidence. First three trails of water and three trails of the PBS solution were tested in
the viscometer/water bath apparatus. Table 6 represents the time recorded for three trials
and the average, using the method described previously for water and PBS.
H20 (seconds)
PBS(seconds)
200.45
208.9
202.25
208.44
203.22
209.88
201.9733
209.0733
Table 6
Further Samples were then put to the test, again receiving three trails each, and Table 7
outlines the results from this experimentation.
Trial
1
2
3
avg
plasma
321.44
325.59
328.72
325.25
0.0025
216.44
216.35
216.22
216.3367
0.01
0.015
217.54
218.91
217.56
220.16
217.53
219.08
217.5433 219.3833
Table 7
0.02
221.76
221.08
222.42
221.7533
0.025
225.78
223.53
224.56
224.6233
0.03
228.01
229.54
227.51
228.3533
The viscosity can now be assessed with the known average concentration run times from
Table 8. As mentioned in the procedure density is also found for water, PBS and all
blood concentrations
Solution
Water
PBS
concentrations
Density(g/ml)
0.99567
0.99746
0.99746
Table 8
Using Equations 1 through 4, the viscosity, the specific viscosity, and the specific
viscosity divided by the exact concentration were calculated. Table 9 illustrates these
values alongside the values of exact concentration and targeted concentration.
Target
Exact
Concentration
Concentration
0.25
0.143235
1
0.647276
1.5
1.058901
2
1.329159
2.5
1.67604
3
2.395781
Viscosity
1.062036
1.067959
1.076992
1.088627
1.102716
1.121028
Table 9
Specific Viscosity Specific Viscosity/Exact
Concentration
0.000392
0.002737
0.005972
0.009226
0.014481
0.013675
0.02544
0.01914
0.038712
0.023097
0.05596
0.023358
Specific viscosity divided by the exact concentration was then plotted against the exact
concentration, Graph 2, this graph yield an intercept equal to the intrinsic viscosity of
horse red blood cells.
Specific Viscosity vs. Concentration
y = 0.0099x + 0.0033
Specific_Viscosity
/Concentration
0.03
0.025
0.02
0.015
0.01
0.005
0
0
0.5
1
1.5
2
2.5
3
Concentration (%hem atocrit)
Graph 2
As shown in the equation displayed on the graph, the y intercept, which is representative
of the intrinsic viscosity, equals 0.0033 mPa sec.
Discussion
For Table 5 it is apparent that concentrations calculated from the absorbance readings
found from the linear regression in Graph 1 show a definite trend of being below the
targeted concentration. In fact they are on average 67% of the targeted concentration.
This occurred because the actual stock of red blood cells after being centrifuged and
cleaned with PBS did in fact still contain some PBS. This is evident since a hematocrit
reading of the cleaned stock RBC’s in PBS was 85.5 0.5%, not a 100% concentration as
the targeted concentrations would assume. Also, even micropipetting of this RBC
solutions can at best still be far from accurate because the error of the device does not
take into account the tendency of the RBC’s to stick to the inside surface of the plastic
pipette tip. This explains the need for a more accurate way to measure the exact
concentrations being tested for viscosity. The spectrophotometer provided this service.
When analyzing the difference between the exact concentrations and the targeted, there
appears to be a relationship between the exact concentration and the amount it differs
from the target value. The trend is that the lower concentrations seem to be more off then
the higher ones.
% off from target concentration
Realtionship with increased concentration
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
Exact Concentration (% hematocrit)
Graph 3
Graph 3 shows this trend. Although the relationship is not drastic, it does exist. For
small concentrations it is more difficult to make a precise mixture of the components.
When pipetting, the red blood cells tend to stick to the inside surface of the plastic
micropipette tip. This effect is not so evident when a greater volume of RBCs are
pippeted as for the higher concentrations. The great error involved in making these
concentrations this way is the reason the spectrophotometer was used. We are dealing
with very small concentrations, whose accuracy is essential to find intrinsic viscosity. A
hematocrit reader was used for finding the concentration of the 85.5% hematocrit horse
blood since the devise is within error for higher concentrations.
With known concentrations viscosity measurements could continue with greater
confidence. The viscometer was first filled with water for two reasons: first to obtain the
time value for the viscometer needed in Equation 1, and also to reassure that the
viscometer was yielding accurate values, since the time it should take for water to run
through the viscometer is known. The viscosity of water is 0.807mPAs from literature
(4). Which can be translated to the time of water to make a viscometer run by dividing
by the viscometer constant given in the (Instuctions for the use of The Cannon-Fenske
Routine Viscometer). For a 50mL viscometer the constant is 0.004 mPa dividing, the
time expected becomes 201.75 seconds. In Table 6 it is evident that the average time
recorded for water is very close to this literate value, only a difference of 0.22 seconds.
The time for the PBS to run through the viscometer is longer than that for water, seen in
Table 6. This makes sense since water is slightly less viscous then PBS. For the
hematocrit range it could then be rationalized that it will gradually take longer time for
the hematocrits to run through the viscometer as the % hematocrit increases. This
rational appears in the data of Table 7 as the time increases as the % hematocrit
increases. Viscosity is the property at work here, where the time is directly related to the
viscosity, once again refer to Equation 1, and as observed time is directly related to the
concentration.
Equation 1 also depends on the density. The density of water is known, and the density
of PBS was found as outlined in the procedures. The density of the blood solutions came
out to be equal to that of PBS. At first this could be thought of as incorrect, that the
RBC’s should have some effect on the density of the PBS in which they are contained. It
was found that at such low concentrations and low presence of RBC’s no appreciable
change is seen in the density of the concentrations. In fact, the density of the
concentrations is essentially equal to that of PBS.
Table 9 shows that the viscosity is increasing with the concentrations of the horse blood.
As can be seen in the table, at the lowest concentration 0.143% hematocrit the viscosity is
calculated to be 1.06mPas as compared to the viscosity at 2.39% hematocrit which is
1.12mPa sec. Also, the specific viscosity over concentration increases linearly with
concentration (Graph 2) as predicted by Castellan in Equation-3. The y-intercept of this
line is the final value obtained for intrinsic viscosity, 0.0033 Mpa sec.
Error Analysis:
During the initial calibration process, the hematocrit of stock red blood cells was
measured with a hematocrit reader, which has a  0.5% HC error. To make small
concentration suspensions from the stock RBC’s for the absorbance calibration, a
micropipette was used. The micropipette provides an error of  0.2%. Since the
concentration was calculated by dividing the volume of RBC pipetted, over the total
volume of RBC/PBS and multiplied by the hematocrit of the stock RBC, using
differential methods, the following equation is obtained for the error in the
concentrations:
c 
VRBC
V  stock _ HC VRBC  stock _ HC
 stock _ HC  RBC

 Vwater
2
Vwater
Vwater
Vwater
Then, these concentrations of RBC’s were measured for their absorbance, which has an
estimated error of  0.002. Upon obtaining these data, a plot of absorbance vs.
hematocrit was made. A linear regression was used to obtain the slope and the yintercept and their uncertainty values. These values allowed us to calculate the error
associated with the concentration of our samples, using differential methods.
Errors associated with the actual samples tested for viscosity were calculated in a similar
fashion. First, an absorbance was taken which carried  0.002 error. Using the linear
regression equation of the calibration and setting concentration in terms of absorbance,
the error of the concentration was calculated differentially.
Another major source of error came from the efflux time measurements. Since the
meniscus of our samples moved relatively quickly through the two indices, an uncertainty
of 0.25 sec was estimated. From this, the uncertainty of the viscosity, relative to PBS,
of the individual sample was calculated. Note that the density of the solutions remained
very constant at all concentrations, and therefore, these error values were omitted in our
calculations. The error in viscosity, in turn, allowed us to calculate the error of specific
viscosity, as well as the quantity, specific viscosity over concentration. In the plot of this
quantity against concentration, a linear regression was employed to find the y-intercept,
which was also the intrinsic viscosity of RBC’s. The uncertainty in the intrinsic viscosity
was found, also using differential methods, to be 0.00236 Mpa sec. Thus, the final
value of intrinsic viscosity of horse red blood cells was found to be 0.00329 0.00236
Mpa sec.
References
1. BE 309 Fall 1997 Laboratory Manual.
2. Castellan, Gilbert W., Physical Chemistry. The Benjamin/Cummings Publishing
Company, Inc, 1983.
3. Craver, Kenneth, Applied Polymer Science. Organic Coatings and Plastics Chemistry,
Inc, 1975.
4. CRC Handbook of Chemistry and Physics, 63rd Edition
5. Dintenfass, Leopold, “Considerations of the Internal Viscosity of red cells and its
effect on the Viscosity of Whole Blood” Angiology v13, Number 8; Angiological
Reserch Foundation, Inc.,1962.
6. Gabelnick, H.L. Ph.D., Litt, M D.Eng.Sc. Rheology of Biological Systems.Charles C
Thomas Publisher; Springfield, Illinois: 1973.
7. Geor, Raymond, The Horse: Diseases and Clinical Management. W.B. Sanders,
Philadelphia:1995.
8. Milnor, William. Hemodynamics. Williams &Wilkins; Baltimore, Maryland: 1989.
Appendix
The following is an example of an intrinsic viscosity lab based on our experimentation to
be used in BE 309. The horse red blood cell is once again the focus, yet it is possible to
use a polymer, such as a protein (actin, myosin, or amino acid). The concentration
calibration using the spectrophotometer is eliminated due to time constraints.
Experiment No. 
Intrinsic Viscosity of Red Blood Cells
Objectives
A. Experimental Goals
1. The main objective of the project is to determine the intrinsic viscosity of horse red
blood cells (RBC) in phosphate buffered saline (PBS).
B. Educational Goals
1. To become familiar with the effects of shape of cells on viscosity.
2. To become familiar with the composition and rheological properties of blood, the
mechanisms for such behavior, and their relevance to mammalian physiology and
pathology.
3. To become familiar with the transport property of red blood cells using the capillary
viscometer.
Background
A. Biomedical Relevance and Importance
Blood: a Colloidal Solution
Blood is made up of a suspension of particles in a solution of proteins and electrolytes
called plasma. It is a living tissue, since it consists of many types of cells. In this
experiment we will be concerned primarily with the physical properties of blood, namely
its flow behavior.
Erythrocytes, leukocytes, and platelets are the main constituents of blood. The
erythrocytes or red blood cells (RBCs) are more than a thousand times more numerous
than the leukocytes or white blood cells (WBCs) and much larger than platelets. For this
reason the flow properties of blood mainly involve the RBCs. The concentration of RBCs
is expressed as the hematocrit or the percent of RBCs in a sample of blood by volume.
Normally a adult human has an hematocrit of 40-45%; less than that is considered
anemia, while more is polycythmia. The normal hematocrit of horses as suggested by
literature is around 37% (7).
Rheology is the branch of chemistry and material science that deals with the flow
properties of materials.
Hemodynamics studies how blood flows in the body and how the hemorheological
properties influence flow rates, pressures, etc. The cardiovascular system consists of a
complex network of branched vessels, which form a closed loop. Blood relies on its
various properties to allow it to pass through tiny capillary passageways and provide all
the functions critical to life. (3)
Rheological Properties
There are several interrelated factors that regulate the rheological properties of blood.
These include the extent of cellular aggregation, the deformability of RBC’s, the
composition of plasma, and even the concentration of RBC’s (hematocrit). It is this last
factor that is, hematocrit that is tested to find the viscosity of red blood cells.
It has been found that many diseases involve changes in various rheological components.
For instance, it has been found that patients with myocardial infarction and arterial
thrombosis have blood viscosities at low rates of shear, which are elevated above normal
values. Patients with anemia or low hematocrit display a lowered value of blood
viscosity. On the opposite end, patients with polycythmia or high hematocrit display
higher values for viscosity.
Intrinsic viscosity is a property that polymer scientists are often concerned with. It can be
an indication of the size and shape of an isolated polymer molecule in a solvent so dilute
that there are no interactions between this molecule and any others other than those of the
solvent.
A normal red blood cell is round and moves through the smallest blood vessels quite
easily. But in people who have sickle-cell anemia, the blood cells break down. They lose
their round shape and take the form of a sickle-a farmer's implement. These sickled blood
cells get stuck in the small veins of the body, blocking other red blood cells from passing.
When the flow of blood to a part of the body is reduced, the oxygen supply to that part of
the body is cut off and cells begin to die.
B. Scientific Background
Determination of Blood Viscosity
The intrinsic viscosity of RBC’s is a measure of the interaction of colloidal particles such
as RBC’s with the suspending solvent. When these are the dominant reactions, particleparticle interactions (e.g. those involving WBC’s or platelets) are negligible. To
determine intrinsic viscosity one must first measure the viscosity of RBC suspensions in
very dilute systems. Then one extrapolates a suitable function to infinite dilution. The
resulting value of intrinsic viscosity is theoretically related to properties of the particles in
the particular medium, which in this experiment is PBS.
Since the solutions are dilute, the measured viscosity will be only slightly greater than
that of the medium itself, so that very precise methods must be used to determine the
viscosity, and great attention must be paid to procedure, temperature control, etc. For our
lab the method of choice in the glass capillary viscometer, a very simple system but one
requiring careful lab procedures to obtain accurate results.
In order to find the viscosity of the RBC/PBS solutions, the viscosity of PBS alone has to
be determined. Using water as a standard, the viscosity of the PBS is found from the
ratio (2):
 PBS
d t
 PBS PBS
 water d water t water
Equation-1
where d represents the density,  the viscosity and t the time for the liquid to flow
through the viscometer from the top line of the capillary tube to the lower line. The
viscosity of the RBC/PBS samples is found in the same fashion (using water as a
standard). Armed with these viscosity values, specific viscosity, SP, for each sample of
RBC/PBS solution can be calculated using the following equation (2):
 sp 
 solution   solvent
 r  1
 solvent
Equation-2
where r is the ratio of the viscosity of the solution to that of solvent, solution/solvent. The
specific viscosity is the relative contribution of RBC to the viscosity of the solution.
When specific viscosity is divided by concentration, i.e. (sp/c), the resulting quantity
increases with concentration. This relationship is approximately linear, represented by
equation-3 (2):
 sp
c
 bc  [ ]
Equation-3
where b is a constant, or the slope. By plotting the quantity (sp/c) vs. the concentration
of the RBC in PBS the intrinsic viscosity [] can be extrapolated from the y-intercept of
the graph which is represented by equation-4 (2):
 sp
[ ]  lim (
c 0
c
)
Required Prelaboratory Work
A. Group work- must be completed prior to start of experiment
1. For a general discussion of blood viscosity, you are referred to sections 3.1 and 3.4 in
the book Biomechanics: Mechanical Properties of Living Tissues by Y.C. Fung.
2. Read Castellan chapter 30.12 and 30.13 for a discussion of capillary viscometry.
3. Read the manual and background for the glass capillary viscometer included in the
Appendix and become familiar with the procedures for setting up the viscometer. Note
the viscometer constant as well.
4. Look up the values for the viscosity and density of water and PBS as a function of
temperature.
5. For each of the blood suspensions described in the procedure section, calculate the
necessary volumes of cells and PBS needed to make the dilutions.
B. Individual Work-must be submitted by 11 AM of day of assigned lab
Take prelab quiz as assigned.
Apparatus, Equipment, and Reagents
1. Haake waterbath and immersion heater/circulator (set at 30°C)
2. Glass Capillary Viscometer
3. Stop watch
4. Horse blood
5. Phosphate Buffered Saline
Specific Procedures
A. Preparation of Blood Samples and Suspensions
The procedures of this experiment can be split up into three sections: washing of the
RBCs and making of PBS solution, blood concentration and concentration calibration,
and viscosity measurements
Step one is to wash the red blood cells from the horse donor in order to separate them
from the blood plasma and achieve as close to a 100% concentration of the RBCs as
possible, also known as a 100% hematocrit. This is done by adding PBS buffer solution
to the horse blood then placing the blood in the centrifuge at a speed of 2500 RPM for 10
minutes.
This procedure should be repeated 3 or 4 times, each time bringing the concentration
closer to 100%. If it is not provided by the lab instructor, the PBS solution that is used to
wash the cells and later to dilute to varying hematocrits should be made using the
chemicals in the indicated amounts from Table 1 (1).
PBS (Phosphate Buffered Saline)
Na2HPO4 (anhydrous)
2.30 g/L
NaH2PO4 (anhydrous)
0.46 g/L
NaCl
8.76 g/L
Table 1
The horse blood will then be ready to be diluted into concentrations, which should fall
within the range of approximately 0.25 - 5.0 %.
Hematocrit cannot be accurately measured with a hematocrit reader (such as was used in
the shear-rate dependent viscosity lab where greater concentrations are used) for the
small concentrations in our experimental range. Therefore, in order to accurately
measure the hematocrit of your samples, a spectrophotometer and a calibration curve of
absorbance vs. hematocrit should be used for optimal precision. However, time will not
permit the spectrophotometer experiment and calibration, so you must be extremely
careful to be exact in making your dilutions.
C. Viscosity Measurements
Viscosity measurements are carried out with a capillary viscometer. The capillary
viscometer should be clamped to a water bath, to keep at a constant temperature of 30
degrees Celsius using a Haake D1 immersion heater/circulator. A thermometer should also
be clamped to the water bath so that the constant temperature could be further monitored.
Water and PBS should be tested first followed by samples of horse blood diluted to various
concentrations with PBS. The lowest concentration of blood should be tested first. The
sample is dropped down the larger hole of the capillary viscometer (see Picture 1: tube G)
and then sucked through the other end with an auto-pipette. Next, clamp it to the water bath
of 30 degrees Celsius and record the time it takes the meniscus of the solution to fall from
point C on the tube to point E (Picture 1). Three trials should be taken for every
concentration with different samples of blood. In between the testing of each different
sample the viscometer should be rinsed twice with the next higher concentration before the
next trials are performed.
Picture 1
Workup of Results
1. Compare the water data with literature values.
2. For each of the cell suspensions, calculate the RELATIVE VISCOSITY, i.e., the ratio of
the measured suspension viscosity to that of the suspending fluid, using water as your
standard. Using this ratio instead of the viscosity itself will eliminate the differences in
the suspending fluid viscosity as an influence and focus the non-linear effects on the role
of the cells. Also, calculate the SPECIFIC VISCOSITY of each dilution.
3. Plot the Specific viscosity/ concentration vs.concentration, and find the y-intercept to
determine the intrinsic viscosity of horse red blood cells.
References
1. Castellan, Gilbert W., Physical Chemistry. The Benjamin/Cummings Publishing
Company, Inc, 1983.
2. CRC Handbook of Chemistry and Physics, 63rd Edition
3. Dintenfass, Leopold, “Considerations of the Internal Viscosity of red cells and its
effect on the Viscosity of Whole Blood” Angiology v13, Number 8; Angiological
Reserch Foundation, Inc.,1962.
4. Gabelnick, H.L. Ph.D., Litt, M D.Eng.Sc. Rheology of Biological Systems.Charles C
Thomas Publisher; Springfield, Illinois: 1973.
5. Geor, Raymond, The Horse: Diseases and Clinical Management. W.B. Sanders,
Philadelphia:1995.
6. Milnor, William. Hemodynamics. Williams &Wilkins; Baltimore, Maryland: 1989.
7. Geor, Raymond, The Horse: Diseases and Clinical Management. W.B. Sanders,
Philadelphia:1995.
8. Milnor, William. Hemodynamics. Williams &Wilkins; Baltimore, Maryland: 1989.