SUPPLEMENTAL MATERIAL
Systematic Characterization of Degas-driven Flow for PDMS
Microfluidic Devices
5
David Y. Liang, Augusto M. Tentori, Ivan K. Dimov, and Luke P. Lee
Physical model
To describe the air flux from the microchannel to the PDMS, we used the equation described by
Hosokawa et. al.14, with the addition of a scaling factor to account for the difference in the geometries of
the two systems. Catm is air concentration in the atmosphere, CPDMS is the concentration of air inside the
10 PDMS after degassing, DPDMS is the diffusivity of air in PDMS, LPDMS is PDMS thickness, and tidle is postvacuum idle time before loading. Equation (1) was derived from Fick’s laws of diffusion assuming a 1-D
system. Our system is best described as finite and three-dimensional as supposed to infinite along two
axes. Additionally, we assume CPDMS (the concentration of air inside the PDMS after degassing and before
the experiments was zero. Both of these factors should be accounted for with the scaling constant.
 C  C PDMS   -  2 DPDMS t  t idle  

exp 
15 Flux air  K 2 * 2 DPDMS  atm

LPDMS
4L2PDMS

 

(1)
To describe the fluid flow, we assumed Pousille-like flow in a square microchannel. We scaled the fluidic
resistance by a constant to account for more complex factors such as surface tension and PDMS
hydrophobicity. η is the fluid viscosity, L, W, and H describe the length, width, and height of the
microchannels, Q describes the volumetric flow rate, and ΔP describes the pressure difference between the
20 inside of the microchannel and the atmosphere.
12LW  H 
WH 3 1  5H 6W
2
R fluidic  K1 *


(2)
1
Q
P
R fluidic
(3)
To relate the phenomena, we used the following relations:
P  Patm 
nchannel RT
V free
(4)
Assuming ideal gas behavior, we can relate the pressure difference to the amount of air inside the
5 microchannel (nchannel) and the fluid-free, gas-filled volume inside the microchannel (Vfree). Patm is the
atmospheric pressure, R is gas constant, and T is temperature.
Nchannel is related to the flux of air using the following relations:
t
nchannel  ninitial   Fluxair A free dt
(5)
0
Ninitial is the amount of air inside the microchannel when the sample is loaded. Afree is the surface area of
10 the microchannel that has not been covered with fluid and is exposed to air.
The surface area exposed to air and air volume in the microchannel are related to the volumetric flow rate
through the following geometrical relations:
t
V free  WHL   Qdt
(6)
0
A free  2 L(W  H )  WH 
2W  H  t
Qdt
WH 0
(7)
15 Combining equations (2), (3), and (4) and combining (1) and (5), we get the following relations:
WH 3 1  5H 6W  

 Patm  nchannel RT 
Q  K1
2
V free 
12LW  H  
nchannel
t
 C  C PDMS
P WHL
 atm
 K 2  2 DPDMS  atm
0
RT
LPDMS

(8)
  -  2 DPDMS t  t idle  
 A free dt
exp 
2


4L
 
PDMS

(9)
To solve the system of equations (6) (7) (8) (9), we took time derivatives and used the ordinary differential
equations system solver, ode15s, in MATLAB 9.
20 The four equations and initial conditions were the following:
2
dA free
dt
A free0
dV free
dt
2W  H 
Q
WH
 2 L(W  H )  Aend

 Q
V free0  WHL
 C  C PDMS
dnchannel
  K 2 2 DPDMS  atm
dt
LPDMS

PatmWHL
RT
 WH 3 1  5 H
dQ
6W
  K 1 
dt
 12LW  H 2

 WH 3 1  5 H
dQ
6W
  K 1 
dt
 12LW  H 2

Q0  0
  -  2 DPDMS t  t idle  
 A free
exp 

4L2PDMS
 

nchannel0 

RT  

RT 


1  dnchannel  n  dV free 
 2

 V  dt 
 V free  dt

 free 




 1 

n 
 K 2 2 DPDMS  C atm  C PDMS
 2 Q  





LPDMS
 V free 

 V free 

  -  2 DPDMS t  t idle  
 A free 
exp 
2


4L PDMS
 


(10)
To solve this system, we used the ode15s solver with 0.001 sec and 0.001 meters for the time and spatial
steps respectively. The parameters used were chosen to match experimental conditions or obtained from
literature18:
  8.9 10 4 Pa  s
2
D PDMS  3.4 10  9 m
5
s
Patm  10 Pa
5
R  8.31472 J
molK
T  298 K
C atm 
Patm
RT
H  50 10 m
6
3
FIG S1. Schematic showing experimental procedure for characterization of degas-driven flow. After
pressing the PDMS device and the glass slide together to form reversible seals, the PDMS device is placed
into a vacuum chamber and degassed for a determined time. To characterize degas time, 10 min, 45 min, 2
5 hr, and 24 hr were used. After degassing, the PDMS device is removed and placed under a microscope
objective. The sample is added to the inlets, and the idle time is recorded. To characterize idle time, 2 min,
4 min, 7 min, and 10 min were used. The data from the last 10.7 mm of the straight microfluidic channels
is recorded, and the number of pixels for each frame is converted to a fluid volume.
10
4
FIG S2. Mask layout of the microfluidic devices used to fabricate the PDMS devices, organized by design
parameter. From left to right: S-curve channels (used for the mathematical model) of varying lengths: 10,
20, 35, 50, and 65 mm, channels of varying surface areas: 8.40, 8.85, 10.02, 12.01, and 16.00 mm2, and
5 channels of varying widths: 50, 100, 200, 350, and 500 µm. All S-curve and surface area channels are 50
µm wide, and the single straight channels in both the surface and width devices are 35 mm long. All
channels are drawn to scale.
5
6
FIG S3. Comparison of physical model predictions and experimental data. Data was collected for two idle
times, (A) 2 min and (B) 10 min, from a microfluidic device of S-curves with a channel height of 50 µm,
width of 100 µm, and varying channel lengths ranging from 25 to 65 mm, as indicated by the legend. (C)
5 shows data collected from a microfluidic device with channel height of 50 µm, PDMS thickness of 2.2
mm, degas time of 24 hr, idle time of 2 min, and varying cross-sectional areas ranging from 0.0025 mm2
to 0.025 mm2, as indicated by the legend. Error bars represent ±1.96σ of the reproducibility measurements.
7
FIG S4. Time-lapse images of channels of varying surface areas being filled by vacuum-driven flow. A
parabolic loading behavior was observed in the fork-like dead-end structures, with the channels on the
edges traveling faster than those in the center. We hypothesize that this is due to a larger amount of bulk
5 PDMS surrounding the outside channels, which causes increased gas diffusion and thus faster flow
velocities.
8
FIG S5. Fluid volume profile during channel filling for the 0.9 mm thick device. Data was obtained from
the device used in Fig. 2A, with a degas time of 2 hr and idle time of 2 min. The 16.00 mm 2 channel
exhibited slow degas-driven flow, but the 8.85 to 12.01 mm2 exhibited no degas-driven flow. Error bars
5 represent ±1.96σ of the reproducibility measurements.
9
FIG S6. Fluid volume profile during channel filling for the 2.2 mm thick device. Data was obtained from
the device used in Fig. 3A, with a degas time of 24 hr and idle time of 10 min. Although the channels with
widths 100 and 50 µm filled completely in less than 30 min, the channels with widths 500, 350, and 200
5 µm did not fill completely before the flow velocity reached zero. Error bars represent ±1.96σ of the
reproducibility measurements.
10