Artigo - MEMS2001 mfluidic

Prévia do material em texto

Simulation and Experimental Validation of Electroosmotic Flow 
 in a Microfluidic Channel 
 
 
Seungbae Hong*, Zhongliang Tang+, Djordje Djukic++, Aurea Tucay++, Sasha Bakhru++, 
Richard Osgood++, James Yardley++, Alan C. West+, Vijay Modi* 
 
++ Department of Electrical Engineering 
+ Department of Chemical Engineering 
* Department of Mechanical Engineering 
Columbia University, New York, NY 10027 
 
 
 
Abstract - In this paper steady electroosmotic and 
pressure driven flows in geometries of interest to 
biomacromolecular detection are considered. For both 
types of flow, experimental data are obtained by imaging 
fluorescent dye propagation. Numerical simulations are 
carried out using finite volume methods. Test structures 
are made of Polydimethylsiloxane (PDMS) mold using the 
negative of the desired structure fabricated by SU-8 thick 
negative photoresist. Steady electroosmotic flow is 
governed by the Laplace equation under certain idealized 
conditions such as when the Helmholtz-Smoluchowski 
relation is satisfied at the inlet and outlet boundaries, and 
when the zeta potential is uniform across the domain. In 
many of these cases, electroosmotic fluid flow can be 
further idealized as two-dimensional when two parallel 
plates confine the flow. Such conditions are frequently 
encountered in many microfluidic devices. In this paper, 
numerical solutions of such an idealized two-dimensional 
electroosmotic flow are obtained and compared to 
experimental data. Equations describing the transient dye 
propagation are then solved in a straight channel followed 
by a downstream circular well. Effects of channel size, 
electric field and possible pressure driven flow 
components are also explored. The effects of flow three-
dimensionality are also examined. 
 
I. INTORDUCTION 
Electroosmosis becomes an increasingly efficient fluid 
transport mechanism as channel cross-sectional dimensions 
become lower than millimeter scale. If the conditions of 
electroosmotic flow meet certain criteria such as uniform 
surface zeta potential, homogeneous fluid properties, 
insulating and impermeable channel walls, negligibly thin 
Debye layer (compared to channel dimensions), and uniform 
total pressure on all entry and exit ports [1], the 
electroosmotic flow can be considered as irrotational. In this 
irrotational flow, velocity everywhere outside the Debye 
layer is proportional to the electric field gradient in the fluid. 
Therefore, in the ideal electroosmotic flow condition, the 
flow field can be obtained by the solution of Laplace equation 
for electric potential. 
Due to the nature of chip manufacturing processes such as 
photo-etching and surface bonding, many micro-channels on 
the chip can be approximated as two-dimensional networks 
whose actual cross section is rectangular. Since most constant 
depth rectangular channels do not have electric field gradients 
perpendicular to the chip plane, the flow that meets the ideal 
electroosmosis condition will indeed become two-
dimensional flow. Patankar and Hu [2] conducted three 
dimensional electroosmotic flow simulation where the 
channel and fluid conditions met the conditions for ideal 
electroosmosis. They concluded that their numerical 
simulation did not have velocity component in the third 
dimension and the flow could be approximated as 2-D flow. 
This confirms our 2-D assumption on such situations. Seiler, 
Fan, Fluri, and Harrison[3] however suggest that a pressure 
driven component may be present in the flow while the 
conditions met the ideal electroosmosis criteria. If the 
channel network contains a branch with weak electric field 
gradient, leakage flow is induced and the electroosmotic flow 
field will no longer be proportional to the electric field 
gradient. Therefore, care needs to be exercised in the choice 
of ideal electroosmotic flow conditions and as a result, we 
limit our simulations to single inlet, single outlet systems so 
that no complications would arise from pressure induced flow 
at channel junctions. We have validated our analysis using 
experiment on a PDMS chip with fluorescence dye that is 
supplied from the inlet reservoir. For fabricating PDMS chip, 
the negative of the desired structure using thick SU-8 
negative photoresist was first created. This is used as a 
molding master for creating a desired channel structure in 
PDMS. 
 
II. THEORY 
We first begin with the solution of electric field in the 
channel. For steady state electric potential gradient E = -∇ Φ, 
we use the Laplace equation: 
02 =Φ∇ (1) 
Since the microfluidic chip and the channel wall are 
usually made out of silicon, glass, or polymeric materials, 
which are insulators for electric currents, we impose a 
Neumann boundary condition at the channel walls. At the 
electrode, a scalar voltage potential is applied. The 
electroosmotic velocity is proportional to the electric field 
gradient by the electroosmotic mobility µeo. 
Φ∇−= eov µ
&
 (2) 
Electroosmotic mobility is a property that depends on the 
type of fluid and solid at their interface. For PDMS and de-
ionized water, it is found to be 2.768×10-5 m2/V⋅s and mass 
diffusion coefficient between the dye and water is defined as 
DAB.= 5.5×10-10.m2/sec. Mass dispersion equation shown 
below is used to calculate dye propagation over time. 
CDCv
t
C
AB
2)( ∇=∇⋅+
∂
∂ & (3) 
The integral forms of equation (1) and (3) are solved using 
the finite volume method. These are: 
02 =⋅Φ∇∫
S
dSn& 
∫∫∫ ⋅∇=⋅+Ω∂∂ Ω SABS dSnCDdSnvCCdt
&&&
)( (4) 
Above, Ω is the volume and S is the surface area of a 
control volume. For numerical calculations, dimensionless 
forms of the above equations are solved. These equations are 
obtained by normalizing velocities with U, the inlet velocity, 
lengths with W, the channel width and concentrations with 
inlet concentration. An important dimensionless parameter, 
Peclet number or Pe given by 
ABD
UWPe = (5) 
emerges from this exercise characterizing the ratio of 
convection to diffusion. For Pe >>1, convection will be 
dominant while for Pe << 1, diffusion will be dominant. For 
microchannels with channel cross-section dimensions of 10 ∼ 
100 µm, Pe numbers vary from 1-100. 
 
III. FABRICATION PROCEDURE 
Rapid prototyping of microchannel structures for flow 
experiments was done by replica-molding PDMS from 
master structures created in thick negative photoresist (SU-8) 
by optical lithography. Commercially available standard 
grade mixtures of EPON SU-8 photoresist, SU-8-5 (with 52% 
solids), and SU-8-25 (63% solids), were spun onto Si wafer 
substrates at 1100 and 2000 rpm yielding 10µm and 30 µm 
thick films, respectively. Pre-exposure bake was done for one 
hour at 95°C on a precisely leveled hot plate and the samples 
were allowed to cool down before further processing [4]. 
Exposure was done using a direct laser writing system. 
Photolithographic setup consists of an Ar-ion laser 
(wavelength λ=350nm), focusing optics, and a computer 
controlled sample stage. The movement of the stage along all 
three axes (x,y,z) is achieved by stepping motors. Desired 
master patterns were created by scanning the samples 
underneath the focused laser beam to expose the outline, and 
then scanning across the interior to fully expose the micro- 
 
Fig. 1. SEM micrograph of the SU-8 master structure. 
 
Fig. 2. SEM micrograph of the PDMS replica 
of the SU-8 master structure. 
channel structure. Dynamical focus correction for the sample 
tilt with respect to the scanning laser beam was the done by 
on-the-fly adjustments of the distance between the focusing 
lens and the sample stage. 
Post-exposure bake was done at 95°C for 15min followed 
by developing in a commercial SU8 developer for 5 min. The 
sample was lightly stirred during developing.Fig. 1 shows a 
100 µm diameter circular well structure with 30 µm wide 
input and output channels created in 30 µm thick SU-8. 
Patterns created in SU-8 were used as molding masters for 
replication in PDMS[5]. PDMS was prepared from the 
mixture of 10:1 ratio by weight of the PDMS precursor and 
curing agent (Sylgard 184 kit, Dow Corning). Before curing, 
the mixture was placed in vacuum to evacuate the bubbles 
formed during mixing. It was then poured over the SU-8 
master, which was previously coated with a thin layer 
(~50nm) of chromium to improve the release of the PDMS 
coating after curing. Curing was done at 70°C for 12 hours. It 
can be seen from Fig. 2, that the PDMS replica exhibits 
smooth, vertical sidewalls, and the required dimensions for 
our microfluidic structure design. 
 
IV. EXPERIMENTAL SETUP 
A. Electrokinetic Flow Experiment 
The chip with circular well (100µm in diameter and 10-30µm 
high, connected to the outside reservoirs by 10-30 µm wide 
channels) on it is rinsed with ethanol five times and then 
rinsed with deionized water three times. The chip is dried by 
compressed air. A flat piece of PDMS is cleaned and dried in 
text
Output
reservoir Well
Input
reservoirW
mµφ 100=
 (a) 
text
W
Cathode Anode
4 mm
 (b) 
Fig. 3. Top view (a) and side view (b) of the chip 
the same way and used as a cover to seal the chip by adhesion 
(Fig. 3). After it is assembled, the chip is flooded by adding 
electrolyte solution in one well and applying a vacuum to the 
other well. Both wells are cleaned and refilled with same 
amount of electrolyte (0.1mM KNO3). Electrodes (platinum 
wires) are then connected to the circuit. A fluorescence dye 
(calcein or bis [N, N-bis(carboxymethyl) - aminomethyl] 
fluorescein, excitation at 490nm, emission at 540nm, MW 
622.55, Dw=5.5×10-10 m2/s [6]) is used as the probe. The 
assembled chip is then put under a fluorescence microscope 
and a voltage is applied across the channel. A CCD camera 
(Sensys0401E, Roper Scientific) is used to record 
fluorescence images at a constant time interval. The images 
are stored in a computer for further processing [7-9]. The 
fluorescence filter set used is Chroma 11001. The flow 
pattern inside the feature is extracted by processing the image 
sequence. The schematic setup of the experiment is illustrated 
in Fig. 3. 
B. Pressure Driven Flow Experiment 
Following the same procedure as in the electro-osmotic 
flow experiment section except that a pressure gradient is 
applied across the channel as the flow driving force instead of 
an electric field. The calculated pressure gradient needed to 
obtain a comparable flow rate to electro-osmotic flow is 
about 5 Pa/mm for this geometry. Thus hydraulic pressure is 
used in this experiment. 
 
V. RESULTS 
Experimental data on electroosmotic flow were obtained 
for two different channel sizes, 10 × 10 µm channel and a 30 
× 30 µm channel leading into a 100 µm diameter circular 
well. The microfluidic structure is made from PDMS with a 
measured zeta potential of -40mV. The applied electric field 
inside the inlet and exit channel is 50, 100, 150 V/cm 
respectively. Initially, calcein (fluorescent probe) is placed in 
the reservoir to the right of the Fig. 4. Figure. 4a-c shows a 
comparison of simulated and measured flows for the 10 × 10 
µm channel case and Fig. 4d for the 30 × 30 µm channel. The 
simulated contour plots are shown in the bottom row, and the 
corresponding experimental plots are shown on the top of the 
figure. Note that in these Figures the flow is from right to left 
and in each of figures. Four plots are shown at four 
consecutive times (from left to right) with time intervals ∆t 
for each case shown in the figure caption. The particular 
instances of time shown are chosen so that the calcein labeled 
solution can be observed in the well region. In each plot of 
Fig. 4, fluorescence intensity levels of 20, 40, 60 and 80 
percent of the inlet intensity of calcein are shown. From the 
results it is seen that the simulations and experiments show 
reasonable agreement for the 10 µm square inlet channel 
case, whereas for the 30 µm square channel case the 
agreement is not as good. The asymmetries in the measured 
concentration contours in the 30 µm case, are believed to be 
errors in leveling of the chip, whereas it is hard to notice for 
the 10 µm thick chip. Moreover dye propagation in the 30 µm 
case seems to be faster as well. The reason for these 
differences could be the relative importance of a spurious 
pressure driven component, as discussed in the next section. 
The results also show differences in dye concentration 
gradients between the simulation and experiment at the side-
walls. The simulations do not show a concentration gradient 
normal to the wall, while in the experiment a gradient 
 
a. 
 
 
 
 
 
b. 
 
 
 
 
 
c. 
 
 
 
 
 
d. 
 
 
 
 
W = 10 µm channel 
a. E = 50V/cm, v = 0.14mm/sec, ∆t = 0.8 sec (Pe = 2.6) 
b. E = 100V/cm, v = 0.28mm/sec, ∆t = 0.4 sec (Pe = 5.1) 
c. E = 150V/cm, v = 0.42mm/sec, ∆t = 0.4 sec (Pe = 7.65) 
W = 30 µm channel 
d. E = 50V/cm, v = 0.14 mm/sec, ∆t = 0.4sec (Pe = 7.53) 
Fig. 4. Measured (upper row) and computed (lower row) 
electroosmotic flows for 10 and 30 µm square channels 
at the wall is readily seen. We suspect that the reason for this 
is as follows. The electroosmotic flow is driven by effectively 
slip conditions that exist at all the four walls (top, bottom, 
and two side walls) of the PDMS structure. It is possible that 
the fabrication process does not lead to smooth side-walls 
causing electric potential gradients to be smaller at the side 
walls than for the top and bottom surfaces walls. The flow at 
the side walls could be somewhat slower and this along with 
the optical refraction at the walls could contribute to what 
appears to be a dragging effect at the side walls in Fig. 4. 
 
VI. DISCUSSION 
We have developed a computer program to predict the 
electroosmotic flow field and mass dispersion. To verify the 
two dimensional nature of the flow in the microchannel, we 
have fabricated a PDMS microchip and conducted 
experiments using a fluorescent dye, and observed the dye 
propagation through CCD camera. The microfluidic flow and 
dye dispersion were successfully modeled and matched with 
the experiment. There are some pressure driven components 
in the experiment which are more prevalent in the low speed 
electroosmotic flow and for the chips with larger dimensions. 
Using the equations for pipe flow, we find that an 
approximately 1mm height difference (h) for a 4mm (L) long 
channel with 30 µm (d) square cross section corresponds to 
77 µm/sec (v) flow velocity, and for the 10 µm (d) square 
cross section corresponds 8.6 µm/sec (v) flow velocity. 
L
dhgv
µ
ρ
5.28
2
= (ρ: density, g: 9.8m/s2, µ: viscosity) (6) 
Due to this difference of almost an order of magnitude in 
speed, we can observe the remnant of pressure driven 
component such as the asymmetrical pattern of dye 
dispersion in 30 µm thick channel more readily than in 10 µm 
thick channel in the circular channel bulge. Fig. 5 shows the 
dye concentration contours obtained by experiment and 
simulation for a pressure driven flow. These are for a 
hydrostatic pressure of h = 2mm of water, corresponding to a 
means velocity in the channel of 153 µm/sec. The Pe number 
for this case is 8.34. Due to the relatively low Pe numbers, 
i.e. high diffusion rate, there is little distinction in the dye 
dispersion shape between the electroosmotic and pressure 
driven flow for the simulation. The same applies for the 
experiment, but pressure driven flow shows higher dye 
concentration gradient. Through close examination, in both 
experimental and simulation cases, the pressure driven one 
showsa sharp angled dye front, while the electroosmotically 
driven flow showed round dye front. Note that the pressure 
driven flow in this system is necessarily three-dimensional 
and that the assumption of two-dimensionality in Fig. 5b may 
not be appropriate. Hence 3-D simulations of the same flow 
were also carried out. The concentration contours for this 
case are shown in Fig. 5c. There are no significant gradient in 
the channel depth direction. 
Overall, the simulations and experimental results show 
generally good quantitative agreement. Using this simulation 
technique, the flow behavior of a microfluidic network can be 
predicted accurately as long as the flow meets the ideal 
 
 
 
 
 
 
 
Fig. 5. Measured and computed pressure driven flow 
for 30 µm square channel 
[h = 2mm, v = 0.153 mm/sec, ∆t = 0.45 sec (Pe = 8.34)] 
electroosmosis criteria. As expected smaller channel 
dimensions and higher electric fields lead to lower 
contamination with pressure driven components and hence 
better agreement between computation and experiment. 
 
REFERENCES 
[1] E. B. Cummings, S. K. Griffiths, R.H. Nilson, 
“Irrotationality of Uniform Electroosmosis”, SPIE 
conference on Microfluidic Devices and Systems II, 
Santa Clara, CA, vol. 3877, page 180-189. (September 
1999) 
[2] N. A. Partankar, H. H. Hu, “Numerical Simulation of 
Electroosmotic Flow”, Analytical Chemistry, vol. 70, 
page 1870-1881. (1998) 
[3] K. Seiler, Z. H. Fan, K. Fluri, D. J. Harrison, 
“Electroosmotic Pumping and Valveless Control of Fluid 
Flow within a Manifold of Capillaries on a Glass Chip”, 
Analytical Chemistry, vol. 66, 3485-3491, (1994) 
[4] H. Lorentz et al., “SU-8:a low-cost negative resist for 
MEMS”, J. Micromech. Microeng., 7, pp 121-124, 
(1997) 
[5] A. Folch et al., “Molding of Deep Polydimethylsiloxane 
Microstructures for Microfluidics and Biological 
Applications”, J. Biomech. Eng., 121, pp.28-34, (1999) 
[6] D. de Beer, P. Stoodley, Z. Lewandowski, “Measurement 
of Local Diffusion Coefficients in Biofilms by 
Microinjection and Confocal Microscopy”, 
Biotechnology and Bioengineering, vol. 53 151-158 
(1997) 
[7] K.D. Kramer, K.W. Oh, C.H. Ahn and et. al., “An 
Optical MEMS-based Fluorescence Detection Scheme 
with Applications to Capillary Electrophoresis”, SPIE 
Conference on Microfluidic Devices (Santa Clara, CA) 
76-85 (1998) 
[8] S.N. Brahmasandra, B.N. Johnson, J.R. Webster and et. 
al., “On-Chip DNA Detection in Microfabricated 
Separation Systems”, SPIE Conference on Microfluidic 
Devices (Santa Clara, CA) 242-251 (1998) 
[9] D.W. Arnold and P.H. Paul, “Fluorescence-based 
Visualization of Electroosmotic Flow in Microfabricated 
Systems”, SPIE Conference on Microfluidic Devices II 
(Santa Clara, CA) 174-179 (1999) 
 
 
	Abstract - In this paper steady electroosmotic and pressure driven flows in geometries of interest to biomacromolecular detection are considered. For both types of flow, experimental data are obtained by imaging fluorescent dye propagation. Numerical sim
	
	A. Electrokinetic Flow Experiment
	B. Pressure Driven Flow Experiment