Numerical investigation on composite porous layers in electroosmotic flow
INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING-GREEN TECHNOLOGY
Numerical Investigation on Composite Porous Layers in Electroosmotic Flow
Taqi Ahmad Cheema 0
Kyung Won Kim 0
Moon Kyu Kwak 0
Choon Young Lee 0
Gyu Man Kim 0
Cheol Woo Park 0
0 1 School of Mechanical Engineering, Kyungpook National University , 1370 Sankyuk-dong, Buk-gu, Deagu , South Korea, 702-701
Applying mechanical pressure on a solid boundary contact using a thin porous layer has been found to reduce the pore size and porosity near the wall region, limiting the flow and mass transport properties. This reduction may affect the overall performance of devices such as the electroosmotic pump that generally uses a porous media with constant porosity in an electric field. Therefore, to improve the performance of such devices, a composite porous layer that uses a combination of different porosity value based on the location in the porous domain, is employed with a higher porosity near the wall region than that in the central region. In this study, a numerical simulation is conducted to investigate the fluid dynamic and mass transport characteristics using a composite porous layer with electroosmotic flow. A comparison of the results with the pressure-driven flow shows the effectiveness of the composite porous layer in compensating for the loss of porosity and in improving device performance. The proposed methodology may also enhance the performance of green energy devices such as fuel cells.
Porosity; Wall region; Mass transport; Electroosmotic flow; Composite porous layer
c = Concentration of tracer (mol/m3)
D = Diffusion coefficient (m2/s)
p = Pressure of fluid (Pa)
u = Fluid velocity vector (m/s)
ι = Current density (A/m2)
z = Tracer charge number
F = Faraday’s constant (C/mol)
ρ = Density of fluid (kg/m3)
µ = Viscosity of fluid (Pa-s)
εp = Base porosity of porous layer
εw = Fluid permittivity (F/m)
ζ = Zeta potential (V)
τ = Tortuosity of the porous media
a = Average pore radius (m)
κ = Conductivity (S/m)
ctop = Peak concentration (mol/m3)
σ = Base width of peak concentration (m)
Electroosmotic flow (EOF) is the bulk motion of a liquid across a
fluid conduit as a result of the interaction between charged surfaces,
ionic solutions and electric fields. The charged surfaces attract the
counter ions and repel the co-ions of the solution in contact, forming
an electric double layer in the vicinity of the wall.1 EOF has been
previously employed in electrochemistry, physics and vascular plant
biology. A number of numerical and experimental investigations on
EOF in porous media have been conducted.2-5 EOF is an attractive
choice for engineers and technologists for pumping the fluid through
small channels and porous membrane materials without the use of
mechanical moving parts. Thus, porous electroosmotic pumps have
attained considerable attention in the last decade. Electroosmotic pump
is a device that uses a porous membrane to exchange selective ions by
EOF and is potentially used for drug delivery, cooling of
microelectronic systems and water management in fuel cells.6-8 In
many applications, EOF through porous media is treated as a flow
through a large number of parallel tortuous microchannels.9
The technological advancement and the importance of porous media
in a variety of industrial applications have made it a prominent research
topic for the last three decades. The focus of previous research has been
mainly on the development of theories related to porous media but this
focus has shifted recently to the performance enhancement of porous
media applications. Porosity, permeability, morphological and
geometrical configurations are some of the variables considered in
former analyses to improve the performance of porous media.10,11
Numerous experimental and numerical studies on different types of
electroosmotic pumps have been conducted, all of which have used a
constant porosity and a constant pore diameter.12,13
Regarding the pressure-driven flows, the solid boundary contact
with porous media has been found to limit flow and mass transfer
properties and to affect the overall device performance. Moreover, the
application of pressure during the assembly of devices containing thin
porous media reduces pore diameter and subsequently the porosity near
the wall region.14,15 In addition, thin porous layers deformed by fluid
load also contribute to the reduction of porosity.16,17 Thus, many
previous researchers had focused on variable porosity to address the
above-mentioned concerns. However, these investigations had
considered the pressure gradient as the only flow-driving force.18-20 So
far the authors’ knowledge, the effects of variable porosity with an
applied electric field have not been studied, and previous studies have
relied only on constant porosity.
The primary objective of the present study is to numerically
investigate the EOF in a composite porous layer with an aim to reduce
the flow resistance, especially in the near wall region. The void fraction
of the porous media is defined by a position based combination of
porosity to counter and compensate the reduced porosity because of
solid boundary contact and application of mechanical pressure. The
proposed composite porous layer makes use of a high porosity value in
the outer region rather than in the central region. The effects of this new
method of composite porosity on the EOF and mass transport
characteristics are investigated by performing a numerical simulation
on a 2D composite porous model. At first, the physics of EOF was
simulated by solving the conservation equations for flow and current
density. The results of this study were then coupled to transient
simulation to evaluate the effects of the composite porous layer on
specie transport. All results obtained by EOF were compared with the
pressure-driven flow in similar conditions. The use of the proposed
composite porous layer is advantageous because it enhances fluid and
mass transport, without increasing the electric potential. Therefore, the
use of a composite porous layer is energy efficient and can be used in
green energy devices, such as fuel cells, to compensate for the loss of
porosity and to improve the device performance.
2. Model Development and Mathematical Modeling
Generally, the orientation of the porous media is normal to the EOF,
as can be observed in an electroosmotic pump. A simple 2D
rectangular porous channel connected to two electrodes at the top and
bottom corners is shown in Fig. 1. The cross section of the channel is
4 mm × 1.5 mm and is divided vertically into three major domains to
implement the concept of a composite porous layer. The porous media
was divided based on the boundary layer developed in the same porous
layer with constant unit porosity. The outer region was assigned with
N = –D∇c – zum Fc∇V + cu
where um denotes the tracer ion mobility (mol-m2/J.s) and can be
evaluated by using Nernst Einstein equation:
Fig. 1 Porous domain model used for computation
a higher porosity (ε = 0.7, 0.8 and 0.9) than that in the central region
(ε = 0.6).
The computational domain was assumed to contain a single-phase
fluid of density 1000 kg/m3 and viscosity of 1.0 E-03 Pa-s. The effects
of electrochemical reaction, compressibility and gravitation had been
ignored and a laminar fluid flow was considered. The flow field was
investigated using the continuity equation for flow and current density.
u = ⎛⎝ –-ε8---µ----τ⎠⎞- ∇p + -------------∇V
Similarly, the current density can be evaluated by using the
For the pressure-driven flow, the inlet was introduced with a
pressure of 1 kPa, while the outlet boundary conditions were fixed to
atmospheric boundary conditions. The walls of the channel domain had
no-slip boundary condition. For EOF, all boundaries were assigned
with an insulated condition except the electrodes with 50 V and 0 V at
anode and cathode surfaces, respectively.
Tracer specie was injected into the channel to investigate the effects
of the transient mass transport in the composite porous layer, with the
assumption that the specie does not influence the porous structure.
Mass transport is governed by the following equation:
----- + ∇.N = 0
where c is the tracer concentration and N is the flux vector that can be
defined by the Nernst–Planck equation.
The inlet and outlet of the channel were assigned flux conditions to
set the diffusion and convection contribution. The walls of the porous
media were set with symmetry boundary conditions. The initial
concentration along the x-axis is given by the following distribution:
c(t = 0) = ctopexp⎛⎝ –0.5⎛⎝ -(--x---–----x------⎠ ⎠
3. Numerical Method and Implementation
We used the commercial software COMSOL-Multiphysics, which
uses a finite element method, to solve discretized equations. The two
new slots introduced outside the central region were assigned with
higher porosity, ranging from 0.7 to 0.9, than that in the central region
that has a base porosity of 0.6. In the first part of the simulation, the
two distinct physics of EOF and pressure-driven flow in the porous
channel were coupled for a steady-state simulation by a PDE equation
solver application mode available in the commercial code. The values
of some important parameters used in this study are listed in Table 1.
The computational domain was discretized using triangular mesh
with maximum element size of 0.1 mm to form 1,538 elements and
6,378 degrees of freedom were solved. In each case, direct solver was
used for 1,000 iterations, with a tolerance factor of 1E-3. In the second
stage of the study, a time-dependent numerical simulation was
implemented to investigate the species concentration using the
steadystate velocity field from the first stage. The solution ran for 1 second,
with an interval of 0.1 second, in each geometrical configuration and
4. Results and Discussion
4.1 Effect on Electroosmotic Flow (EOF) Velocity
Fig. 2 shows the EOF velocity surface plots, with arrows showing
the direction of the flow in the four cases of porosity. Moreover, the
contour lines represent the voltage potential distribution in the fluid
domain. The figure clearly indicates that as porosity near the wall
region increases, the flow rate in that region increases. However, the
effect of this increase in the central region is small at the interface of
the two regions, which can be of significant amount if the domain is
scaled down to micro level. This kind of increase can eventually
enhance device performance in which such combinations of porosity
are introduced. From the results, the increase is shown to potentially
compensate for the effects of reduction in porosity because of the
application of external pressure and solid boundary contact.
The visualized plots of Fig. 2(c), (d) clearly show that
electroosmotic velocity increased in the central region that has
constant porosity, the difference in porosity is high in the two distinct
regions. The absence of viscous and wall shear effects results in a
uniform velocity profile in EOF. However, relatively smaller pore
Fig. 2 Effect of composite porosity on electroosmotic velocity
magnitude in mm/s (surface plot); voltage potential in V (contour
plot) and flow velocity field (arrow plot) for (a) porosity = 0.6, (b)
porosity = 0.7, (c) porosity = 0.8 and (d) porosity = 0.9
sizes near the wall region may restrict the velocity field to feature a
complete uniform flow. The proposed composite porous layer has
solved this issue to some extent, and pumping the fluid in energy
devices with the same electric potential such as fuel cells, can be
4.2 Effect on Pressure-driven Flow Velocity
Fig. 3 shows the surface plots for the pressure-driven velocity to
compare the EOF velocity results on the composite porosity. Here, the
arrow and contour plots represent flow velocity field and the voltage
potential distribution, respectively. The effect of increased porosity near
the wall region is more prominent in this case than EOF. The color
gradient clearly shows the difference in velocity between two distinct
regions, demonstrating the importance of the composite porosity
phenomenon for the pressure-driven flows. An important feature that
the EOF flow field lacks is the increase in flow rate in the central
region in addition to the near wall region. This phenomenon reflects the
strength of pressure-driven flows compared with EOF.
Fig. 4 shows the graphical plot for the EOF velocity magnitude at 2 mm
from the inlet of the channel. A maximum difference of 0.27 mm/s was
found in this case which is small when compared with a significant
velocity difference of 1 mm/s for pressure-driven flows. The latter case also
presents a slight variation in the velocity including in the central region,
and which may become more prominent at a micro scale. The common
feature of the two flow physics in the composite porous layer is the velocity
gradient, which validates the model used in this study. Moreover, these
effects may become more significant for improved boundary conditions of
Fig. 4 Effect of composite porosity on: (a) electroosmotic velocity
magnitude and (b) pressure driven velocity magnitude
high applied voltage and pressure. An interesting feature also exists in both
flow types. The velocity at the interface of the two regions has a slight
variation and is lesser than that in the constant porosity case. However, the
velocity recovered quickly in the central region. Though the flow is strictly
laminar in most of the domain; however, the velocity vectors tend to move
across the interface of two distinct porous regions near the entrance and
exit of the domain. This effect appears near the electrodes where a
significant velocity gradient is observed.
4.3 Effect on Specie Mass Transport and Concentration Profile
Figs. 5 and 6 show the contour plots representing the transport of the
tracer specie at four different times for the two combinations of constant
porosity 0.6 and composite porosity of 0.8 in the outer region. Clearly, an
increase in porosity increases the mass transport of the tracer. The
composite porosity not only affects the concentration in the outer region
but also the central region to some extent. This effect started early, and
a part of the tracer in the outer region moved faster than that in the central
region. Therefore, an increase in porosity improves the mass transport
and compensates for the reduced porosity regions.
Fig. 7 shows the cross sections of the pulse along the interface of
the two distinct porosity regions with different porosity near the wall
region and the central region. Each graph represents the concentration
profile for the following times: t = 0 s, t = 0.2 s, t = 0.4 s and t = 0.6 s.
The mechanical diffusion of the tracer specie is responsible for the
generation of this pulse, whereas the pulse is translated and sheared by
migration and convection. The uniform porosity in the two regions
represents the same peak concentration for different times (Fig. 7(a)),
whereas an increasing porosity near the wall region indicates the
gradual reduction of peak concentration over time. These trends reflect
the effect of composite porosity in the two regions (Fig. 7(b), (c), (d)).
A concentration gradient at the interface was found at different times
representing a strong porosity gradient. Thus, a relation between the
two variables can be predicted with this result.
A numerical study addressing the issue of reduced porosity of
porous layers because of the effect of solid boundary contact in EOF
was carried out. This study emphasized the need for a composite
porous layer with high porosity near the wall region. The results show
an appreciable increase in velocity magnitude in the central region and
near the wall region. This increase in velocity has also been
prominently found in the case of pressure-driven flows.
The effects of composite porosity remain valid and significant for
the mass transport of tracer specie in both regions, and a quicker mass
transport was found in regions with high porosity, which will
eventually compensate for the effect of the loss of porosity. Therefore,
the authors propose the development of composite porous layers with
a combination of different porosity value based on position in the
porous domain to enhance the performance of devices such as an
electroosmotic pump. Further detailed study considering the fluid
structure interaction, viscous and shear effects of the fluid in porous
media will provide more insight to the phenomenon of composite
porosity and composite porous layers.
This work was supported by a National Research Foundation of
Korea (NRF) grant funded by the Korea Government (MEST) (No.
2012R1A2A2A01046099), and a grant from the Priority Research
Centers Program through the National Research Foundation of Korea
(NRF) funded by MEST (2012-0005856).
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