This document summarizes a computational simulation of inertial effects on low Reynolds number microfluidic flow using COMSOL Multiphysics software. The simulation models two-phase immiscible fluid flow through an S-shaped microchannel. It was found that microfluidic turbulence increased as inlet velocity decreased. Even at very low velocities of 1 micron/second, vortex shedding and interface breaking were observed, demonstrating that inertial effects can induce instability in laminar microscale flows. The computational results provide insight into inertial effects on two-phase microfluidic flows that can be validated through future microchip fabrication and testing.

1. March 2012 1
Computational Simulation of Inertial Effects on Low Reynolds Number
Microfluidic Flow
Gerardo Camarena Gomez
Baltimore Polytechnic Insitute
The “Lab-on-a-chip” technologies have a direct impact on both industrial and academic study of biochemical processes, allowing for
faster and more efficient analysis of these biochemical processes. Simulating such complex systems allows for rapid and cost efficient
method of analyzing fluid behaviour in microsystems. We utilize a physics-coupling program called COMSOL, which solves the partial
differential equations that govern fluid flow. We extract data to thoroughly analyze how inertial effects impact the interface and
behaviour of two phase flows.
1. INTRODUCTION
We model incompressible two-phase flows through various
microfluidic devices using the Level Set Method through
COMSOL Multiphysics. This method allows for tracking
interfaces that change topology over time without the need
to parameterize these interfaces. Specifically, the immiscible
fluids we investigate have a sizable difference in density.
therefore we can implicitly track the interface by representing
the surface as a smooth zero level set function
(Sussman et al, ), while anything outside such function can be
represented as being greater than zero and anything inside
as being less than zero. This allows for differentiation of the
fluids as the interfaces merge or break up (Sussman et al).
Other computational methods such as the boundary integral
methods, volume of fluid methods, phase field methods,
and capturing methods (Sussman et al) have been found to
not be as effective as the LSM.
We investigate the effects of different changes in direciton
on the behaviour of an incompressible two-phase flow using
The LSM through COMSOL Multiphysics, a program that
Utilizes the Finite Element Method (FEM) to solve
partial Navier Stokes differential equations. The development
Of a microfluidics device that aids in separation of fluids with
distinct densities, such as a two-phase flow consisting of
a cell culture dissolved in water and pure water, can have
important applications in the biological field and in the
development of lab-on-chip technologies (Drazer, Frechette,
Et al).
The separation technique of barriers that abruptly change
the direction of two-phase flow is being proposed. The
geometry consisted of two semi-circle turns to create what we
called a Snake channel. The geometry also consisted of two
distinct inlets, where the two fluids with different densities
were introduced into the device with equal inlet velocities.
In this article we thoroughly discuss the process and results of
these simulations.
We strive to achieve a wide range of simulations consisting
of variations in inlet velocity, density contrast, and fluid
position.
Due to the effects of inertia on this problem, I predict that the
interface will sharply change as the fluid flow develops in the
microchannel. As the more dense fluid is introduced into the
Channel, I believe that it will act as the dominant fluid and
take a position closest to the outermost wall of that particular
Turn, allowing for a separation effect for the two fluids.
COMSOL Multiphysics was used here to model the inertial
effects on two-phase flow with contrasting densities in a
microfluidic device. COMSOL makes use of a mathematical
technique known as the Finite Element Method (FEM) to
approximate the solutions of partial differential equations
(PDE), in our case the Navier Stokes Equations that govern
fluid flow, by approximating them to simpler differential
equations and integrating to attain data such as volume fraction
and velocity. The FEM also consists of creating a mesh across
the geometry, allowing the program to break up the geometry
into triangles and then solve the PDE in that smaller region.
The finer the mesh the more triangles that exist in the geometry,
Translating to an increase in the accuracy of the solution.
However, the disadvantage exists in that as the mesh gets finer,
computational resources needed to complete the simulation
increase. A mesh of about 4000 triangular members was
determined to be sufficiently accurate and efficient.
COMSOL Multiphysics also uses a mathematical technique
called the Level Set Method (LSM) to track moving interfaces
that change topology. By using the level set function,
the program can accurately determine which of the two
Occupies a given space in the microchannel. The level set
method is an integral part of the program. It enables us to
Differentiate between two distinct flows in the two-phase
flow problem.
The geometry consists of two distinct inlets that merge into
the S-shaped microchannel (see figure). The channel consists
Of two curves of radius of curvature 350 um each, and the whole
2. Goals and Hypothesis
Microchannel is 700 um long. Once the geometry was
Constructed in COMSOL Multiphysics, the boundary conditions
were as follows:
3. Materials and Methods

2. March 2012 Gerardo Camarena Gomez 2
1. All of the outer walls were assigned the no-slip condition.
2. The outlet was specified to have zero pressure drop.
3. The inlet was specified to have a range of velocities:
V1
: 1e-2
m/s
V2
: 1e-3
m/s
V3
: 1e-4
m/s
V4
: 1e-5
m/s
V5
: 1e-6
m/s
The two-phase flow problem was tested with two fluids
of the same surface tension yet contrasting density. One fluid
was kept constant at 1000 kg/m^3, yet the other fluid was
varied to give a density of 1:2, 1:3m 1:5, and 1:10 ratios.
the two fluids were differentiated by the names “light fluid”
for the one with the least density and “heavy fluid” for the
other. The inlet for the “heavy fluid” was varied, where
the velocities stated above were tested for both cases where
the fluid was injected from the left inlet and when injected
from the right inlet.
The volume fraction, velocity, and Reynolds number plots
Were extruded and analyzed. Such plots give an accurate
Portrayal of inertial effects on the two-phase flow.
Figure 1 : The S-shaped Microchannel
4. Results
Figure 2: The parabolic profile velocity
profile inside of the microchannel coincides
with theoretical expectations.
First an initial test with very basic outputs was
performed in order to determine if the software did
give physically viable results. As seen in Figure 2, the
velocity profile as displacement from the inner wall
increases towards the outer wall is parabolic, which is
the physically expected outcome that arises from
classic Couette flow.
We tested out the parameters outlined in the materials
and methods and discovered that microfluidic
turbulance increased as velocity decreased. In figure 3,
we can observe that at one centimeter per second
velocity the boundary between the two fluids is still
mostly intact after the flow has developed.
Figure 2: The parabolic profile velocity
profile inside of the microchannel coincides
with theoretical expectations.
Figure 3: The interface between the two fluids
flowing did not change much from when v=0 m/s
(top) to when v=1cm/s (bottom).
As the velocity decreased to one micron per second
vortex shedding and extreme turbulence was evident
even at the microscale. Figure 4 supports this observed
votex shedding and turbulence at low reynolds
numbers.
Figure 4: The interface between the two fluids
flowing began intact when v=0 m/s (top) but
when v=1um/s (bottom) vortex shedding and
breaking up of the interface was observed.

3. March 2012 Gerardo Camarena Gomez 5
References
[1]
[2]
Manuel Balvin, German Drazer and Joelle Frechette. “
directional Locking and the role of irreversible interactions
in deterministic hydrodynamics separations in microfluidic
Devices” Physical Review Letters (2009). Print.
[3]
[4]
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5. Discussion
We analyzed the ten simulations and all had inertial
effects. Even extremely laminar flow, as is the case
with velocities of one micron per second, experienced
instabilities that should traditionally not exist. This
proves that laminar flow can experience chaotic
behavior because of inertial effects. Volume fraction
plots further proved the hypothesis of the fluids
experiencing this instability.
The volume fraction, velocity, and Reynolds number
plots were extruded and analyzed. Such plots give an
accurate portrayal of inertial effects on the two-phase
flow.
While computational simulations allow for cheap
and efficient alternatives to laboratory testing, the
transition to such laboratory alternatives will be
eventually made. Future plans include fabricating the
Snake-channel microchip and analyzing these inertial
effects in a real-life physical setting.