This summary provides an overview of the document: 1) The document studies the effect of geometrical shape (rectangular vs circular) on hydrodynamic focusing in microfluidic flow cytometry through simulation. 2) The results show that a circular shape maintains a higher concentration at the center of the channel and produces higher fluid velocity compared to a rectangular shape. 3) A circular shape also better sustains the focused stream and peak concentration across the length of the channel compared to the decreasing concentration profile seen in a rectangular channel.

1. Effect of geometrical shapes on 3D hydrodynamic
focusing of a microfluidic flow cytometer
Muhammad Syafiq Rahim, Norasyikin Selamat, Jumril Yunas, Abang Annuar Ehsan
Institute of Microengineering and Nanoelectronics IMEN), Universiti Kebangsaan Malaysia,
43600 Bangi, Selangor,
E-mail: syafiqrahim@siswa.ukm.edu.my
Abstract— This paper focuses on the effect of geometrical cross
section between rectangular and circular shapes on the
hydrodynamic focusing of a micro flow cytometer device. The
effect of fluid flow ratio between the main and sheath channels on
the focusing width is studied. This study has been performed using
a COMSOL Multiphysics simulation tool. The results showed that
focusing width decreases as the ratio between main channel and
sheath channels are increased. The concentration at long-range is
studied and indicated that circular shape can sustain a higher
concentration at the centre along the channel compared with
rectangular shape. The velocity at the cross-section of the channel-
junction shows that circular shape produces higher velocity at the
centre of the channel compare to that of the rectangular shape.
The effect of flow ratio and geometrical shape are significantly
vital for microfluidic system which utilizes hydrodynamic focusing
for biological and chemical analysis. From the result, micro flow
cytometer studied able to use for human body cells such as glucose,
virus, red blood cells and white blood cells which have a range size
of 2-120 microns.
Keywords— comsol; microflow cytometer; hydrodynamic
focusing; microfluidics; microchanne; fluid flow; microfluidics
devices
I. INTRODUCTION
Flow cytometer has been successfully used for many
years. In the past, microfluidic application of microsystem
technology has shown great potential for portable low-cost
devices in the various field, from chemical synthesis and
biological analysis to optics and information technology. [1]
[2][3][4] due to the ability to use in very small sizes of samples
and detections with high resolution and sensitivity, low cost and
precise fluid flow control[1]. Most of the micro flow cytometers
apply sheath flows for hydrodynamic focusing at the center
stream. The effect of the device geometry or shape on the
hydrodynamic focusing still need to be explored. It is known
that the sheath and sample flow rates are important to control
the width of the focused stream or channel. The size of the
width which reaches a typical cell size become a critical design
parameter [5]. Hydrodynamic focusing is one of the critical
technique needed to develop highly efficient particles sorting
method using microfluidics devices approach.
Hydrodynamic focusing uses two sheath flow usually
in low concentration and squeeze the middle sample flow which
is usually in high concentration, in order to focus the sample
flow on a specific channel region. To ensure only one particle
pass through the detection area, the particles need to be focused
at the center of the channel. Particle damage often occurs when
the biological sample moves closer to the microchannel walls.
Hydrodynamic focusing of particles prevents these problems.
As the realization of 3D hydrodynamic focusing is not
an easy task, there are only few details analysis on the 3D
geometrical structure of the microchannel which affect the
hydrodynamic focusing[6], the comparison on the simulation
results between rectangular and circular shapes that effect the
width focusing and velocity need to be done.
In this work, the effect of 3D geometrical cross
section between rectangular and circular shapes on the
hydrodynamic focusing of a micro flow cytometer channel-
junction is being studied. The simulation of the hydrodynamic
focusing property for the micro flow cytometer device is done
using COMSOL software. The study of the width focusing will
focus on the mixing of concentration values and the velocity
study will focus on the velocity peak and velocity profiles.
Certain micro sizes of focusing width needed to achieved to
ensure its ability to do cell sorting and counting for specific
micro sizes cell such as glucose, virus, red blood cells and white
blood cells which have a range size of 2-120 microns[7].
II. THEORY
The present study focuses on single-phase symmetric
hydrodynamic focusing technique, in which the sample flow
(supplied from the inlet channel) is constrained laterally within
the center of the microchannel by two neighboring sheath flows
from the side channels [4]. Fig. 1 shows a 2D layout of a four-
junction flow cytometer device. From Fig. 1, flow rate of the
sample and sheath can be used to control the width of the
focused stream. This can be done by solving the equation of the
fluidic system, which is the Navier-Stoke equation. From the
Equation (1) and figure 1, and are the volume flow rate of
the sample and sheath. is the mean flow speed ratio, and
are the focusing width and output width, and f is focusing
fraction[8][9].
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2. Fig. 1. Symmetric Hydrodynamic Focusing[10]
The flow fraction can be defined as follows [10] :
. (1)
This can be used to estimate the flow fraction. However, this
model flow takes no account of 3D behavior of the velocity
profiles. From Bahrami equation shown in Equation (2),
geometrical effect with flow fraction can be associated [8][9]
given by;
∆ 16 (2)
∆P is pressure drop, μ is fluid dynamic viscosity, Q is flow
rate, L is channel length, A is channel’s area cross section and Ip
is specific polar momentum of inertia microchannel cross
section.
III. SIMULATION
A Multiphysics finite element simulation tool, COMSOL is
used for modeling the 3D hydrodynamic focusing which
includes the integration between numerical analysis of the
continuity, momentum and energy equations for the fluid flow.
Prior to modeling, an important assumption has been made
which is the characteristics of fluid flow must be in laminar flow
and not turbulent flow. Moreover, the effect of electro kinetic
phenomena and gravity effect have been neglected. All the
assumptions above are made to ensure continuum approach by
Navier-Stoke is applicable. In addition, the Stokes flow equation
has been used for incompressible steady-state simulation with
convection and diffusion.
To capture the concentration distribution between sheath
flow and sample flow concentration, a very fine grid mesh is
needed. However, in this study, normal mesh has been used and
the work is focused on the differentiation between circular and
rectangular shape as shown in Fig. 2 and Fig. 3.
The sheath flow rate and sample flow rate are set as shown
in Table 1. The constant used in simulation are shown in Table
1 and dimension of channel are shown at Table 2. The input
flow rate at the center is 10 µl/min and the input flow rate at the
sheath (both sides) are varied with values of 5, 10 and 15
µl/min, as those are typical and suitable values been used for
microfluidics device in hydrodynamic focusing studies[11].
The sample stream has a relatively high concentration which is
1 mol/m , whereas both sides of sheath stream has a relatively
low concentration which is 0 mol/m as shown at Table 1. The
length of the rectangular microchannel is 3000 μm, while the
width and channel depth are 200 μm and 50 μm respectively.
The channel geometry is chosen by considering the reasonable
design for fabrication purpose. Similarly, the length of the
circular microchannel is 3000 μm whereas its radius is 56.419
μm which gives a cross sectional area of 10,000 μm , similar
to that of the rectangular channel. Both rectangular and circular
shape were drawn using COMSOL shown at Fig. 2 and Fig. 3.
TABLE 1. CONSTANT USED IN SIMULATION
Expression Description Symbols
1e3 [kg/m^3] Density P
1.803e-3 [Pa*s`] Dynamic Viscosity µ
10 [µl/min] Input Flow Rate (Center) Qi
5,10 and 15 [µl/min] Input Flow Rate (Sheath) Qs
1 [um] Entrance Length L(ent)
1 [mol/m^3] Concentration (Center) c1
0 [mol/m^3] Concentration (Sheath) c2
Fig. 2. Circular shape using normal mesh
Fig. 3. Rectangular shape using normal mesh
TABLE 2. DIMENSION OF CHANNEL
Channel Width
( )
Depth
( )
Length
( )
Radius
( )
Rectangular 200 50 3000 -
Circular - - 3000 56.419
IV. RESULTS AND DISCUSSION
A. Relationship between ratio of flow rate ratio and
concentration (focusing width)
From COMSOL simulation using “Transport of Diluted
Species” module package, Fig. 4 and Fig. 5 shows the
simulation of concentration by changing of its sheath flow and
sample flow ratio. The highest ratio in this case give the
smallest focusing width. The sheath flow rate will squeeze the
sample fluid, in which the focusing width will decrease with the
increase of the Qs/Qi ratio. This study indicates that the
hydrodynamic focusing width can be controlled by changing
the sheath flow rate whether in rectangular or circular
microchannel shape Both cross-sectional areas for circular and
rectangular microchannel shapes are similar which is 10,000
μm where the diameter for circular microchannel cross-section
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3. is 112.838 and the width for rectangular microchannel
cross-section is 200 .
Firstly, from Fig. 4 and Fig. 5, we can investigate
relationship between Qs and Qi which influence flow fraction.
Qs and Qi flow ratio can be expressed as r. From the simulation
based on Fig. 4 and Fig. 5, the variation of sheath flow rate
using values of 5 µl/min, 10 µl/min and 15 µl/min caused the
concentration to change significantly especially for rectangular
shape. The focusing width for ratio of flow rate 1.5 has smaller
focusing width and higher concentration value compared with
ratio of flow rate 0.5. It can be concluded that as the flow rate
ratio between sheath flow rate and sample flow rate gets higher,
the focusing width will begin to decrease.
Fig. 4. Shows the comparison between concentration at cross section of width
channel by varying ratio Qs/Qi ( r = 15/10 =1.5 , r = 10/10 = 1 and r = 5/10 =
0.5) for circular shape.
(a) Concentration for ratio of flow rate 1.5 .
(b) Concentration for ratio of flow rate 1.
(c) Concentration for ratio of flow rate 0.5.
(d) Concentration for ratio flow rate (a)1.5,(b)1 and (c)0.5
Fig. 5. Shows the comparison between concentration at cross section of width
channel by varying ratio Qs/Qi ( r = 15/10 =1.5 , r = 10/10 = 1 and r = 5/10 =
0.5 ) for rectangular shape.
(a) Concentration for ratio of flow rate 1.5 .
(b) Concentration for ratio of flow rate 1.
(c) Concentration for ratio of flow rate 0.5.
(d) Concentration for ratio flow rate (a)1.5,(b)1 and (c)0.5
B. Parabolic velocity profile
Fig. 6. Velocity magnitude at cross section of channel for circular shape, at the
(a) start of mixing point, (b) at the middle, and (c) at the end of the channel
Fig. 7. Velocity magnitude at cross section of channel for rectangular shape, at
the (a) start of mixing point, (b) at the middle, and (c) at the end of the channel
Fig. 8. Velocity(m/s) at channel width (a) circular and (b) rectangular
The velocity profiles indicates that the flow is fully
developed laminar flow. The velocity for both circular and
rectangular shapes as shown in Fig. 6, Fig. 7 and Fig. 8 changes
into parabolic flow velocity profile. If the center velocity is
higher, the pressure will become lower, hence it can sustain the
cells to remain in the center stream and continue to travel
individually along the focusing channel. From the simulation,
the higher momentum of the sheath flow towards the center line
of the cytometer can increase the velocity gradients in the
merging layer of the sheath and sample flow. Thus,
compressing the sample fluid to produce smaller focusing width
[12]. From Fig. 6. and Fig. 7. It is shown that the velocities at
the end of channel are highest compare with those at the start of
mixing point and at the middle of the channel for rectangular
shape. However, for circular shape, the change of velocity from
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4. the beginning to the end is not signifcant. As the highest
velocity will occur at the end of the channel, this velocity will
be used as comparison between circular and rectangular shapes.
From Fig. 8, it is shown that the fluid velocity for the circular
shape is higher than velocity for the rectangular shape.
C. Relationship Between Differences Of Geometrical Shape
And Concentration (Focusing Width) Along Channel.
In Fig. 9 and Fig. 10, the sheath flow rate and sample flow
rate ratios are set at 1.5 as it is sufficiently high to give
reasonable focusing width. In these figures, circular shape
maintains its peak concentration along the microchannel at
specific values.
However, the peak concentration for the rectangular shape
decreases from the starting point down to end of channel.
Although larger flow rates ratio can improve the concentration
value, the geometrical shape is significantly important to ensure
the concentration remain at the desired values from the start to
the end of the channel.
Fig. 9. Concentration at cross section of channel for rectangular shape, at the
(a) start of mixing point, (b) at the middle, and (c) at the end of the channel
Fig. 10. Concentration at cross section of channel for circular shape, at the
(a) start of mixing point, (b) at the middle, and at the (c) end of the channel
V. CONCLUSION
In this paper, the effect of geometrical shape on the
hydrodynamic focusing for micro flow cytometer is
investigated. The simulation results showed that changes of
geometrical shape which include circular and rectangular
shapes can change the behavior of hydrodynamic focusing. In
addition, the results also indicated that the circular shape can
maintain the focusing width significantly across the channel
compare to rectangular shape. Likewise, the velocity of circular
shape and rectangular shape in laminar flow will change into
parabolic velocity flow profile with the highest velocity at the
center of the flow channel and a zero velocity at the wall. From
this study, micro flow cytometer studied able to use for human
body cells, however, further studied needed to ensure only one
particle pass through the detection area at one time.
ACKNOWLEDGEMENT
The authors wish to thank Universiti Kebangsaan Malaysia and
The Ministry of Higher Education of Malaysia for providing the
grant used in this project under the project code
FRGS/1/2014/TK03/UKM/03/1. Appreciation also goes to all
the team members in the Institute of Microengineering and
Nanoelectronics (IMEN), Universiti Kebangsaan Malaysia.
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