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Journal of Micromechanics and Microengineering
J. Micromech. Microeng. 25 (2015) 125006 (12pp)
doi:10.1088/0960-1317/25/12/125006
Microfluidic hydrodynamic focusing for
high-throughput applications
Jingjing Zhao1,2,3,4 and Zheng You1,2,3,4
1
Collaborative Innovation Center for Micro/Nano Fabrication, Device and System, Tsinghua University,
Beijing 100084, People’s Republic of China
2
State Key Laboratory of Precision Measurement Technology and Instrument, Tsinghua University,
Beijing 100084, People’s Republic of China
3
Department of Precision Instrument, Tsinghua University, Beijing 100084, People’s Republic of China
4
Beijing Laboratory for Biomedical Detection Technology and Instrument, Tsinghua University,
Beijing 100084, People’s Republic of China
E-mail: Yz-dpi@mail.tsinghua.edu.cn
Received 17 July 2015
Accepted for publication 2 September 2015
Published 20 October 2015
Abstract
Microfluidic hydrodynamic focusing is critical for chip-based bioanalytical systems to
increase throughput and sensitivity, especially for microflow cytometers, enabling a sample
flow to be confined to the center of a microchannel with a narrow cross-section. Current
microfluidic hydrodynamic focusing designs are usually unable to maintain stable focusing
in high flow velocity conditions, resulting in a large cross-section or even failed focusing.
To overcome this challenge, this paper aims to develop a design that can achieve effective
microfluidic hydrodynamic focusing at high velocity with favorable performance. For this
purpose, specially designed structures and arc-shaped channels are used. Two focusing regions
are modeled and optimized mathematically, and flow behavior is investigated using numerical
simulations. The functional relationship between flow rates and the cross-sectional dimensions
of the focused sample flow is explored, and a measurement method for testing the dimensions
is developed. The design is implemented in glass chips and characterized experimentally. In a
rectangular channel with a cross-section of 300 μm × 150 μm the sample flow can be focused
down to 5–11 μm horizontally and 10–21 μm vertically at a roughly constant velocity of
4.4 m s−1 when the sample flow rate varies between 10 and 60 μl min−1. Effective focusing is
accessible within a wide velocity range from 0.7 to 10 m s−1. The experimental results validate
that the focusing design performs better than existing microfluidic designs at high velocities,
while its performance is close to that of the designs used in conventional flow cytometers
with much less volume and a simpler structure. The focusing design can serve as the basis for
microflow cytometers or it can be integrated into various microfluidic systems where complete
focusing is needed.
Keywords: hydrodynamic focusing, microflow cytometer, microfluidics
(Some figures may appear in colour only in the online journal)
1. Introduction
of their large size, complicated structure and high cost, as well
as the high-level competence requirements for operation personnel. Recently, advances in microfluidic technology have
raised the possibility of developing compact, user friendly,
portable and inexpensive microflow cytometers. Microfluidic
focusing of biological particles or a sample flow is an essential functionality for microflow cytometers and is critical to
As powerful instruments for biomedical research and clinical
diagnosis, conventional flow cytometers have been widely
used and developed for more than 50 years [1]. Though
capable of analyzing biological particles accurately and rapidly, conventional flow cytometers are not easy to use because
0960-1317/15/125006+12$33.00
1
© 2015 IOP Publishing Ltd
Printed in the UK
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
horizontal focusing regions. The sheath flow rates for vertical
and horizontal focusing are controlled separately, mainly to
enhance the ability to adjust the vertical and horizontal dimensions of the focused sample flow. Because of the limitations
of planar microfabrication technology, channels can be curvy
in the horizontal direction but not in the vertical direction,
meaning that the vertical focusing region has a larger local
loss coefficient than the horizontal focusing region. Taking
into consideration the fact that the flow rate and velocity in the
first focusing region are much lower than those in the second,
vertical focusing is implemented before horizontal focusing in
order to maintain smooth flows and improve focusing stability.
There are four symmetrical sheath flow channels and
a main channel in the vertical focusing region, where the
sample flow is confined vertically by the four vertical focusing
sheath flows. Then, in the horizontal focusing region two symmetrical sheath flow channels merge into the main channel, all
of the channels within the same layer, and the sample flow is
squeezed between the two horizontal focusing sheath flows.
After being vertically and then horizontally focused, the
sample flow is completely encircled by sheath flows and confined in the center of the main channel, and it becomes very
narrow. Laminar flows are critical for hydrodynamic focusing
and smooth transitions are necessary to lead the sheath flows
and the sample flow into the main channel. Hence microfluidic
channels are designed with curved profiles, which are useful
for keeping flows stable, typically at high velocities. The
details of the design are presented in the following sections.
The relationship between the flow rates and the dimensions
of the focused sample flow is investigated. According to the
hydrodynamics principle [34], the velocity profile of a fully
developed laminar flow in a straight rectangular channel can
be formulated as equation (1) (see figures 1(b) and (c)),
the performance of cytometers for counting, analyzing and
sorting biological particles [2]. To date, a number of focusing
methods based on different physical mechanisms have been
developed, with the main ones being hydrodynamic focusing;
electrokinetic focusing (electrophoresis [3], electroomosis
[4, 5] and dielectrophoresis [6–8]); acoustic focusing [9, 10];
inertial focusing [11–14]; and microstructure focusing (micro
grooves [15], stepped channels [16, 17], micro weirs or obstacles [18–20]). In comparison to other methods, hydrodynamic
focusing benefits from its low sensitivity to flow rates and from
having no requirement for particular electrokinetic or acoustic
properties for the biological particles or fluids, while it can
operate effectively at high flow velocities, easily achieving a
high throughput. Due to sheath flow demands and the limitations of planar microfabrication techniques, hydrodynamic
focusing in microfluidic chips is usually implemented in the
horizontal direction [21–23]. It is difficult to accomplish vertical focusing or three-dimensional (3D) focusing (vertical
and horizontal). Even so, some 3D hydrodynamic focusing
designs have been established in microfluidic chips by manipulating multiple sheath flows to fully envelop the sample flow
[24–33]. But the focusing performance of these designs is
inferior to that of conventional flow cytometers with slower
sample flow rates and larger focused dimensions, as listed in
table 1. In addition, these designs generally require complex
fabrication processes, some of which are incompatible with
conventional microfabrication processes.
To overcome these challenges, this work studies a 3D microfluidic hydrodynamic focusing design for high-throughput
applications, in particular microflow cytometers. It aims to
achieve a similar focusing performance to conventional flow
cytometers. The design mainly comprises two parts: vertical
and horizontal focusing regions. The regions are modeled,
analyzed, simulated and optimized for the purpose of keeping
flows laminar over a wide velocity range, particularly at high
velocities. High velocities are essential for high throughput.
In addition, the functional relationship between flow rates
and the cross-sectional dimensions of the focused sample
flow is explored, which can be used to control or predict the
focusing results, and a measurement method for testing the
dimensions is developed. For experimental testing, the design
is established in a microfluidic chip formed by laminating five
micromachined glass plates. The chip then exhibits a focusing
performance close to that of BD Accuri C6, a conventional
flow cytometer. It is proved that this 3D focusing design is
effective and powerful. Furthermore, the design process, the
method for predicting focusing performance and the measurement method can be useful for designing other microfluidic
systems.
∞
cosh[(2n + 1)πy /b] ⎫
4b 2 ⎛⎜ dP ⎞⎟
(−1)n ⎧
⎨1 −
⎬
−
∑
3⎝
3
cosh[(2n + 1)πa /2b] ⎭
μπ
dx ⎠ n = 0 (2n + 1) ⎩
(2n + 1)πz
× cos
,
(1)
b
v=
where a is the channel width, b is the channel height and P
is the pressure. Obviously, the velocity is along the channel
direction and the velocity component in the cross-section is
zero. In addition, the maximum velocity occurs at the center.
Equations (2) and (3) respectively present the formulas of the
maximum velocity VMAX and the average velocity VAVR, as
shown below:
4b 2 ⎛⎜ dP ⎞⎟
(−1)n
−
∑
3⎝
dx ⎠ n = 0 (2n + 1)3
μπ
⎧
⎫
1
⎬
× ⎨1 −
⎩
cosh[(2n + 1)πa /2b] ⎭
∞
VMAX = v y = z = 0 =
2. Design
2.1. Principal design
VAVR =
The hydrodynamic focusing design is composed of three
layers of rectangular microfluidic channels, whose concept is
illustrated in figure 1(a). In terms of function, the focusing
design is divided into two major parts: the vertical and
2
⎛
⎞
∬A vdAA = 12bμπ 3 ⎝− ddPx ⎠
⎜
⎟
∞
⎧
192b
tanh[(2n + 1)πa /2b] ⎫
⎬,
× ⎨1 − 5 ∑
π a n=0
(2n + 1)5
⎩
⎭
2
(2)
(3)
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
Table 1. 3D hydrodynamic focusing performance of microfluidic chips and conventional flow cytometers.
Focusing channel
a
b
Dimensions
(μm)
Focused sample flow
Cross-section
Hydraulic
diameter (μm)
Flow rate
(μl min−1)
Velocity
(m s−1)
Shape
Dimensions (μm)
Ellipse
Circle
23b × 8.5b
30 (Designed value)
350b × 80b
13b × 25b
20b × 30
10 × 10
4 × 6, 7 × 6,
12 × 10, 14 × 13
5 × 5, 5 × 6, 9 × 8,
10 × 13, 22 × 11
6.5a, 11a, 15a
10, 16, 22
Type
Shape
Micro 1 [26]
Micro 2 [27]
Micro 3 [28]
Micro 4 [29]
Micro 5 [30]
Micro 6 [31]
Micro 7 [32]
Rectangle
100 × 95
Square
300
Rectangle
1000 × 500
Rectangle
100 × 50
Rectangle
100 × 110
Square
100 × 100
Quasi-circle 125 × 125
97
300
670
67
105
100
125
3.3
60
0.16
3
2.5
1
up to 3
0.1, 2, 16, 20
0.13a–0.15a Rectangle
0.15
Spindle
Square
3
Quasi-circle
Micro 8 [33]
Quasi-circle
100 × 100
100
0.2, 1, 10, 24, 48 3
Ellipse
BD Calibur
BD Accuri C6
Rectangle
Circle
430 × 180
200
254
200
12, 35, 60
14, 35, 66
Circle
Circle
6
3a
The values are calculated roughly, using the relationship between the flow rate, velocity and dimensions.
The dimensions are measured from the published microscopic images.
Figure 1. (a) Schematic diagram of the 3D hydrodynamic focusing design. (b) Flow in a rectangular channel. (c) Velocity profile in a
straight rectangular channel, the blue-to-red rainbow represents the flow-velocity magnitude distribution. (d) Flows distribution in a channel
cross-section.
⎧
⎪QS = A v dA = VSwh
S
⎪
⎪
v dA
⎨Q VS =
,
(4)
AVS
⎪
⎪
v dA
⎪QHS =
⎩
AHS
where A is the cross-sectional area of the channel. It is assumed
that after 3D focusing the sample flow and sheath flows are
represented by the rectangular cross-sections in figure 1(d).
Combining this assumption, the velocity profile and mass
conservation, the relationship between the flow rates and the
cross-sectional dimensions is given by
∬
∬
∬
3
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
where w and h are respectively the width and height of the
focused sample flow, QS is the sample flow rate, VS is the
sample flow velocity after 3D focusing, QVS is the total flow
rate of the vertical focusing sheath flows, QHS is the total flow
rate of the horizontal focusing sheath flows, and AS, AVS and
AHS represent the cross-sectional areas of the sample flow,
vertical focusing sheath flows and horizontal focusing sheath
flows respectively. Absolutely, the distributions of the sample
flow and the sheath flows described in figure 1(d) are very
simple, without taking account of details of the interfaces
between neighboring flows. However, the relationship can
give an approximation to the above parameters and predict the
focusing performance.
This design aims to achieve a similar focusing performance to conventional flow cytometers, specifically in terms
of sample flow rate, sample flow velocity and the dimensions
of the focused sample flow. Referring to conventional flow
cytometers, the main channel is designed to be 300 μm in
width and 150 μm in height, with a hydrodynamic diameter
of 200 μm. For fabrication convenience, all the microchannels are 150 μm in height. According to equations (2) and (3),
the maximum velocity VMAX at the center of the main channel
is 2.05 times the average velocity VAVR of the fluid. In addition, the sample flow velocity VS is almost equal to the
maximum velocity VMAX, because of the central position and
the narrow profile of the focused sample flow. To achieve high
throughput, the sample flow rate QS is set within a range of
10–75 μl min−1. For a narrow flow, the cross-sectional dimensions of the focused sample flow are expected to be below
22 μm in both the horizontal and vertical directions. Assuming
the focused sample flow is with a square cross-section, several sets of parameters are designed (as listed in table 2) that
conform to the functional relationship established above. Sets
1–3 are chosen according to the rates of conventional flow
cytometers in table 1, to test the focusing performance when
the sample flow rate varies between 10 and 60 μl min−1 with
roughly constant velocities. In sets 1, 4 and 5, the flow rate
ratios among QS, QVS and QHS are the same, theoretically
leading to the same dimensions of the focused sample flow.
The three sets will demonstrate that the flow rate ratios are
available to control the sample-flow cross-section dimensions.
Set 6 is to further explore the potential of effective focusing
at high velocities. These sets will be used to investigate the
focusing characteristics through numerical simulations and
practical experiments.
Table 2. Five sets of flow rates to test focusing performance.
Flow rate
(μl min−1)
Flow velocity
(m s−1)
Dimensions
No.
QS
QVS
QHS
VS
VAVR
w = h
(μm)
wh
(μm2)
1
2
3
4
5
6
60
30
10
30
10
75
360
260
160
180
60
650
5800
5900
6000
2900
967
14750
4.44
4.13
4.63
2.22
0.74
10.33
2.30
2.29
2.29
1.15
0.38
5.73
15
11
6
15
15
11
225
121
36
225
225
121
The curved profile of sheath flow channels is the key to
keeping flows stable, so it is modeled and optimized. The
inner and outer curves of one sheath flow channel are two
circular arcs, and circles of the arcs are tangent to the main
channel at points Ci and Co respectively. The radii of the two
arcs are Ri and Ro, the central angles are α and (α − αo), and
the centers are points Oi and Oo (Oi is out of sight). Lo is the
distance between the points Ci and Co. Ls is the length of the
downstream main channel. Ws approximately represents the
width of the sheath flow channel at the confluence of the three
flows. Wsh represents the width of the sheath flow channel
at the entrance. θ is the angle between the y-direction and
the cross-section of the sheath flow channel at the entrance.
W, d, β and αo are auxiliary parameters, defined as shown in
figure 2. The parameters mentioned above can be expressed
by equation (5). It shows that Ri, Ro, α, αo and Lo are a set
of independent geometrical parameters for completely
describing the design.
⎧
W
⎪ β =arctan
Lo
⎪
Lo
⎪
⎪ Ri = sin 2β
⎪
⎪ d = R (1 − cos α )
o
o
⎨
.
⎪Ws = W2 + (Ro sin αo )2
⎪
⎪Wsh = [L o + (Ro − Ri ) sin α]2 + [(Ri − Ro )(1 − cos α)]2
⎪
⎪ θ = arctan L o + (Ro − Ri ) sin α
(5)
⎪
(Ri − Ro )(1 − cos α)
⎩
For a more reasonable design, the effects of the parameters
on focusing performance are analyzed. Numerical simulations
(using COMSOL Multiphysics software) prove that increasing
Ri and Ro and keeping α below 45° are practical measures
to reduce secondary flows, which can aggravate flow disturbances and deviate the sample flow from the central position.
Specifically, Ri and Ro are at least three times as large as Ws.
In addition, increasing Lo and decreasing β can improve the
stability and eliminate vortices in the main channel. Where
the sample flow and the two sheath flows meet, the pressure
difference between them should be reduced in order to prevent
mixing and achieve effective focusing. Thus the velocities of
the three flows should be similar and the ratio of QHS/2Ws to
QA/b close to one. Wsh and θ need to be close to Ws and α respectively with respect to smooth flowing. When considering glass
2.2. Horizontal focusing design
The microfluidic structure of the horizontal focusing region
is simpler than that of the vertical focusing region, and it is
discussed first. Figure 2 shows the schematic of the horizontal focusing region. Along the two symmetrical curved
channels, sheath flows turn smoothly to the direction parallel
to the main channel and gradually confine flow QA horizontally. The flow rate of each horizontal focusing sheath flow is
QHS/2 and the rate of the fluid flowing into the main channel is
QA (QA = QS + QVS).
4
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
Figure 2. Schematic of the horizontal focusing region.
horizontal focusing design featuring straight sheath flow channels, as shown in figure 3. The cross-sectional dimensions of
the channels of the commonly used design in figure 3(a) are
all 300 μm × 150 μm, and are the same as those for the main
channel in figure 3(b). The flow rates in the two conditions are
the same and the average velocity after focusing is 2.3 m s−1
for both. The focusing fails in the commonly used design
(effective focusing can be achieved when the average velocity
is lower than 0.3 m s−1). This is mainly because the sample
flow is severely affected by the two sheath flows, and the
sample flow can even be broken up into several small flows
as the velocity increases. There are two factors involved: first,
the straight sheath channels cannot reduce the y-direction
momenta brought in by the sheath flows; second, the velocity
(dynamic pressure) difference between the sample flow
and the sheath flows is large. In our design, the symmetric
momenta and the velocity difference are reduced respectively
by the curved shapes and the larger widths of the sheath channels. Obviously, the design developed here has advantages of
smooth flow, effective focusing at high flow velocity, a more
uniform pressure gradient and greater stability.
micromachining and bonding, it is better that d be no less than
100 μm. In geometry, ∠AOiCi is larger than ∠BOiCi. Based
on the above considerations, the constraint relations between
the parameters and the value ranges are presented in equations (6) and (7). Furthermore, several solutions are obtained
using MATLAB software and then simulated via COMSOL.
Among them, it is found that the solution of Ri = 17500 μm,
Ro = 6600 μm, α = 30°, αo = 10° and Lo = 6500 μm has
good stability, few secondary flows and low pressure loss, so
it is selected for the design. Additionally, the simulated results
show that in the main channel a distance of at least 5–6 mm is
necessary for the focused sample flow to fully accelerate and
reach a stable state. Therefore, Ls is assigned at 10 mm for
redundancy.
⎧ Ro ⩾ 3Ws
⎪Q
⎪ SH − 1.5 ⩽ Ws ⩽ QSH +1.5
b
2QA
⎪ 2QA
⎪α > 2β
⎪
⎪
θ
⎨ 0.8 ⩽ ⩽ 1.2
(6)
α
⎪
⎪
Wsh
⎪1 ⩽ W ⩽ 1.25
s
⎪
⎪ β < 20°
⎪ d ⩾ 100 μ m
⎩
2.3. Vertical focusing design
The structure of the vertical focusing region is composed of
three layers of rectangular microfluidic channels. There are
two curved channels in both the upper layer and the lower
layer, and there is a straight main channel in the medium
layer. The dimensions of the main channel have been discussed above and the upper and lower layers have the same
microfluidic structure. Therefore, the design is focused on the
upper/lower layers, for which the channel configuration is presented in figure 4(a). Two sheath flow channels combine into
a straight channel. At the end of the straight channel, sheath
⎧ 4000 μ m⩽ L o ⩽ 8000 μ m
⎪
⎪ 20° ⩽ α ⩽ 45°
⎨ 5 °⩽ α o ⩽ 15°
.
(7)
⎪ 3b ⩽ W ⩽ 6b
⎪
⎩15b ⩽ Ro ⩽ 25b
To show the improvement in focusing performance, this
design is simulatively compared with a commonly used
5
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
Figure 3. The flow rates from the first parametric set in table 2. The rainbow-colored streamlines represent the flow QA and the green
streamlines represent the sheath flows. (a) Simulated results for a commonly used horizontal focusing design. (b) Simulated results of
the design developed in this paper.
⎧Ws = (Ri cos α o + Lo sin α o + Ro sin2 α o )
⎪
⎪ −[(Ri cos α o + Lo sin α o + Ro sin2 α o )2 − (Lo + Ro sin α o )2 ]1/2
⎪
⎪α =arccos⎛⎜1 − b ⎞⎟
⎪ o
⎝
2Ro ⎠
⎪
Ws cos α o
⎪ β=arctan
⎨
Lo + (Ro − Ws ) sin α o
⎪
L
+
⎪ Ri = o (Ro − Ws ) sin α o
⎪
sin 2β
⎪
⎪Wsv = [L o + (Ro − Ri ) sin α ]2 + [(Ri − Ro )(1 − cos α ) − b /2]2
⎪
L o + (Ro − Ri ) sin α
⎪θ = arctan
(8)
(Ri − Ro )(1 − cos α ) − b /2
⎩
flows are pressed into the main channel and the sample flow
in the main channel is focused vertically by the two sheath
flows from above and below. The two symmetrical sheath
channels of the upper/lower layers contribute to the reduction
of the horizontal momentum caused by the two sheath flows,
enhancing stability. Similar to the horizontal focusing design,
the inner and outer curves of one sheath flow channel are circular arcs. The inner arc is tangent to the straight channel at
point Ci, and the circle of the outer arc touches the middle
line of the straight channel at tangent point Co. The channels
are modeled as expressed by equation (8). Equations (9) and
(10) are constraint relations and value ranges. Using the same
method as for the horizontal focusing design, a relatively
optimal solution is found, with Ri = 11300 μm, Ro = 9900
μm, α = 30°, Lo = 900 μm, Lsv = 1500 μm and Ls = 2000
μm. The focusing performance is predicted by the simulations
in figures 4(b) and (c). The vertically confined sample flow
features a flying-saucer shape.
⎧Ws ≈ b
⎪
⎪α > 2β
⎨ 0.8α ⩽ θ ⩽ 1.2α
(9)
⎪W ⩽ W ⩽ 1.5W
sh
s
⎪ s
⎩ β < 20°
6
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
Figure 4. (a) Schematic of the vertical focusing region and design parameters. (b) The simulated results for vertical focusing and the flow
rates are from the first parametric set in table 2 (only the sample flow is visible). (c) The cross-section of the focused flows, the rainbowcolored streamlines represent the sample flow and the blue streamlines represent the sheath flows.
Figure 5. Flows distribution in the channel cross-section: the rainbow-colored streamlines are for the sample flow, the blue streamlines are
for the vertical focusing sheath flows and the green streamlines are for the horizontal focusing sheath flows. A rectangle approximates the
cross-section of the focused sample flow.
⎧ 500 μ m⩽ L o ⩽ 5000 μm
⎨
.
(10)
⎩ 20° ⩽ α ⩽ 45°
3. Experimental methods
3.1. Chip fabrication
For practicality, the 3D focusing design developed above is
furnished with inlet and outlet channels for the introduction
of flows into and out of the focusing regions, as illustrated in
figure 6(a). Microfluidic chips were fabricated to experimentally characterize the focusing performance of the design.
To fabricate one chip, five micromachined glass plates
were used, as shown in figure 6(b). The three inner plates
were 150 μm thick, and in these the microfluidic channels were caved. The two outer plates served as covers
2.4. Simulation testing
Simulations show that the design can achieve 3D focusing, as
illustrated in figure 5. The focused sample flow features quasirectangular cross-sections, which is similar to the assumption
shown in figure 1(d). And the cross-section is approximated
to a rectangle with a height h and a width w. It indicates that
numerical simulation is able to predict the dimensions of the
focused sample flow.
7
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
Figure 6. (a) The focusing design is furnished with five inlets and an outlet. (b) Five glass plates for one chip. (c) Photograph of a chip; the
chip is filled with blue dye solution for visualization.
Figure 7. Experimental setup.
for protection, optical observation, fluid connection and
installation. The five plates were successfully bonded
using two methods, thermal and UV adhesive bonding.
Figure 6(c) is a photograph of the chip.
3.2. Experimental setup
Figure 7 illustrates the experimental setup utilized to visualize flows in the chip and quantify the dimensions of the
focused sample flow. The sheath flows were distilled water,
8
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
Figure 8. Schematic diagram of the measurement method.
Figure 9. This experiment was run with the first set of flow rates listed in table 2. (a) Flow behaviors in some key regions. (b) Microscopic
image of the focused sample flow with α = 0. (c) Microscopic image of the focused sample flow with α = 30°.
and the sample flow was distilled water dyed with Remazol
Brilliant Blue dye. Three syringe pumps were manipulated to drive flows, enabling individual control of the
sample flow and the vertical and horizontal focusing sheath
flows. The two inlets for the vertical/horizontal focusing
sheath flows were connected to one syringe pump using
an off-chip Y-shaped connector. Microscopic images were
obtained from a microscope equipped with a CCD camera.
The dimensions were measured using an image processing
technique.
3.3. Measurement method
As discussed above, the cross-section of the focused sample
flow is approximated by a rectangle with a height h and a width
w. A method is developed to measure h and w. It consists of
two steps. First, keeping the flow rates constant, several microscopic images are captured when α (the angle between the
microscope and the direction perpendicular to the chip) varies,
and the sample flow width m at every angle is measured, as
shown in figure 8. The functional relationship between α, h,
9
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
Figure 10. The fitted curves and the measured data: (a) experiment 1, (b) experiment 2, (c) experiment 3, (d) experiment 4, (e) experiment
5 and (f) experiment 6.
4. Results and discussions
w and m is expressed by equation (11), where nw is the refractive index of water. Second, a fitted curve of the independent
variable α versus the dependent variable m is obtained using
MATLAB. With the curve and equation (11), the values of h
and w can be obtained. In experiments, α was set to 0°, 5°,
10°, 15°, 20°, 25°, 30° and nw was 4/3. By this method, the
width and height of the main channel were calculated to be
306 μm and 148 μm respectively, which was very close to the
actual values 313 μm and 153 μm observed directly by microscope. It proved that this method is reasonable.
Experiments were implemented to test the focusing performance of the microfluidic chips. Figure 9(a) presents the actual
flow behaviors in some key regions, which agreed well with
the simulated results. There existed a sharp interface between
the sample flow and the sheath flows, implying that the flows
in the channels stayed laminar and no mixing occurred. It
proved that the focusing design has good stability under high
flow velocity conditions. Figures 9(b) and (c) are two typical
microscopic images of the 3D focused sample flow in the main
channel. The former is the top view and shows that the sample
flow was confined to the horizontal center. The latter image
⎛
sin α ⎞
m = w cos α + h cos α tan⎜arcsin
⎟.
(11)
⎝
nw ⎠
10
J Zhao and Z You
J. Micromech. Microeng. 25 (2015) 125006
Table 3. Dimensions of the focused sample flow.
Designed valuea
a
b
Experimental value
Simulated value
No.
QS (μl min−1)
VS (m s−1) wh (μm2)
w (μm)b
h (μm)b
wh (μm2)
VS (m s−1) w (μm)
h (μm)
1
2
3
4
5
6
60
30
10
30
10
75
4.44
4.13
4.63
2.22
0.74
10.33
10.72 ± 0.34
6.04 ± 0.58
4.27 ± 0.23
10.85 ± 0.31
11.87 ± 0.51
6.89 ± 0.38
21.03 ± 1.49
18.86 ± 2.52
9.74 ± 1.00
20.2 ± 1.34
18.45 ± 2.21
17.74 ± 1.67
225
114
42
219
219
122
4.44
4.38
4.00
2.28
0.83
10.24
24
19
12
22
22
20
152 = 225
112 = 121
62 = 36
152 = 225
152 = 225
112 = 121
11
7
4
12
14
6
The designed values are coincident with the values in table 2.
Mean value ± 95% confidence interval (CI).
focused sample flow, and the performance is comparable to
that of some conventional flow cytometers.
was captured at α = 30° and shows that the sample flow width
was much smaller than channel height, indicating that vertical
focusing was accomplished successfully.
To quantify the focusing performance, experiments were
carried out according to the sets of flow rates listed in table 2,
and the measurement method developed above was utilized.
The measured data and the fitted curves relating to each set
are plotted in figure 10. Referring to the fitted-curve formulas,
the experimental values of w and h under every flow condition
were obtained and listed in table 3. Simulations were utilized
as an auxiliary method to qualitatively describe the dimensions, as presented in figure 5. The simulated values of w and
h were also listed in table 3, showing good agreement with
the experimental values for all the cases studied. Although
both the experimental and the simulated results showed that
the focused sample flow had a quasi-rectangular cross-section
(w ≠ h), which was different from the square shape (w = h)
designed in table 2, the sectional areas (w × h) calculated by
the experimental values were similar to the designed values.
It proved that the functional relationship between the flow
rates and the cross-sectional dimensions of flows expressed
by equation (4) was practical, offering a way to control the
dimensions by adjusting flow rates. The sample flow velocities (VS = QS /wh) were calculated using the experimental
results of w and h, which were in good agreement with the
theoretical velocities, as shown in table 3.
In table 3, experiments 1–3 show that this focusing design
was able to confine the sample flow effectively down to 5–11
μm horizontally and 10–21 μm vertically, when the sample
flow rate varied between 10 and 60 μl min−1 with a roughly
constant velocity of 4.4 m s−1. In experiments 1, 4 and 5,
the flow rate ratios among QS, QVS and QHS were the same,
resulting in almost the same dimensions for the focused sample
flow. It was noted that the flow rate ratios were available to
control the sample-flow cross-section dimensions, which was
in accordance with equation (4). Experiment 6 demonstrates
that the design was able to focus effectively at high velocities of 10 m s−1, thus having the potential for a very high
throughput. Effective focusing was accessible within a wide
velocity range from 0.7 to 10 m s−1. Compared with the other
microfluidic hydrodynamic focusing designs listed in table 1,
this design features superior performance in terms of sample
flow rate, velocity and the cross-sectional dimensions of the
5. Conclusions
This paper describes a 3D hydrodynamic focusing design
that is based on the microfluidic technique and is capable of
effective focusing at high flow velocity. Multiple attempts are
made to maintain stable flows and achieve better focusing
performance, including modeling and optimizing the channel
geometry and establishing simulating tests. The research
studies two further aspects: the mathematical relationship
between the flow rates and the focusing results, and a measurement method. Both of them are verified by experiments.
The design is easily constructed in a multilayer glass microfluidic chip. In practical terms, this design is able to confine
the sample flow down to 5–11 μm horizontally and 10–21 μm
vertically within a sample flow rate range of 10 to 75 μl min−1
and a velocity range of 0.7 to 10 m s−1, which is necessary for
high-throughput flow cytometry analysis. The design offers
a similar hydrodynamic focusing performance to some conventional flow cytometers, while occupying a much smaller
volume and using a simpler structure. The 3D hydrodynamic
design proposed in this paper seems suitable for microflow
cytometers, especially for those requiring high-throughput
analysis. In addition, this design has the potential to be incorporated into other microfluidic systems where 3D focusing is
needed.
Acknowledgments
This work was supported by the Beijing Municipal Education
Commission (Fund for Joint Project of Beijing).
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