Sensors and Actuators A 115 (2004) 508–515
Pressure barrier of capillary stop valves in micro sample separators
Tzong-Shyng Leu∗ , Pei-Yu Chang
Department of Aeronautics and Astranautics, National Cheng Kung University, No. 1 University Road, Tainan 701, Taiwan, ROC
Received 22 September 2003; received in revised form 21 January 2004; accepted 1 February 2004
Available online 30 April 2004
Abstract
This paper presents a simple and accurate method for characterizing pressure barrier of capillary stop valves inside micro sample
separators based on active CD-like microfluidics platforms. The capillary stop valves and micro sample separator were fabricated on
polycarbonate (PC) substrates by using hot embossing techniques. The capillary valves stop the flow of liquid inside the microfluidic
devices using a capillary pressure barrier when the channel geometry changes abruptly. Experiments are performed by rotating micro
sample separator on a platform. The liquid sample stopped inside the micro sample separator is expected to be segmented by using density
gradient centrifugation. Various density segments of samples required for an analysis can be separated by simply rotating at different speeds.
Design parameters of the capillary valves used in micro sample separator have been analyzed theoretically. It is shown that the pressure
barrier of capillary valve design can be better predicted by using current modified 3-D meniscus model. Detailed theoretical analyses of
valve behavior is presented and compared with experimental measurement. A model for the valve is then extracted that characterizes the
valve performance for various parameters of capillary stop valves.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Capillary stop valve; LabCD; Micro sample separator; Microfluidic control
1. Introduction
The concept of a micro total analysis system, or a
lab-on-a-chip [1] for integrated chemical and biochemical
analysis or synthesis systems has caused a wide interest recently. An essential part in lab-on-a-chip devices is
the ability to control the sample as it flows through the
device. To fulfill this task, typical lab-on-a-chip devices
have demonstrated controlling the liquid flow by using
pumps, diaphragm valves or electrokinetic methods. These
methods, however, either require both moving parts and
an external actuation mechanism or are very sensitive to
the physicochemical properties of the components and the
presence of trapped air. These factors often complicate the
implementation and integration of a device and cause an
increase of cost in lab-on-a-chip devices.
Current trends in lab-on-a-chip technology suggest a
rapid growth in the need for high throughput, as well as
cost-effective, diagnostic tools in biomedical applications.
One of current technologies proven to be fast, disposable,
and cheap is so-called LabCD [2], a lab-on-a-chip based on
∗ Corresponding author. Tel.: +886-6-275-7575/63638;
fax: +886-6-238-9940.
E-mail address: [email protected] (T.-S. Leu).
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.sna.2004.02.036
CD-like technology and platform. Different from conventional lab-on-a-chip technology, an essential ingredient in
LabCD devices is the ability to control the spatial and temporal position of the sample as it flows through the device with
a CD-player like platform. LabCD devices use centrifugal
force to drive fluid flow by simply rotating the devices on a
platform and exploit the surface tension force to stop flows
in microchannels. The principle of operation is based on
pressure barrier that develops when cross-section or surface
properties of the capillary changes abruptly. These valves
have the advantage of not requiring any moving diaphragm.
Microfluidic capillary-driven valves recently have attracted considerable attention [3–12] and present strong
appeal for applications to various microfluidic systems.
Several fluidic functions on LabCD have been demonstrated
by using capillary valves. Virtanen [13] have presented an
on-chip technique to meter discrete nanoliter-sized liquid
inside microchannel by using micropipette principle. Liquid
flow inside micron-sized channels on LabCD platform can
be controlled by manipulating the centrifugal force and the
capillary force. A sudden expansion (or contraction) channel, called capillary stop valve, is usually used to stop the
fluid by changing the channel geometry. When rotational
speed increases, centrifugal force becomes larger than capillary force. Liquid starts to flow downstream. An angular
T.-S. Leu, P.-Y. Chang / Sensors and Actuators A 115 (2004) 508–515
509
velocity ω called burst frequency [14] is given if centrifugal
force is equal to capillary force as
ω=
γ cos θc
(π2 ρRRdH )1/2
where ω is the angular velocity of CD platform, ␥ the surface tension force per unit length, θ c the contact angle, ρ
the density of liquid, R equals to R2 − R1 , the distance
difference from the center of CD to the capillary stop (R2 )
and reservoir (R1 ), R equals to (R2 + R1 )/2, and dH is the
hydrodynamic diameter of the channel.
When angular velocity is smaller than burst frequency,
liquid will first stop at capillary stops of the micropipettes.
Therefore, liquid sample will first be metered inside a number of micropipettes and excessive liquid overflows into a
bypass chamber.
2. Design, fabrication, and experimental setup
In this paper, we designed and fabricated several passive
capillary stop valves that exploit an easy and accurate analytical model for characterizing pressure barrier of capillary
stop valves using the measurement of pressure barrier on a
LabCD platform. The capillary stop valves will be applied
to a micro sample separator. For sample separation methods
based on density, the sample suspension is metered and layered over a density barrier medium in a separation chamber
followed by centrifugation. After centrifugal separation, low
density and high density samples are separated above and
below the density barrier medium. For conventional method,
low density sample segment is collected by using a pipette.
The proposed micro sample separator uses three overflow
concentration chambers with capillary stop valves for continuous sample separation. For each overflow concentration
chambers, one half of low density part sample is separated.
After several overflow concentration chambers, concentrated low density sample is collected. The design of micro
sample separator is shown in Fig. 1(a). Micro sample separator consists of a separation chamber with two reservoirs on
upstream end and a capillary stop valve on the downstream
end, and three overflow concentration chambers with capillary stop valves. The micro sample separator was fabricated
on polycarbonate (PC) substrates by using hot embossing
techniques. Detailed microfabrication processes are described elsewhere [14]. Fig. 1(b) shows the polycarbonate
micro sample separator chip after hot embossing process.
Experiments are performed by rotating micro sample separator on a platform. The experimental setup consists of a
disk mounted on a dc motor manufactured by Hitachi company. The maximum speed of the motor can reach 4200 rpm.
On the edge of rotational disk, a photo sensor is used to trigger a LED light for synchronized imaging. A CCD camera
coupled to a microscope is used to aid in micro flow visualization. A motor controller is used to control rotational
speed and the rotational speed of motor is monitored by a
Fig. 1. (a) Sketch and (b) photograph of micro sample separator.
digital counter (Autento APD-2P4R) for RPM display. Experiments are performed by rotating micro sample separator
at a angular velocity larger than the burst frequency. Time
evolution of the flow is observed using a microscope (Navita
microscope) and a CCD camera (Toshiba IK-642F). The resulting image sequences are digitized by a frame grabber at
30 frames/s and flow visualization images are used to characterize the surface tension controlled flow phenomena in
the microfluidic devices.
At first, liquid will first stop inside the separation chamber and be segmented using density gradient centrifugation.
As rotational speed increases, valve 1 opens and densitygradient fluid flow into concentration chamber 1 and stops
at valve 2. Various densities of samples required for an
analysis can be separated by simply rotating at different
speeds. For example lower density fluid will be flow into
concentration chamber 2 when the rotational speed is further
increased.
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3. Theoretical analysis of capillary stop valves
The specific problem that we analyze in this paper is the
pressure barrier of fluid using capillary stop valves driven
by centrifugal force. The overall objective is to demonstrate
how to design these valves. For effective implementation,
the physics of capillary stop valves has to be understood,
including the design parameters that it is sensitive to. These
design parameters are difficult to explore experimentally,
theoretical analytical tools, on the other hand, provide an
effective mechanism, and is the focus of this paper.
For better characterizing capillary stop valves, a special
capillary stop valve chip was fabricated on polycarbonate
substrates by using hot embossing techniques, as shown
in Fig. 2(a). On the chip, capillary stop valve was formed
within a region of the microchannel with horizontal sudden expansion at an angle β. The close-up sketch of liquid
front stopped at the capillary stop valve region was shown
in Fig. 2(b). For a typical capillary stop valve, the width
and height of the microchannels are 140 and 30 ␮m, respectively. The aspect ratio (AR) of the microchannel is only
0.214 Two-dimensional (2-D) meniscus model proposed by
Man et al. [12] is no longer valid in such low aspect ratio microchannel. Three-dimensional (3-D) meniscus effects
have to take into consideration even the capillary junctions
expand two-dimensionally.
3.1. Pressure barrier calculation by using 3-D meniscus
model
From the energy perspective, the pressure barrier caused
by surface tension can be explained in terms of energy
changes in a liquid–solid–gas interface system. The total interfacial energy UT of the system is
UT = Asl γsl + Asa γsa + Ala γla
(1)
where Asl , Asa , and Ala , are solid–liquid, solid–air, and
liquid–air interface area and γ sl , γ sa , and γ la its corresponding surface tension forces per unit length. The surface
tension forces per unit length are related to equilibrium
contact angle θ c by Young equation
γsa = γsl + γla cos θc
(2)
Therefore, using Eq. (2) in (1) yields the reduced expression
UT = (Asl + Asa )γsa − Asl γla cos θc + Ala γla
= U0 − Asl γla cos θc + Ala γla = U0 + U
Fig. 2. (a) Picture of a micro capillary stop valve experimental chip. It
consists of reservoir (i), microchannel (ii), capillary stop valve (iii), and
collector (iv). (b) Close-up sketch of capillary stop valve region.
(3)
where U0 (=γla (Asl + Asa )) is a constant since Asl + Asa ,
remain invariant and U is defined as Ala γla − Asl γla cos θc ,
which is variant part of the total interfacial energy UT .
The total interfacial energy UT is a function of the liquid
volume Vl . When Vl increases, the wetted area changes. The
effective pressure P applied on the fluid column can be
deduced from derivative of total interfacial energy UT of the
system with respect to liquid volume Vl .
P = −
dUT
dU
dAsl
dAla
=−
= γla cos θc
−
dVl
dVl
dVl
dVl
(4)
For better predict pressure barrier of a capillary stop valve,
2-D meniscus analysis reported by Man et al. [12] has been
improved to take 3-D meniscus effects into analysis. In 2-D
meniscus analysis, meniscus is assumed to be a circular arc
of angle in only horizontal direction. But in 3-D meniscus
analysis, meniscus shape is assumed to be two circular arcs
of angles in both horizontal and vertical directions. The circular arc angles, as shown in Fig. 2(b), are denoted as 2ah
in horizontal direction and 2av in vertical direction. When
a liquid sample is first introduced in the reservoir (i) in
T.-S. Leu, P.-Y. Chang / Sensors and Actuators A 115 (2004) 508–515
511
Fig. 2(a), it wets in the straight microchannel region (ii) in
Fig. 2(a) and stops at the edge of a sudden expansion (iii)
in Fig. 2(a). At this point, the liquid can be moved forward
only if an external pressure is applied. The pressure needed
for moving liquid forward is defined as the pressure barrier
Ps of capillary stop valve. During fluid moving forward
at the capillary valve, liquid meniscus must change angle to
meet the equilibrium contact angle at the slanted walls. In
this regime, liquid volume increases through a change in aH
and av but the meniscus position remains at x = L position.
Therefore, total interfacial energy UT becomes
∗
UT = U0 − γla cos θc 2L(w + h)
w2
−
2 sin αh
αh
− cos αh
sin αh
whαh αv
sin αh sin αv
liquid volume Vl is
Fig. 3. Interfacial energy vs. sample volume in the capillary system.
(5)
αh
− cos αh
sin αh
αv
wh2 αh
−
− cos αv
4 sin αv sin αh sin αv
w2 h
Vl = wLh −
4 sin αh
(6)
where π/2 − θc ≥ αh ≥ π/2 − θc − β, π/2 − θc ≥ αv ≥
θc − π/2.
Fig. 2(b) shows the design parameters of a capillary stop
valve including: (1) channel height h, (2) channel width w,
and (3) expansion angle β. These design parameters of a
capillary valve will be analyzed theoretically and compared
with experimental results in the following section.
4. Results and discussion
In 3-D meniscus model, both horizontal and vertical
meniscus circular arc angles are considered in the analysis. By first plotting interfacial energy U (= UT − U0 )
as function of liquid volume Vl , the effective pressure P
of the capillary system can be easily calculated derivative
dUT /dVl (=dU/dVl ), by using Eq. (4). Figs. 3 and 4 show
the system interfacial energy U and pressure P as function of liquid volume Vl inside a microchannel of height
h = 30 ␮m, width w = 140 ␮m with different β expansion
angles. Initially, the energy decreases as the liquid sips into
the microchannel with a fixed slope until the capillary stop
region is reached. Beyond the stop outer edge the meniscus must expand. This expansion requires external energy,
therefore, a pressure barrier Ps (shown in Fig. 4) develops
that stops the flow.
Fig. 4. Pressure vs. sample volume in the capillary system.
is also performed for the comparison with 3-D meniscus
analytical and experimental results. In Fig. 5, it is found
that 2-D meniscus analysis reported by Man et al. [12] did
not well predict current experimental results. 3-D meniscus
analysis is found to better predict the experimental results.
The pressure barriers predicted with 3-D meniscus model
0
-10
-20
∆ Ps (KPa)
+ γla
-30
-40
-50
Experimental data
2D model by P.F.Man[12]
3D meniscus model
-60
4.1. Effects of expansion angle β
The results of β expansion angle effects were shown in
Fig. 5. 2-D meniscus analysis reported by Man et al. [12]
20
30
40
50
60
70
80
90
100
Expansion angle β (degree)
Fig. 5. Pressure barrier vs. expansion angle β of the capillary stop valve.
512
T.-S. Leu, P.-Y. Chang / Sensors and Actuators A 115 (2004) 508–515
match the experimental data until β is 50◦ . It is also noticed
the prediction becomes overestimated when β is larger than
50◦ since current simple 3-D meniscus analysis does not
have good enough modeling for the meniscus shapes at four
corners of the capillary junction.
20um β=30
o
20um β=60
o
20um β=90
o
40um β=30
o
40um β=60
o
40um β=90
o
30um β=30
o
30um β=60
o
30um β=90
o
0
-10
In this section, aspect ratio effects of a channel are investigated. The aspect ratio is defined as the channel height to
channel width ratio in the current analysis. Fig. 6 shows the
pressure barrier versus aspect ratio parameter AR of capillary stop valves. For the case of aspect ratio smaller than 1
(AR < 1) in Fig. 6(a), the channel height h is 30 ␮m and
channel width w is increasing from 30 to 300 ␮m. For the
case of aspect ratio larger than 1 (AR > 1) in Fig. 6(b), the
channel width w is 30 ␮m and channel height h is increasing
from 30 to 300 ␮m.
For both capillary stop valve with AR < 1 and AR > 1
channel, the highest pressure barrier (define as the maximum absolute value of Ps since Ps is a negative value)
happens at AR = 1 case. This is because of AR = 1 channel have smallest cross-section area (or hydraulic diameter)
for both AR < 1 and AR > 1 cases. For AR < 1 case
in Fig. 6(a), pressure barrier (Ps ) changes linearly from
AR = 1 to AR < 1. However, the change of pressure barrier (Ps ) becomes nonlinear for AR > 1 cases in Fig. 6(b).
Aspect ratio parameters of a capillary stop valve have dramatically different pressure barrier behavior in AR < 1 and
AR > 1 cases. For AR < 1 case, the width of the channel
increases while the height of the channel is kept at a constant. Because the channel are horizontally expanded with
-50
-60
-70
-80
0
0.2
0.4
0.6
0.8
1
AR
Fig. 7. Pressure barrier vs. aspect ratio (AR) of the capillary stop valve
at different channel heights h and expansion angles β.
different angle β at the capillary stop valve position, channel
width is not the major section of perimeter related to the horizontal sudden expansion of capillary stop valve. Therefore,
it is reasonable that a simple linear relationship between AR
and Ps was found in the analysis. Fig. 7 shows the plot of
linear relationship between Ps and AR for different channel heights h and expansion angles β. In Fig. 7, we can conclude two linear relationships to collapse the data into three
linear curves. The first linear relationship is the same channel height. For example channel height h = 20 ␮m case can
be formulated as
Ps-AR-h20 = mβ (1 − AR) + Ps-w20 h20
(7)
-20
-30
s
∆P ( KPa )
-10
-40
where Ps-AR-h20 is defined as the pressure barrier of channel with aspect ratio AR and height h = 20 ␮m. The mβ
parameters can be found from the analytical results in Fig. 7
and shown as a function of expansion angle β of a capillary
stop valve.
β=30 degree
β=60 degree
β=90 degree
0
-30
s
4.2. Effects of aspect ratio (AR)
∆P (KPa)
-20
-40
β = 30◦
β = 60◦
β = 90◦
-50
-60
0
0.2
0.4
(a)
0.6
0.8
1
AR
0
-20
-30
s
∆P (KPa)
-10
-40
β=30 degree
β=60degree
β=90 degree
-50
-60
(b)
mβ
−17.6244
−51.24
−64.11
0
2
4
AR
6
8
10
Fig. 6. Pressure barrier vs. aspect ratio (AR) of the capillary stop valve
(a) AR < 1 (b) AR > 1.
For the same aspect ratio, but different channel height, we
can conclude the data can be collapse into one linear curve
for each expansion angle by Eq. (8)
20
Ps-AR-h =
× Ps-AR-h20
(8)
h
where Ps-AR-h20 is defined as the pressure barrier of channel with height h = 20 ␮m. Ps-AR-h is the pressure barrier of channel with height h and the same aspect ratio as
Ps-AR-h . By using Eq. (8), Fig. 7 data can be plotted again
in Fig. 8. For the same aspect ratio channel, Fig. 8 shows
the pressure barrier of capillary valve can be simply scaled
by channel height by using Eq. (8).
T.-S. Leu, P.-Y. Chang / Sensors and Actuators A 115 (2004) 508–515
o
o
o
30um β=60
o
30um β=90
20um β=60
20um β=90
0
o
30um β=30
20um β=30
40µm β=30
o
o
40µm β=60
o
40µm β=90
o
-10
∆Ps-AR-h (KPa)
-20
-30
-40
-50
-60
-70
-80
0
0.2
0.4
0.6
0.8
1
AR
Fig. 8. Pressure barrier vs. aspect ratio (AR) of the capillary stop valves
at different channel heights h can be collapsed into one linear curve for
each expansion angles β.
U with respect to sample volume Vl
dAsl
dUT
dU
dAla
P = −
=−
= γla cos θc
−
dVl
dVl
dVl
dVl
513
(4)
In a straight microchannel, P is positive which indicates
the surface tension drives fluid and flow is moving forward.
As soon as the cross-section of the microchannel expands
abruptly, P becomes negative for a hydrophilic surface.
In this situation, surface tension turns out to be a retarded
force that stops the fluid moving forward. Pressure barrier Ps develops and reverse pressure gradient happens
at the capillary stop valve. From the plots of U and P
(=−dU/dVl ) in Figs. 3 and 4, the maximum pressure
barrier Ps happens at the point when the pressure barrier of capillary stop valve breaks and the fluid is moving
forward under external pressure force. At the point, the
shape of meniscus needs to satisfy the boundary condition
for the fluid to move into expansion region. Therefore, to
find the pressure barrier of Eq. (4) can be reformulated
as
dU
dU dx
U2 − U1
x
Ps = −
=
=
(9)
dVl
dx dVl
x
Vl2 − Vl1
Current hot embossing fabrication methods in LabCD
technology suggest most of LabCD device be less-than
1 aspect ratio (AR < 1) channel with horizontal expansion geometry capillary valves design since channel
structures have difficulties to achieve high aspect or vertical expansion by using hot embossing technology. Other
technology for high aspect ratio channel structure, such
LIGA or LIGA-like technology, is not cost-effective in
batch fabrication of LabCD diagnostic biomedical devices.
Current analysis results found to be able to fast and accurately predict a AR < 1 capillary stop valve with horizontal expansion angle β are described as the following
steps:
where subscript 1 and 2 means the physical properties just
before and after the fluid moves into expansion region. For
interfical energy U and sample volume Vl , one can easily
derive the U1 and U2 , as well as sample volume Vl1
and Vl2 just before and after the transition point. Finally,
Eq. (9) becomes
(1) For any AR < 1 capillary stop valve, the pressure barrier
Ps-AR-h with any channel height h and aspect ratio AR
can be calculated by finding its corresponding pressure
barrier Ps-AR-h20 , the same aspect ratio AR but the
channel height h is equal to 20 ␮m, by using Eq. (8).
(10)
20
Ps-AR-h20
h
(2) From the existing database for Ps-w20 h20 , pressure barrier (Ps-AR-h20 ) with the different aspect ratio, but the
same channel height can be easily calculated by using
Eq. (7).
Ps-AR-h =
Ps-AR-h20 = mβ (1 − AR) + Ps-w20 h20
4.3. Analytical solution for pressure barrier at expansion
angle β = 90◦
From Eq. (4), we can calculate the surface tension driven
pressure P by finding the derivative of interfical energy
Ps =
2γla [(cos θc w/cos β) + h
+ (h tan β/sin αh )((αh /sin αh ) − cos αh )
− (αh αv w tan β/sin αh sin αv )]
w[h − (h tan β/sin αh )((αh /sin αh ) − cos αh )
− (w tan βαh /2 sin αh sin αv )
× ((αv /sin αv ) − cos αv )]
Eq. (10) shows the analytical solution for the maximum
pressure barrier valid when expansion angle β = 90◦ . The
analytical solution is proven to be the same as the results
of 3-D meniscus model analysis under the condition at
expansion angle β = 90◦ . For expansion angle less than
90◦ (β < 90◦ ), the 3-D meniscus model analysis provide
more accurate solution to the experimental results than the
analytical solution of Eq. (10).
4.4. Test of micro sample separator
Finally, micro sample separator is put to test while rotational speeds increase from 0 to 1050 rpm. The designed
burst frequency for capillary stop valves 1, 2, and 3, as shown
in Fig. 9(a), are w1 = 640, w2 = 870, and w3 = 1020 rpm,
respectively. At first, liquid stopped (w < w1 ) inside the
separation chamber can be segmented using density gradient centrifugation. As rotational speeds increase to 640 rpm
514
T.-S. Leu, P.-Y. Chang / Sensors and Actuators A 115 (2004) 508–515
Fig. 9. Micro sample separator is tested at different rotational speeds. (a) Dry chip, (b) 640 rpm, (c) 900 rpm, (d) 1050 rpm.
(w1 ≤ w < w2 ), 900 rpm (w2 ≤ w < w3 ) and 1050 rpm
(w3 ≤ w), valves 1, 2, and 3 open sequentially and separate
fluid flow into concentration chamber 1, 2, and 3 based on
the density gradient, as shown in Fig. 9(b–d).
5. Conclusions
We have derived a modified 3-D meniscus model, based
on the 2-D model proposed by Man et al. [12]. The new
3-D meniscus model can better predict the pressure barriers
of capillary stop valves for the micro sample separator. The
results can also provide a simple design tool for capillary
stop valves with any channel height h and aspect ratio AR
as long as the aspect ratio AR is smaller than 1. An analytical solution for the maximum pressure barrier is also provided for LabCD designers. Finally, micro sample separator
is tested to demonstrate the design of capillary stop valves
at different burst frequencies successfully.
Acknowledgements
The project funding was provided by NSC Taiwan
under the contract of “Development of MEMS-based
Lab On A CD Technology for Microfluidic Chip Applications” (NSC-91-2212-E-006-138).
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Biographies
Tzong-Shyng Leu was born in 1963 in Taipei, Taiwan, ROC. He received the both BS and MS degrees in Department of Aeronautics and
Astranautics from National Cheng Kung University, Taiwan in 1985
and 1989. In 1994, he received his PhD degree in mechanical engineering from the University of California, Los Angeles, USA. After graduated from UCLA, he became as a post doctoral scholar in
UCLA. In 1995, he jointed David Sarnoff Research Center in New Jersey as a member of technical staff. During his 3-year stay at David
Sarnoff Research Center, he worked on microsystem imaging by using
X-ray microtomography techniques. In 1999, he jointed School of Mechanical and Production Engineering, Nanyang Technological University
(NTU), Singapore. After staying with NTU, he has been an assistant
professor with Department of Aeronautics and Astronautics, National
Cheng Kung University, Taiwan since August, 1999. His interests are
in the fields of micro thermal/fluidic system. He published more than
20 technical papers in MEMS, Bio-MEMS, and fluid mechanics related
fields.
Pei-Yu Chang received Master of Science degrees from Department of
Aeronautics and Astranautics, National Cheng Kung University in June
2003. Her master research focused on the experimental study of surface
tension control flow phenomenon in microfluidic devices.