INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF MICROMECHANICS AND MICROENGINEERING
J. Micromech. Microeng. 13 (2003) S125–S130
PII: S0960-1317(03)59919-3
Design and theoretical evaluation of a
novel microfluidic device to be used for
PCR
Minqiang Bu1, Tracy Melvin1, Graham Ensell1,
James S Wilkinson2 and Alan G R Evans1
1
Microelectronics Research Centre, Department of Electronics and Computer Science,
University of Southampton Highfield, Southampton, SO17 1BJ, UK
2
Optoelectronics Research Centre, University of Southampton, Highfield, Southampton,
SO17 1BJ, UK
E-mail: [email protected]
Received 24 February 2003, in final form 7 May 2003
Published 13 June 2003
Online at stacks.iop.org/JMM/13/S125
Abstract
The design of a novel, microfluidic chip with an integrated micro
peristaltic pump and chambers for DNA amplification is described.
This chip contains three reaction chambers stable at 90 ◦ C, 72 ◦ C and
55 ◦ C for PCR amplification, a bi-directional peristaltic pump and
optical integrated detection of the droplet. A reactant droplet is to be
introduced into the device, pumped back and forth between the chambers by
the micro peristaltic pump for sample processing. The static behaviour of
the micro pump was modelled theoretically in order to evaluate the optimal
dimensions for the pump membranes and to obtain the maximum flow rate.
Thermal analysis by the finite element method was performed to optimize
the location of the heaters and the temperature uniformity over the three
reaction chambers. Transient thermal analysis indicates that the reactant
droplet can be heated/cooled in the proposed device in less than 1 s to
achieve the desired temperatures.
1. Introduction
The creation of µTAS devices for a number of applications
for biological sample processing involving a PCR step has
been reported. All involve the seamless pumping of fluids
from one process step to the next via the whole fluidic circuit
[1–4]. The transfer of microlitre volumes of reactants as
droplets around µTAS devices between reaction chambers
remains a challenge and will offer significant advantages
[2]. Most notably, realization of this concept will offer the
potential for multi-step processing of very small volumes of
sample as well as, if necessary the addition of reagents within
one of the steps in a multi-step process. PCR is perhaps
one of the most common procedures used for the analysis
of clinical samples, genetically modified foods, detection of
bacterial warfare agents and forensic analysis. However,
in addition, PCR reactions are an integral part of many
(highly laborious) biomedical research assays for recombinant
0960-1317/03/040125+06$30.00
DNA/protein techniques and gene expression studies using
DNA microarrays.
Miniaturized PCR chips have many advantages over
conventional PCR devices, such as portability, quicker thermal
cycling, smaller reactant quantities and more convenient
integration of DNA amplification with sample preparation [1]
or product detection [1, 3–6]. The micro PCR chips developed
so far can be classified into two types, chamber PCR chips
[3–10] and continuous flow PCR chips [11–17]. The first,
chamber PCR devices consist of a small reservoir etched into
silicon often with a Pyrex cover and integrated heaters [5–10].
The practical advantage of these devices is in the small sample
size, the very rapid thermal heating and cooling and the
relative ease of temperature cycling programme control and
modification needed for the PCR reaction of different DNA
samples. The continuous flow PCR devices, pioneered by
Kopp et al, consist of a serpentine channel etched in glass
[11–15]. The PCR reactants are flowed over three [11–14] or
© 2003 IOP Publishing Ltd Printed in the UK
S125
M Bu et al
Z
Inlet
hole
Etched pump
membrane
Outlet
hole
PZT disc
Pyrex
wafer
Section line
Y-Y’ for figure
5 (d), (e)
Y’
Silicon
wafer
Wire
bonding
hole
Z’
Section line
X’ X-X’ for
figure 5 (a)
Heat sink
Pt Temperature
sensor
Pt heaters
90°C
72°C
55°C
Reaction
chambers
Thermal
isolation
recess
pn-diode
X
Optical
fibre
Pyrex
Connection channel
between pump
chambers
Connection channel
Y
between pump and
reaction chamber
PZT disc
Silicon
Optical fibre
pn-diode
Connection channel
Cr membrane
Pump structure from cross sectional area Z-Z’
Figure 1. A schematic view of the pump PCR chip. For simplification the upper glass wafer and the lower silicon wafer are illustrated apart,
although in the actual device both wafers are connected by anodic bonding. The lower left insert figure shows an expanded view of the
reaction chamber and the lower right insert shows the cross section of the micro pump.
two [15] temperature zones. Extension and elaboration of this
approach has been reported by a number of groups [16, 17],
with notable adaptations including the rotary device of Quake
et al [17]. Whilst the designs are all highly innovative, there is
little scope for change in the conditions for the PCR thermal
cycling programme in any of these reported devices.
The novel micro pump microfluidic device proposed here
includes some of the best design innovations from the chamber
and serpentine PCR chips described above. Some of the
design concepts have been adapted and further new concepts
for reactant handling have been included. The novelty in the
proposed device is the fact that the reactants are to be pumped
in a microlitre droplet between three reaction chambers of
different temperatures by a peristaltic bi-directional micro
pump. In addition to this the liquid droplet location is to
be detected automatically by light scattering as the droplet
passes integrated photodetectors and illuminated optical fibres
at the entrance and exit of the reaction chambers. The design
we propose offers the advantages of flexibility for the control
of the PCR thermal cycling, easy access of sample/products
and the potential for post-PCR processing and analysis.
2. Principle of the proposed pump PCR chip
As illustrated in figure 1, the proposed pump PCR chip consists
of a Pyrex wafer anodically bonded to a silicon wafer with a
heat sink beneath the silicon. Three reaction chambers in
series, the connection channels between them and the thermal
S126
isolation recesses are etched into the silicon. The reaction
chambers are heated by platinum thin film resistors and the
temperature is monitored by temperature sensors (see insert
figure). The heaters and the temperature sensors are patterned
onto the top of the silicon chip and located on both sides of
each of the reaction chambers. A bi-directional peristaltic
pump is connected to the third reaction chamber by a channel.
The micro peristaltic pump is actuated by three piezoelectric
discs located in a recess etched in the Pyrex. The design
of the peristaltic pump is a modification of that previously
reported by Veenstra et al [18] for ammonia measurement.
The construction is slightly different; here selective anodic
bonding of Pyrex and silicon is used to meet the requirement
of bi-directional pumping of both liquids and gas. The fluid
inlet and outlet holes are etched into the Pyrex wafer together
with the pump membrane. Six wire bonding holes are also
etched into the Pyrex wafer to provide electrical access.
The PCR is to be achieved by introducing the reactant
droplet of 1 µl into the inlet hole then, by driving the micro
bi-directional pump, the reaction droplet is to be moved back
and forth between these three reaction chambers at 90 ◦ C,
72 ◦ C and 55 ◦ C. The position of the droplet is detected and
controlled as a result of an optical signal detected by a pndiode integrated in the chip as the droplet meniscus scatters
the illumination light. After 20–30 thermal cycles, the PCR
products will be pumped into the inlet reservoir to be collected
and analysed by gel electrophoresis.
Micro pump PCR chip
8
t2
p
b
D2
(a)
M0
M 2=M 0 -M1
O 2 w2(r)
O
A w1(r)
O1
B M1 M 1
r
+
U
M0
M 2=M0 -M1
M1 M1
r
(b)
Figure 2. Deflection of the pump membrane. D1: diameter of PZT;
D2: diameter of Pyrex; S: distance between Pyrex and PZT edges;
membrane thickness t1 = t2 = 0.2 mm; M0: moment caused by
actuation of PZT; M1: moment between bimorph and outer part;
M2: equivalent moment applied on the bimorph.
To aid in the micro pump design, an analytical model based
upon the theory of plates and shells has been developed. A
schematic diagram of the pump is shown in figure 2; the
analytical model based on this is used to determine the optimal
pump membrane dimensions to achieve the maximum pump
stroke volume/flow rate. The pump membrane is divided into
two sections: the central part (a bimorph) of diameter D1 and
the outer region (an annulus with inner diameter of D1 and
outer diameter of D2). A voltage of 100 V is applied to the
PZT disc. The deflection caused by pressure p exerted on the
membranes is neglected for the evaluation.
According to the theory of plates and shells, for the central
part, simply supported at r = a, the deflection at point A
relative to the supporting point O1 is
M2
(a 2 − r 2 ),
2De (1 + νe )
(0 r a),
(1)
where De and ν e are the equivalent stiffness and the equivalent
Poisson’s ratio of the bimorph, respectively.
For the outer part, fixed supported at r = b, the deflection
at point B relative to the supporting point O2 is
M1 a 2 (r 2 − b2 ) + 2b2 ln br
, (a r b), (2)
w2 (r) =
2Ds2 [(1 + ν2 )a 2 + (1 − ν2 )b2 ]
where Ds2 and ν 2 are the stiffness and Poisson’s ratio of the
Pyrex, respectively.
The equivalent moment applied on the bimorph is: M2 =
M0 − M1 . From [19], we know the moment caused by
actuation of the PZT is
M0 = De
h
2
+
D2=6mm,analytical
D2=6mm,FEM
D2=8mm,analytical
D2=8mm,FEM
D2=10mm,analytical
D2=10mm,FEM
D2=12mm,analytical
D2=12mm,FEM
7
6
5
4
3
2
1
0
t1=t2=0.2 mm, U=100 Volts
-1
0
0.1
0.2
0.3
Ratio of S/D2
0.4
0.5
Figure 3. Analytical results and FEM results for the maximum
deflection of the pump membrane (wmax ) with respect to the ratio of
the distance between Pyrex and PZT edges to the diameter of the
PZT (S/D2).
3. Micro pump design
w1 (r) =
Maximum Membrane Deflection wmax [um]
S
D1
a
t1
Pyrex PZT
−d31 U/t1
.
+ E12 t2 (Ds1 + Ds2 )
2
1
h E11 t1
(3)
Here U is the voltage applied on the PZT disc and h is the
thickness of the biomorph. Ds1, E11 and d31 are the stiffness,
Young’s modulus and the piezoelectric charge constant of the
PZT, respectively.
The maximum deflection of the pump membrane at point
O is determined to be
wmax = w1 (0) + w2 (a)
a 2 − b2 + 2b2 ln ab
M0 a 2
=
2(1 + k) Ds2 [(1 + ν2 )a 2 + (1 − ν2 )b2 ]
+
k
,
De (1 + νe )
(4)
where
De (1 + νe )(b2 − a 2 )
.
(5)
Ds2 [(1 + ν2 )a 2 + (1 − ν2 )b2 ]
Then, the stroke volume of the micro pump, Vstroke is
expressed as
w1 (0)
w2 (a)
πr 2 dw1 +
πr 2 dw2 + πa 2 w2 (a)
Vstroke =
0
0
M0 πa 2
b2 (b2 − a 2 )
ka 2
=
+
1 + k 4De (1 + νe ) 2Ds2 [(1 + ν2 )a 2 + (1 − ν2 )b2 ]
k=
+ πa 2 w2 (a).
(6)
According to equation (4), the maximum deflections wmax
with respect to the ratio of S/D2 was calculated and is shown
in figure 3. The diameter of the pump membrane varies from
6 mm to 12 mm.
The finite element method (FEM) results shown in figure 3
are used to verify the analytical results of wmax . Both methods
yield results showing the same trend for wmax , where wmax
reaches a maximum when the distance S reaches 10% of D2,
even though there is a difference of 15% at the maximum
point (figure 3) due to the errors caused by different models
and approaches used in FEM and the theoretical analysis.
The stroke volume of the pump with various membrane
sizes can be calculated according to equation (6). To obtain
a maximum flow rate, the following pump parameters are
selected: the PZT membrane diameter D1 = 10 mm, the Pyrex
membrane diameter D2 = 12 mm, the membrane thickness
S127
Deflection of Pump Membrane w(r) [um]
M Bu et al
1mm
0.5mm
Heater
(model2)
14 mm
Pyrex
1mm
1.5mm
0.4mm
1mm
D2=12 mm, D1=10 mm, t1=t2=0.2 mm, U=100 Volts
FEM results:
Analytical results:
p= 0kPa
p= 0kPa
p=20kPa
p=20kPa
p=40kPa
p=40kPa
p=50kPa
p=50kPa
6
p=60kPa
p=60kPa
0.5mm
M
Silicon
Heat
Sink
5
6mm
1mm Reaction
Chamber
Heater(model1)
(a)
4
3
2
1
(c)
(b)
Heat 90 C
72 C
55 C Heat
Sink Heater Pyrex Heater Silicon Heater Sink
0
-1
-2
-6
4
-4
-2
0
2
Distance r to Pump Membrane Centre [mm]
6
Figure 4. Plot of the results obtained using the finite element
method (FEM) and the analytical method for the pressure
differential of the micro pump.
t1 = t2 = 0.2 mm, the driving voltage U = 100 V. This set of
parameters gives a stroke volume of 314 nl. At an equivalent
driving frequency of 10 Hz, the micro pump can provide a
flow rate of 3.14 µl s−1, which is sufficient to pump a reactant
droplet of 1 µl between adjacent chambers in 0.6 s through a
connection channel of 1 µl.
The maximum pressure differential p is estimated by an
analytical model and FEM is based on the optimized sizes of
pump membranes. The results in figure 4 indicate that the
maximum pressure differential that the pump can withstand is
50–60 kPa.
4. Thermal analysis
4.1. Optimization of the location of the heater
Temperature uniformity is a very important factor for the PCR
reaction. Optimization of the location of the heater can greatly
improve the temperature uniformity over the reaction chamber.
The two FEM 2D models used for the optimization are shown
in figure 5(a), which is a cross section along the section line
X-X in figure 1. For model 1, the heater is located below
the silicon wafer; for model 2, the heater is located between
the Pyrex and the silicon. For the theoretical simulation, the
heaters and the heat sink are fixed at 90 ◦ C and 20 ◦ C,
respectively, as the boundary conditions. The simulation was
done with no fluid in the reaction chamber. Figures 5(b) and
(c) show the temperature distributions around the cross section
of the reaction chamber. By comparison of figures 5(b) and (c),
it is clear that the temperature uniformity around the reaction
chamber of model 2 is much better than that of model 1. The
S128
1.5mm V-groove 3mm
1.5mm
1mm
1mm
3.5mm 3mm 3.5mm
3.5mm
(d)
Trapezoid-groove
3.5mm
1mm1.5mm
3.5mm
3.5mm
1.5mm1mm
3mm for model 4
9.5mm for model 5
(e)
{
Figure 5. Figures illustrating the models and results obtained for
finite element simulation (FEM) for the optimization of the
geometry of the reaction chamber and the location of heater.
(a): Figure illustrating the geometry of the reaction chamber (insert)
and the optimization for the location of the heater. (b) and (c): The
temperature distribution around the cross section of reaction
chamber from model 1 and model 2 illustrated in figure 5(a),
respectively. The temperature gradient of the reaction chamber is
illustrated by the greyscale. (d) Geometry for the reaction chambers
for model 3 (with 0.4 mm deep V-grooves), (e) geometry for the
reaction chambers for model 4 (with 0.4 mm deep, 3 mm long
trapezoid grooves) and model 5 (with 0.4 mm deep, 9.5 mm long
trapezoid grooves).
lowest temperature is at the left upper corner of the reaction
chamber in model 1 and this is mainly caused by the low
thermal conductivity of Pyrex and the greater distance from
the heater to the Pyrex. In the final design the heater is placed
beside the reaction chamber as in model 2.
4.2. Thermal analysis along the reaction chamber
Appropriate thermal isolation between the reaction chambers
is necessary to prevent thermal interference. Three 2D
FEM models for evaluation of the thermal isolation methods
illustrated in figure 5 (5(d) shows model 3, 5(e) shows
model 4 and 5) were employed for improvement of the
temperature uniformity along the reaction chamber. Table 1
lists the FEM thermal analysis results along the section
Micro pump PCR chip
Table 1. Temperature difference between the heaters and reaction
chambers using models 3, 4 and 5 (illustrated in figures 5(d)
and (e)).
Thermal
isolation method
Heater temperature
◦
90 C
72 ◦ C
55 ◦ C
each reaction chamber during the simulation while the heat
sink is fixed at 20 ◦ C. The power needed can be obtained by
multiplying the area by the heat flux. The total input power
needed by six heaters (three pairs) in the chip was found to be
18.62 W.
Temperature difference T
6.846 ◦ C
4.549 ◦ C
4.548 ◦ C
Model 3
Model 4
Model 5
1.121 ◦ C
0.543 ◦ C
0.167 ◦ C
3.455 ◦ C
3.287 ◦ C
3.286 ◦ C
Temperature [ oC]
90
Heating
Cooling
80
70
60
50
40
30
20
0
1
2
3
4
5 6
7
Time [seconds]
8
9
10
Figure 6. Plot of the calculated thermal analysis results at point M
in the reaction chamber (illustrated in figure 5(a) insert).
line Y-Y in figure 1. The largest temperature difference
between the heaters and the silicon below the heater, T,
is used for the evaluation of these three models. For the
simulation, the three heaters are fixed at 90 ◦ C, 72 ◦ C and
55 ◦ C, respectively, and the heat sinks under the silicon are
fixed at a room temperature of 20 ◦ C. The results indicate that
the 9.5 mm long trapezoidal groove provides a best thermal
isolation for the chip.
4.3. Transient thermal analysis
A transient thermal analysis using a 3D FEM model, with
the cross sectional size shown in figure 5, is used to estimate
the thermal cycling rates. For simulation of the temperature
rising, the reaction chamber is fixed at 90 ◦ C. A water droplet of
1 µl at 20 ◦ C is pumped into the chamber and then heated to
90 ◦ C. The temperature variations at point M in the middle of
the cross-sectional area (see figure 5(a) insert) with respect to
time are shown in figure 6. The FEM results indicate that only
1 s is needed for the water droplet to be heated from 20 ◦ C to
90 ◦ C. For simulation of the temperature falling, the reaction
chamber is fixed at 20 ◦ C and the water droplet cools from
90 ◦ C to 20 ◦ C. For the temperature of the water droplet to fall
from 90 ◦ C to 55 ◦ C, which is the lowest temperature in the
PCR temperature cycle, 0.4 s is needed.
4.4. Estimation of the heat power needed by the microfluidic
device for PCR
A 3D FEM model is used to estimate the required heat power
for every heater to achieve the desired temperature in the three
reaction chambers. The input parameter is the heat flux input
into each heater with a heating area of 1.225 mm2 beside
5. Conclusion
Theoretical simulation and the design of a novel integrated
microfluidic chip integrated with a micro peristaltic pump have
been obtained. The pump membrane diameter is optimized
to obtain a maximum flow rate for the PCR. The analytical
formula for calculating the maximum deflection of a circular
pump membrane driven by a PZT disc is derived and verified
by a 3D FEM model. A flow rate of 3.14 µl s−1 and a
pressure differential of 50 kPa are evaluated for the final
bi-directional micro pump designed for our proposed PCR
chip. Thermal analysis using 2D and 3D FEM models was
carried out to evaluate the best design for the reaction chamber
with respect to the temperature uniformity. The power needed
by each heater is estimated to be 5.45 W for the 90 ◦ C chamber,
1.84 W for the 72 ◦ C and 2.02 W for the 55 ◦ C. Transient
thermal analysis by FEM illustrates that the time constant of
the reaction chamber is less than 1 s and thus will ensure the
rapid thermal cycles required by the PCR.
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