Submitted to Microfluidics and Nanofluidics
Supplementary Material
for
Comparison of continuous flow and static chamber μPCR devices through a
computational study: The potential of flexible polymeric substrates
Vasileios E. PAPADOPOULOS, George KOKKORIS*, Ioanna N. KEFALA, and Angeliki
TSEREPI*
*Corresponding authors: Tel.: ++30 2106503238; Fax: ++30 210 6511723; Email:
g.kokkoris@inn.demokritos.gr, a.tserepi@inn.demokritos.gr
Institute of Nanoscience & Nanotechnology, NCSR “Demokritos”, Greece
Temperature controller
The manual tuning of the Proportional-Integral-Derivative temperature controller, used for
evaluation of a Static Chamber (SC) micro-Polymerase Chain Reaction (μPCR) performance,
involved a series of separate time dependent simulations, performed in a trial-and-error
manner. Simulation included only solution of heat transfer in both solid and fluid and Joule
heating models, with the presence of the temperature control feedback.
For t=0 the SC μPCR device is set at ambient temperature (273 K) and no current is applied
to the microheaters. The objective is to find the optimal values of KP, KI, and KD in order to
quickly (fast) and accurately reach the temperature setpoint of 345 K without any oscillations.
At first KI and KD were set to zero and KP was increased until the system output started to
oscillate; KP was set to half of that value, but the setpoint was not reached. In order to correct
this offset, KI is increased until the setpoint is reached. Finally, for a quick reach of the
setpoint, KD is increased until the duration of the control process reaches its minimum. The
time in which the system reaches the setpoint is called settling time. These simulations are
applied for heat coefficients of 5 and 10 W/(m2K) leading to a combination of KP, KI, and KD
optimal values. These values and the corresponding maximum overshoot percentages (see
Fig. S1) with their settling times are shown in Table S1. The threshold for concluding that the
temperature setpoints are reached is considered to be ±1oK.
Fig. S1 PID temperature controller performance for a transition from 328 K to at 345 K.
Settling time and overshoot percentage is shown.
Table S1 PID temperature controller parameters and performance for various combinations
between substrate types, substrate thickness and heat coefficient.
PCB
Controller specifications
Kp
Ki
Kd
72 K to 95 K settling time
Controller inactivity
95 K to 55 K settling time
55 K to 72 K settling time
72 K to 95 K overshoot
95 K to 55 K overshoot
55 K to 72 K overshoot
50μm
50μm
500μm
1000μm
W
h5 2
mK
W
h  10 2
m K
W
h5 2
mK
h5
0.1000
0.0320
0.0045
4.2 s
16.2 s
6.9 s
4.2 s
1.6%
0.6%
3.8%
0.1000
0.0400
0.0040
3.8 s
10.9 s
6.0 s
3.8 s
1.6%
0.8%
3.4%
0.0700
0.0070
0.0040
16.6 s
39.6 s
29.9 s
16.1 s
2.7%
0.0% **
3.5%
0.0500
0.0020
0.0040
53.0 s
67.1 s
0.0 s *
50.4 s
0.0% **
0.0% **
0.0% **
W
m2 K
Glass
1000μm
h5
W
m2 K
0.1600
0.0250
0.0000
6.5 s
59.6 s
0.0 s *
6.5 s
1.8%
0.0% **
5.8%
*During transition from denaturation to annealing phase, controller is switched off. In cases of thicker substrates
the temperature drop (K/s) is very low. Therefore there is sufficient time for the PCR mixture to remain in
annealing temperature without the operation of the controller, and controller starts again its operation for reaching
the extension temperature.
**No overshoot was observed: PCR mixture remained within acceptable bounds of temperature (temperature
setpoint ±1 K), but without overshooting beyond the setpoint.
Summary of the results
Table S2. Comparison of CF and SC devices in terms of DNA amplification, energy
consumption, and duration for different PCR protocols and heat transfer coefficients. The
durations in parentheses include the pumping time.
Device type
CF
SC
PCR protocol
3s:4.2s:6.2s
1.8s:2.5s:3.7s
3s:4.2s:6.2s
1.8s:2.5s:3.7s
2
2
2
2
2
Heat coefficient
5 W/m K 10 W/m K
5 W/m K
5 W/m K 10 W/m K
5 W/m2K
DNA amplification
Energy consumption
(J)
10 cycle duration (s)
645
253
630
363
300
150
657
69
630
85
436
61
353
353
212
463 (590)
391(519)
409 (536)