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Thermal analysis of the vortex tube based thermocycler for fast Thermal analysis of the vortex tube based thermocycler for fast
DNA ampli>cation: Experimental and two-dimensional numerical DNA ampli>cation: Experimental and two-dimensional numerical
results results
V. Raghavan
University of Nebraska - Lincoln
Scott E. Whitney
Megabase Research Products, Lincoln, Nebraska
Ryan J. Ebmeier
Megabase Research Products, Lincoln, Nebraska
Nisha V. Padhye
Megabase Research Products, Lincoln, Nebraska
Michael Nelson
Megabase Research Products, Lincoln, Nebraska
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Raghavan, V.; Whitney, Scott E.; Ebmeier, Ryan J.; Padhye, Nisha V.; Nelson, Michael; Viljoen, Hendrik J.;
and Gogos, George, "Thermal analysis of the vortex tube based thermocycler for fast DNA ampli>cation:
Experimental and two-dimensional numerical results" (2006).
Hendrik J. Viljoen Publications
. 8.
https://digitalcommons.unl.edu/cbmeviljoen/8
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Thermal analysis of the vortex tube based thermocycler for fast DNA
amplification: Experimental and two-dimensional numerical results
V. Raghavan
Department of Mechanical Engineering, University of Nebraska—Lincoln, Nebraska 68588
Scott E. Whitney, Ryan J. Ebmeier, Nisha V. Padhye, and Michael Nelson
Megabase Research Products, 2726 North 48th Street, Lincoln, Nebraska 68504
Hendrik J. Viljoen
Department of Chemical Engineering, University of Nebraska—Lincoln, Nebraska 68588
George Gogos
Department of Mechanical Engineering, University of Nebraska—Lincoln, Nebraska 68588
共Received 8 March 2006; accepted 26 July 2006; published online 28 September 2006兲
In this article, experimental and numerical analyses to investigate the thermal control of an
innovative vortex tube based polymerase chain reaction 共VT-PCR兲 thermocycler are described.
VT-PCR is capable of rapid DNA amplification and real-time optical detection. The device rapidly
cycles six 20
l96bp-DNA samples between the PCR stages 共denaturation, annealing, and
elongation兲 for 30 cycles in approximately 6 min. Two-dimensional numerical simulations have
been carried out using computational fluid dynamics 共CFD兲 software
FLUENT v.6.2.16. Experiments
and CFD simulations have been carried out to measure/predict the temperature variation between
the samples and within each sample. Heat transfer rate 共primarily dictated by the temperature
differences between the samples and the external air heating or cooling them兲 governs the
temperature distribution between and within the samples. Temperature variation between and within
the samples during the denaturation stage has been quite uniform 共maximum variation around ±0.5
and 1.6 ° C, respectively兲. During cooling, by adjusting the cold release valves in the VT-PCR
during some stage of cooling, the heat transfer rate has been controlled. Improved thermal control,
which increases the efficiency of the PCR process, has been obtained both experimentally and
numerically by slightly decreasing the rate of cooling. Thus, almost uniform temperature
distribution between and within the samples 共within 1 ° C兲 has been attained for the annealing stage
as well. It is shown that the VT-PCR is a fully functional PCR machine capable of amplifying
specific DNA target sequences in less time than conventional PCR devices. © 2006 American
Institute of Physics. 关DOI: 10.1063/1.2338283兴
I. INTRODUCTION
The polymerase chain reaction 共PCR兲 is a powerful and
sensitive enzymatic technique used to exponentially increase
the number of copies of a specific sequence of template
DNA. It is an important biomolecular diagnostic technique
with applications in fields ranging from agriculture to bio-
medical research 共Saiki et al.,
1
Kogan et al.,
2
Erlich,
3
Saiki et
al.,
4
Persing et al.,
5
Mullis et al.,
6
and Nicoll et al.
7
兲. For this
reason, the PCR process has gained much attention by instru-
ment developers and researchers working to produce a vast
array of devices and operating conditions necessary to per-
form the reaction efficiently.
The PCR process is conducted in a series of three steps,
namely, 共1兲 sample preparation, 共2兲 DNA amplification, and
共3兲 product detection. The sample preparation includes DNA
extraction from bacteria, viruses, blood or body fluids, etc.
The DNA sample is then mixed with primers, deoxyribo-
nucleotide triphosphates 共dNTPs兲, magnesium, and DNA
polymerase into a desirable sample volume 共typically
1–100
l for amplification. During the amplification step,
the sample is thermally cycled between specific denaturation,
annealing, and elongation temperatures for 30– 40 cycles.
The typical range of denaturation temperature is 90–95 °C
and of annealing is 50– 65 ° C. Elongation occurs around
72 ° C 共Saiki
8
兲. Each cycle should theoretically double the
existing amount of DNA. In a practical PCR process, typical
PCR amplification has an efficiency of 70%–80% and re-
quires approximately 35 cycles for 10
8
-fold amplification.
In a typical PCR reaction, template DNA sequences
lying between the ends of two specifically designed oligo-
nucleotide primers can be amplified in approximately
30 min to 2 h. This time can vary considerably according to
the protocol employed and the instrument used to carry out
the reaction. Gel electrophoresis is the standard for product
detection. However, real-time product detection can be
achieved by measuring the fluorescence of dye/DNA com-
plexes during the amplification stage of the reaction 共Higuchi
et al.,
9
Svanvik et al.,
10
and Nazerenko et al.
11
兲. This consid-
erably reduces the total assay time by combining amplifica-
tion and product detection into a single step of the PCR
process.
The automated PCR devices may generally be classified
REVIEW OF SCIENTIFIC INSTRUMENTS 77, 094301 共2006兲
0034-6748/2006/77共9兲/094301/9/$23.00 © 2006 American Institute of Physics77, 094301-1
Downloaded 19 Apr 2007 to 129.93.17.223. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp
into two categories: robotic devices, which move the DNA
samples to the heat, and thermocyclers, which bring the heat
to the samples. Robotic devices are, in general, very slow;
the rate of heating and cooling is approximately
2 min/cycle. These robotic machines also require a warming
up period to bring the water baths to the correct temperatures
for performing PCR. Several such devices have been re-
viewed by Johnson.
12
The two basic types of thermocyclers
are programmable heat blocks and forced hot air thermocy-
clers. In commonly employed heat block thermocyclers, the
amplification stage consists of cycling the temperature of the
samples using computer controlled heat blocks and typically
requires hours of operation time. Forced hot air thermo-
cyclers have substantially reduced typical amplification time
by eliminating the large thermal mass of heat blocks and
utilizing convection heat transfer between air and thin-walled
capillary tubes. Therefore, the temperature transition time
and the extra time needed for capillary equilibration are
reduced. With these devices, PCR amplification consisting of
30 cycles can be performed in as little as ⬃10– 30 min
共Ref. 7, Wittwer et al.
13–16
兲.
An improved system which uses compressed gas to in-
crease thermocycler performance has been developed 共Quin-
tanar and Nelson,
17
and Whitney
18
兲. These devices have
higher gas velocities and a specially designed flow field to
optimize heat transfer to the capillaries with DNA samples.
The concept of a compressed gas thermocycler is the basis
for the development of the vortex tube based polymerase
chain reaction thermocycler 共VT-PCR兲. VT-PCR is a com-
pact thermocycler 共Ebmeier et al.,
19
and Ebmeier
20
兲.
Like with any thermocycler, there are two important
performance criteria for VT-PCR. First, the most important
performance criterion is the ability of VT-PCR to accurately
control the temperature of the PCR samples. The VT-PCR
performs thermal control by using a thermocouple placed
inside an additional capillary within the sample chamber. A
computer uses the feedback from the thermocouple to
control the flow of hot and cold air streams. The design of
the sample chamber minimizes the temperature variation
between the samples. The second important performance
criterion is the ability of VT-PCR to reduce the temperature
variation within each sample. In this study, by using both
experiments and numerical simulations, the thermal control
of the VT-PCR is presented in detail. It is shown that by
reducing the heat transfer rate during the annealing stage,
namely, by adjusting the cold release valves in the de-
vice, the temperature variation between and within the
samples during the annealing stage can be restricted to less
than 1 °C.
II. EXPERIMENTAL SETUP AND PROCEDURE
VT-PCR is an extension of its previous model, which
was capable of amplifying three DNA samples.
19
In the cur-
rent model, there are nine capillaries placed in a modified
reaction chamber. The first two capillaries are primarily used
as air-flow distribution devices. A thermocouple is placed
within one of the capillaries to control the process tempera-
tures. The other six capillaries carry the DNA samples for
amplification. VT-PCR, like the previous device, relies on
taking advantage of the natural heating and refrigeration ca-
pacities of the Ranque-Hilsch vortex tube 共Ranque
21
and
Hilsch
22
兲. Computer control and electronically actuated flow
valves are employed as necessary to use both the hot and
cold exhaust streams produced from the vortex tube, to rap-
idly heat/cool the PCR samples. The compact design of VT-
PCR gives it overall dimensions of approximately 16⫻12
⫻6 in.
3
In addition, it has very limited dependence on elec-
tricity 共⬃30 W兲 and can be controlled using a personal com-
puter. In this device, 30 PCR thermal cycles between 90 and
56 ° C without any holds 共0 s at 90 ° C, 0 s at 56 ° C, and 0 s
at 72 ° C兲 can be completed in less than 6 min. The compo-
nent layout of the VT-PCR is shown in Fig. 1 共more details
are given in Ref. 20兲.
As previously mentioned, the primary difference be-
tween the current device and the previous device
19
is the
modified sample chamber 共F, Fig. 1兲 to accommodate nine
capillaries instead of four 共current sample chamber is de-
scribed in a later section兲. The other components remain the
same as in the previous device.
19
The system heats the
samples by allowing only the hot air to pass through the
sample chamber. The cold flow valve 共D, Fig. 1兲 is closed,
while the two cold release valves 共B and C, Fig. 1兲 are open.
This valve configuration provides two exhausts for all of the
cold air produced by the vortex tube to exit the system with
negligible back pressure. Meanwhile, the air exiting the hot
end of the vortex tube flows across the samples located in the
sample chamber before exiting the system via the sample
chamber exhaust. The vortex tube is adjusted so that the hot
gas temperature is approximately 105 °C and the corre-
sponding volumetric flow rate of hot gas produced is ap-
proximately 6.4⫻ 10
−4
m
3
/s. The machine can heat the
samples at an average rate of approximately 3.2 °C/s.
The transition from heating to cooling is performed
without interrupting the vortex tube operation. The cold flow
valve 共D, Fig. 1兲 is opened and then the cold release valves
共B and C, Fig. 1兲 are closed. Adequate cooling is achieved
under this configuration where the cold and hot gases mix in
the mixing chamber before reaching the sample chamber.
FIG. 1. Component layout of VT-PCR thermocycler. Components labeled
A–G; A, Ranque-Hilsch vortex tube; B, primary cold release valve; C, sec-
ondary cold release valve; D, cold flow valve; E, mixing chamber; F, sample
chamber; G, exhaust mufflers.
094301-2 Raghavan et al. Rev. Sci. Instrum. 77, 094301 共2006兲
Downloaded 19 Apr 2007 to 129.93.17.223. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp
The mass flow rate of cold gas is about four times greater
than that of the hot gas and the resulting stream is adequate
to cool the samples rapidly to the annealing temperature. The
cold gas exiting the vortex tube is approximately at −5 ° C.
The cold/hot gas mixture entering the sample chamber is
typically around 25 ° C. The samples are cooled at a
maximum rate of about 16 °C/s. By proper control of the
cold release valves, intermediate cooling rates can also be
obtained.
Reaction progress at the end of each cycle is monitored
by measuring the fluorescence emitted at 520 nm by SYBR
Green bound to double-stranded DNA complexes upon exci-
tation at 470 nm.
III. NUMERICAL METHOD
The fundamental equations of fluid flow and heat trans-
fer are governed by conservation of mass, conservation of
momentum, and conservation of energy. In the present study,
the problem is considered transient and two dimensional.
The mass, momentum, and energy transports are basically
through diffusion and forced convection; the effects of radia-
tion and natural convection are neglected. The fluid is con-
sidered to be of constant thermophysical properties. Hence,
the incompressible flow solution methodology has been
adopted to derive the pressure field. The transient governing
equations, in terms of primitive variables can be written as
follows: Continuity equation,
u
x
+
v
y
=0. 共1兲
Momentum equation in the x direction,
冉
u
t
+ u
u
x
+
v
u
y
冊
=−
p
x
+
冉
2
u
x
2
+
2
u
y
2
冊
. 共2兲
Momentum equation in the y direction,
冉
v
t
+ u
v
x
+
v
v
y
冊
=−
p
y
+
冉
2
v
x
2
+
2
v
y
2
冊
. 共3兲
Energy equation,
C
p
冉
T
t
+ u
T
x
+
v
T
y
冊
=
冉
2
T
x
2
+
2
T
y
2
冊
. 共4兲
For pressure and velocity coupling,
SIMPLE algorithm
共Patankar
23
兲 is used. For a guessed pressure field, p
*
, the
corresponding velocity field is obtained. Then, the pressure
correction field 共p
⬙
兲 is obtained by solving the following
pressure Poisson equation:
ⵜ
2
p
⬙
=
⌬t
冉
u
*
x
+
v
*
y
冊
. 共5兲
In the above equation, superscript
*
implies a guessed ve-
locity field. The pressure field for the 共n +1兲
th
time step is
updated as p
n+1
= p
*
+ p
⬙
. The corresponding velocity field is
corrected in a similar fashion,
u
⬙
=−
⌬t
p
⬙
x
, u
n+1
= u
*
+ u
⬙
, 共6兲
v
⬙
=−
⌬t
p
⬙
y
,
v
n+1
=
v
*
+
v
⬙
. 共7兲
For the hot flow simulations, the Reynolds number 共Re兲
based on the hot flow velocity and the average width of the
sample chamber is around 1850. For the cold flow simula-
tions, since the mass flow rate is five times higher than that
of the hot flow 共Re= 9250兲, the flow becomes turbulent.
Thus, a standard k- model 共Launder and Spalding
24
兲 has
been employed. The equations for the standard k- model are
given below in tensor form.
Equation for turbulent kinetic energy 共k兲,
t
共
k兲 +
x
i
共
ku
i
兲 =
x
j
冋
冉
+
t
k
冊
k
x
j
册
+ G
k
−
+ S
k
.
共8兲
Equation for rate of dissipation 共兲,
t
共
兲 +
x
i
共
u
i
兲 =
x
j
冋
冉
+
t
冊
x
j
册
+ C
1
k
G
k
− C
2
2
k
+ S
. 共9兲
In the above equations, G
k
represents the generation of tur-
bulence kinetic energy due to the mean velocity gradients,
calculated as
G
k
=−
u
i
⬘
u
j
⬘
u
j
x
i
. 共10兲
The primes in the above equations represent fluctuating
quantities. S
k
and S
are the source terms and are equal to
zero for the current problem.
k
and
are turbulent Prandtl
numbers and for standard k- model they are equal to 1.0
and 1.3, respectively. C
1
and C
2
are constants and are equal
to 1.44 and 1.92, respectively. The turbulent or eddy viscos-
ity
t
is calculated using the equation given below:
t
=
C
k
2
, 共11兲
where C
in the above equation is a constant 共C
=0.09兲.
The governing equations are solved by employing
FLUENT v.6.2.16, a commercial computational fluid dynamics
共CFD兲 tool. The transient, two-dimensional 共2D兲, laminar,
and implicit solver available in
FLUENT v.6.2.16 has been
employed for the hot flow simulations. For the cold flow
simulations, the standard k- model has been employed.
FIG. 2. Computational domain.
094301-3 Vortex tube thermocycler Rev. Sci. Instrum. 77, 094301 共2006兲
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