Three-Dimensional Transient Thermal Analysis for a Silicon PCR Microreactor

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Three-Dimensional Transient ThermalAnalysis for a Silicon PCR MicroreactorOmar Ibrahim a b c , Benjamin Jones b , Mohammed Hassab c &Maaike Op de Beeck ba KACST-Intel Consortium Centre of Excellence for Nano-manufacturing Applications (CENA) , Riyadh , KSAb imec vzw , Leuven , Belgiumc Mechanical Engineering Department , Alexandria University ,Alexandria , EgyptPublished online: 17 Mar 2014.

To cite this article: Omar Ibrahim , Benjamin Jones , Mohammed Hassab & Maaike Op de Beeck(2014) Three-Dimensional Transient Thermal Analysis for a Silicon PCR Microreactor, Numerical HeatTransfer, Part A: Applications: An International Journal of Computation and Methodology, 65:11,1069-1088, DOI: 10.1080/10407782.2013.851569

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THREE-DIMENSIONAL TRANSIENT THERMALANALYSIS FOR A SILICON PCR MICROREACTOR

Omar Ibrahim1,2,3, Benjamin Jones2, Mohammed Hassab3, andMaaike Op de Beeck21KACST-Intel Consortium Centre of Excellence for Nano-manufacturingApplications (CENA), Riyadh, KSA2imec vzw, Leuven, Belgium3Mechanical Engineering Department, Alexandria University,Alexandria, Egypt

Three-dimensional, time-dependent, finite element analysis is employed to study temporal

and spatial thermal behavior inside discrete silicon microreactors designed for polymerase

chain reaction. Results recommend employing transient thermal analysis in studying

cycles with very short temperature dwell-times. A thermal isolation-gap surrounding the

microreactor is essential for realizing rapid thermal transients. Although the addition of

pillars were of limited utility during steady-state, the improvement in temperature uniformity

during a short transience is clear. An array of 15 by 15 pillars resulted in 84% reduction

in temperature dispersion. The suitability of micro-reactors with pillars, having increased

surface-area-to-volume ratio, is experimentally verified.

1. INTRODUCTION

Chemical and biochemical reactions often require precise temperature controlfor optimal conversion of reactants to products. Sometimes these processes evenrequire a cyclical change in temperature to manage the kinetics of a sequence ofreactions. An example of such a process is the polymerase chain reaction (PCR),widely-used as a molecular diagnostic technique for producing a large number ofcopies of deoxyribonucleic acid (DNA) fragments. PCR involves cycling a mixtureof DNA, primers and enzymes between three discrete temperature steps, commonlyreferred to as the denaturation, annealing and extension temperatures, respectively.During denaturation, the double-stranded DNA is converted into single-strandedDNA (ssDNA) at a temperature around 364 to 371K. Following denaturation, thetemperature is reduced to 323–338K allowing the primers to anneal onto the ssDNA.Next, extension step takes place around 343K. During this step, the primers are elon-gated to form a new DNA strand complimentary to the target DNA fragment. In

Received 12 April 2013; accepted 9 September 2013.

Address correspondence to Benjamin Jones, imec vzw, Kapeldreef 75, B-3001, Leuven, Belgium.

E-mail: [email protected]

Color versions of one or more of the figures in the article can be found online at

www.tandfonline.com/unht.

Numerical Heat Transfer, Part A, 65: 1069–1088, 2014

Copyright # Taylor & Francis Group, LLC

ISSN: 1040-7782 print=1521-0634 online

DOI: 10.1080/10407782.2013.851569

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theory, the amount of DNA target can double after each extension step. Thus, thePCR cycle leads to an exponential increase in the number of DNA fragments. Theprocess is typically repeated for 25–30 cycles, which results in a sufficient numberof DNA copies for many commonly employed laboratory analytical techniques [1].

Recent efforts have focused on miniaturizing and integrating a PCR analyticaltool into a lab-on-a-chip (LoC) system [2, 3]. Advances in micro-fabrication technologyand MEMS processing have enabled these developments [4]. Miniaturization of thePCR has been driven by several inherent advantages that a smaller system offers.

. Reduced analysis and response time thanks to rapid heating rates, which are enabledby the reduced diffusion times, increased surface area to volume ratios (SVR) andlower heat capacities.

. Improvements in process control driven by the enhanced heat transfer and the fas-ter response of the system.

. Lower reagent consumption and the associated material costs combined withreduced waste production and lower sample volume required for diagnostics.

. Compactness reduces the system footprint and improves portability, which isimportant in point-of-care applications.

. Automated and integrated sample handling reduces time and number of samplemanipulations by the user while simultaneously reducing the risk of contamination.

Two main architectures for PCR microreactors have been detailed in theliterature: (1) a discrete reactor containing the liquid reaction mixture that isthermally cycled [5, 6] and (2) a continuous flow PCR where the liquid reaction

NOMENCLATURE

A area

Cp specific heat capacity, J=kg �KDp pillar diameter

G isolation gap width

h convective heat transfer coefficient,

W=m2K

k thermal conductivity, W=m �Kl diffusion length

m mass

Np number of pillars

P perimeter

qg heat generation rate per volume,

W=m3

Qin input heat flux, W=m2

S pillars spacing

SVR surface area to volume ratio, mm�1

T temperature, K

t time

V volume of the reactor

W width, mm

a thermal diffusivity

Ds time-step size, s

q density, kg=m3

r standard deviation of temperature

from average, K

Subscripts

a air

amb ambient

av average

D diffusion

E effective

g glass

h heated width

i reactor inner

l lower

max maximum

o reactor outer

ps pillar-set

s silicon

sp set Point

t chip total

u upper

w water

zþ above interface

z� below interface

1070 O. IBRAHIM ET AL.

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mixture is passed between the fixed temperature zones to achieve the desiredtemperature cycle [7, 8]. In theory, a continuous flow PCR can achieve more rapidthermal transients because only the liquid needs to be thermally cycled, whereasin a discrete PCR, the reactor vessel walls undergo thermal cycling as well. Theproblem is that different biological assays require different temperature cyclingconditions. The discrete reactor provides more flexibility in adjusting the thermalcycle than a contiuous flow PCR. For instance, the number of PCR cycles isgenerally fixed by design for a continuous flow PCR whereas this can be freelychosen in a discrete PCR. The flexibility in tailoring the PCR cycle means a singlemicroreactor design can be used for a multitude of amplification conditions andtherefore, a discrete PCR is the focus of this current study.

Careful thermal design is needed to ensure rapid amplification of the targetDNA while minimizing the microreactor temperature non-uniformity, which isessential to allow ampification with good specificity [9] and efficiency [10]. For rapidthermal transients, the microreactor design should minimize the thermal mass thatneeds to be cycled. This can be facilitated by effective thermal isolation betweenthe reactor and surroundings, especially when a highly conductive material, suchas silicon, is used to fabricate the chip [11–13]. Selective insulation of the hightemperature regions from the rest of the device by dicing or etching an air trencharound the microreactor has been a commonly used method for achieving thermalisolation and limiting thermal crosstalk [10, 14]. Majeed et al. [6] and Jones et al.[15] improved the isolation by adding spiraled inlet and outlet ports to increasethe path length of the highly conductive silicon between the reactor and the restof the surrounding chip.

Notable effort has also been devoted to enhancing the temperature uniformityinside the PCR cavity [16]. Park et al. used cylindrical silicon pillars inside themicroreactor. A more intense amplification was successfully obtained for a micro-fabricated cavity with pillars [17]. Several numerical modeling studies were usedfor the thermal characterization of PCR microreactors [8, 18–20]. Jones et al. studiedthe effect of pillars and the effect of isolation gap size during steady-state [15].However, questions arise over the applicability of steady-state thermal simulationresults to experimental cases where the dwell time is very short or practicallynon-existent, such as those reported in [21–23]. For these cases, transient thermalsimulations may be more appropriate.

In this study, a three dimensional finite element model (FEM) is presentedusing COMSOL4.2a multiphysics. This work expands on previous numericalstudies containing only steady-state results because both steady-state and transientsimulations results are essential to encompass a wider range of PCR operatingconditions. Steady-state simulations are demonstrated to be applicable to PCRcycles with long dwell times whereas transient simulations are needed to resolvethe temperature distribution during rapid thermal cycling. Furthermore, a noveland simple proportional controller scheme is implemented in the transient numericalmodel and utilized to mimic a temperature-controlled microreactor that undergoesa PCR heating step. In particular, the width of the isolation air trench and therole of silicon micropillars contained within the PCR cavity are studied in detailin this work. Lastly, a micro-PCR amplification experiment is performed in a micro-reactor cavity with pillars to explore the inhibition effect of the increased SVR.

TRANSIENT THERMAL ANALYSIS FOR A SILICON PCR MICROREACTOR 1071

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2. NUMERICAL PROCEDURE

2.1. Geometry and Governing Equations

The basic design of the chip being studied (see Figure 1a) was previouslydetailed in references [6] and [15]. Air trenches around the reactor are etched outof the silicon wafer to provide thermal isolation between the microreactor and thesurrounding chip [14, 19]. Moreover, the inlet and outlet channels were woundaround the chamber to further decrease the heat loss [6]. Values for the importantgeometric parameters of the various designs considered in our study are listed inTable 1. A few different pillar designs were investigated (further called A2, A3,and A4). For comparison purposes, the liquid volume, pillar volume, cavity width(Wi) and consequently, porosity (0.77) were fixed. This ensures that the thermal massof the systems are held constant and thus, the overall thermal response of the systemsare roughly the same. Therefore, designs A2, A3, and A4 only differ in the interpillarspacing distance (S), the pillar diameter (Dp) and the number of pillars (Np). For thesame Wi, any cavity having pillars (A2, A3 or A4) will have a reduced liquid volumecompared to a cavity without pillars (design A1), so an extra design was proposed(called B) having a smaller Wi¼ 2.8mm (versus 3.2mm for A1) such that the liquidvolume is the same and, consequently, the thermal masses of the systems are equal.The width of the isolation air trench G surrounding the microreactor was also varied(designs C1, D1, and E1).

Since a stationary, chamber-based micro-PCR is the focus of this study, onlyconduction heat transfer (the liquid inside the reactor is assumed to be quiescent)

Figure 1. Geometric parameters of the modeled chip. a) Cross section in XY plane (plan view),

including an enlarged view of the square reactor; and b) 2-D cross section in XZ plane.


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is considered in the numerical model. Conduction heat transfer is governed by theFourier equation.

qCpqTqt

¼ rðkrTÞ þ qg ð1Þ

Where T is the temperature, q is the density, Cp is the specific heat capacity atconstant pressure, k is thermal conductivity, and qg is the heat generation rate perunit volume. Isotropic, temperature-independent material properties were assumed.The isolation gap is modeled as stagnant air. The fluid properties of water are usedfor the liquid inside the microreactor. The thermal conductivity, density and specificheat capacity (from references [15, 24–26]) of the materials used in our model aregiven in Table 2.

2.2. Initial and Boundary Conditions

Figure 1b shows a cross section of the 3-D domain wherein the external appliedboundary conditions are also illustrated. Convection heat transfer coefficients of huand hl were applied at the top of the glass cover and the remainder of the silicon chipbottom, respectively. The ambient temperature was set to Tamb¼ 298K. The heateris modeled as a uniform heat flux boundary condition (Qin) applied at the bottomsurface of the reactor. The external boundary conditions for the model can begiven as follows.

Table 1. Values of the different geometric parameters used in the study (see Figure 1 for definitions of

the dimensions)

Wi (mm) G (mm) Volume (mL) Dp (mm) Np

Design (A1) 3.2 0.5 3.072 N=A N=A

Design (B) 2.8 0.5 2.37 N=A N=A

Design (A2) 3.2 0.5 2.37 0.115 152¼ 225

Design (A3) 3.2 0.5 2.37 0.157 112¼ 121

Design (A4) 3.2 0.5 2.37 0.246 72¼ 49

Design (C1) 3.2 0.25 3.072 N=A N=A

Design (D1) 3.2 0.1 3.072 N=A N=A

Design (E1) 3.2 0 3.072 N=A N=A

Table 2. Material properties used in the study [15, 24–26]

Material

Density (q)(Kg=m3)

Thermal conductivity

(k) W=mK

Specific heat capacity

(Cp) J=kgK

Silicon 2330 120 704.6

Glass=pyrex 2230 1.26 840

Water 975 0.58 4197

Isolation air 1.2 0.03 1000


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. For Z¼Zu

�kgqTqz

¼ hu � ðT � TambÞ for�Wt

2 � x � Wt

2�Wt

2 � y � Wt

2

� �ð2Þ

. For Z¼Zl

�ksqTqz

¼ Qin for�Wh

2 � x � Wh

2�Wh

2 � y � Wh

2

� �ð3Þ

ksqTqz

¼ hl � ðTamb � TÞ for�ðWt�WoÞ

2 � x � ðWt�WoÞ2

�ðWt�WoÞ2 � y � ðWt�WoÞ

2

( )ð4Þ

Where, Zu (¼0.5mm) represents the top surface of the glass cover and Zl

(¼�0.4mm) represents the lower surface of the silicon chip. The initial input heatflux for design A1 was set to Qin¼ 19,350W=m2. The upper and lower convectiveheat transfer coefficients were set to hu¼ 10 and hl¼ 50W=m2K, respectively.The rest of the external boundaries were assumed to have negligible heat fluxes.

The boundary conditions at the glass-chip interface (Z¼ 0) are expressed asfollows.

Tzþ ¼ Tz� ð5Þ

knqTz�

qz¼ �kg

qTzþ

qzð6Þ

The entire region just below the interface (from the chip-side) contains threedifferent materials, as shown in Figure 1. Therefore, based on the type of materialfound in the chip, the interface can be divided into three regions. The physicalproperties of the materials included in these regions (just below the interface) arewritten as follows.

. kn¼ ks, Cp¼Cp,s, q¼ qs for region 1 (the silicon chip)

. kn¼ ka, Cp¼Cp,a, q¼ qa for region 2 (the quiescent air in the thermal isolationgap)

. kn¼ kw, Cp¼Cp,w, q¼ qw for region 3 (the quiescent liquid inside the reactor)

Here, the dimensions of each of the three regions expressed by the range of thecoordinates (X, Y) can be easily obtained from Figure 1. The subscripts (z� and zþ)refers to the regions just below and above the interface between the silicon chip anglass cover (Z¼ 0) and the subscripts (a, g, s, and w) refers to air, glass, silicon andwater, respectively.


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2.3. Temperature Control Scheme

A proportional control scheme was implemented in the numerical model tohold the reactor temperature constant at the targeted set point (SP), which isTsp¼ 371K, after rapid heating. The average temperature of the liquid withinthe reactor at each time step (Tav) was utilized as the process variable (PV). Anapproximate controller system model for the transient rapid heating period can besuggested as follows.

Qin ¼ mCpðTsp � TavÞ=ADs ð7Þ

Where Qin is the input heat flux, m is the mass of the liquid inside the reactor, A isthe area where the heat flux is applied (3.6� 3.6mm2), and Ds is the time step used inthe numerical simulations (10ms). Utilizing the geometric parameters for design A1,the final output equation is given by the following.

Qin ¼ 97000� ð371� TavÞ ð8Þ

Where Tav is in K and Qin is in W=m2. It is important to note that the same outputequation is used for all cases to keep the proportional gain of the controller constantfor comparison purposes. The input heat flux Qin was limited to a maximum value of8� 105W=m2 (corresponding to the maximum heat flux of the heater used for themicro-PCR experiments in Majeed et al. [6]).

It should be noted, that the proportional controller scheme will generallyyield a steady-state error between the PV and the SP. Experimentally, aproportional integral derivative (PID) or fuzzy logic temperature controller istypically used, which significantly reduces this steady-state error. A more sophis-ticated control scheme could be implemented in the numerical study; however,it was desirable to keep the control scheme relatively simple to reduce the numberof tuning parameters. In practice, using the aforementioned proportional controlresulted in a steady-state error less than 1K, which is considered acceptable forthis type of study.

2.4. Mesh and Time-Step Independence Tests

A mesh independence analysis was performed for design A1. It was found thata mesh containing 78,793 tetrahedral elements provided acceptable accuracy.Figure 2 shows an image of the mesh used in our study. The high element densityfor the reactor as well as near its inlet and outlet is particularly notable. A time-stepsensitivity analysis was also performed using time-steps of 40, 20, 10, and 5ms,as summarized in Figure 3. Since the temperature controller response depends onthe time-step, a relatively small time step is needed to ensure adequate response.As shown in Figure 3, variations in the input heat flux curves with differenttime-steps, Ds, are significant for Ds� 20ms. A time-step of 10ms was found toprovide an acceptable controller response and sufficient accuracy over the tempera-ture range of interest.


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3. RESULTS AND DISCUSSION

As mentioned earlier, the main objective is to study the temperature distri-bution inside the cavity. Normalized histograms of the liquid temperature insidethe cavity have been plotted for the different designs mentioned. In these histograms,the normalized frequency of the histogram plots is presented as the percent volume(vertical axis) of liquid in the cavity having a temperature that falls within the rangeof each bin (horizontal axis). Temperature bin widths of 0.2K for initial resultsand 2K for transient results are used.

The standard deviation (r) of the liquid temperature within the reactor fromthe average liquid temperature is used as a statistical measure of the temperatureuniformity (see Eq. 9). This statistical parameter is used to quantify the amount ofdispersion in the temperature of the reactor.

r ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRV

ðT � TavÞ2dV

V

vuutð9Þ

Where Tav is the volume average of the liquid temperature within the reactor cavity,and V is the volume of the reactor cavity.

3.1. Initial State

A temperature contour through a plane at the mid-height (i.e., Z¼�0.15mm)of reactor A1 at the initial state (steady-state solution with Tav� 334K) is presented

Figure 2. Tetrahedral mesh used for the study with 78,793 elements (design A1).


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in Figure 4. A large temperature differential is noted between the thermallyisolated microreactor and the surrounding silicon substrate. Histograms of theliquid temperature inside the reactor at the initial state for different insulation gapwidths, G, are shown in Figure 5a. The uniformity of the temperature is enhancedby increasing the width of the air gap (i.e., the steady state value of r decreases withincreasing G). The reduction in heat loss from the reactor chamber with increasing Gresults in a reduced temperature gradient inside the reactor.

The temperature distributions of the liquid within the microreactor cavities atthe initial state (334K) are shown in Figure 5b for both cases with and withoutpillars. Improved temperature uniformity is noted in a reactor with pillars (A2,A3, and A4) when compared to a reactor without pillars in the case of a fixed innercavity width Wi¼ 3.2mm (A1). However, design B (where Wi¼ 2.8mm to yield thesame liquid volume as designs A2, A3, and A4), which is without pillars, yieldsimproved temperature uniformity over the other designs (A1, A2, A3, and A4). Thismeans that, for steady-state conditions, the foreseen benefit of adding the pillarsis likely less than the benefit of decreasing Wi. In other words, the decrease of the

Figure 3. Time step sensitivity analysis (using design A1). a) Average temperature of the reactor (Tav);

and b) input heat flux (Qin).


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temperature gradient due to the presence of high thermally conductive silicon pillarsis smaller than the decrease of the gradient due to decreasing Wi. The steady-statevalues of r provide further confirmation of this result. Design A2 (with pillars)was found to have a 10% decrease in r compared to design A1 (without pillars).However, design B (without pillars but reduced Wi) was found to have a 29%decrease than design A2 (with pillars), which means less dispersion duringsteady state condition. Nonetheless, as will be discussed later in this article,for rapid thermal cycling micro-PCR applications, steady-state conditions maynever be reached. Therefore, the transient thermal performance should also beinvestigated.

3.2. Transient Thermal Performance

3.2.1. Influence of thermal isolation. To illustrate the importance ofthermally isolating the PCR chamber, transient thermal simulations were conductedfor designs with (A1) and without (E1) the isolation gap. The time needed to heatthe liquid contained within the microreactor from an initial average temperature of334K to 371K, as a function of a constant input heat flux, is shown in Figure 6.Note that for these simulations, the proportional control scheme described in

Figure 4. Steady-state temperature contour for the chip at a depth of Z¼�0.15mm for design A1.


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section 2.3. was not implemented. At a given heat flux, the design with thermalisolation (A1) has much lower heating times than that without (E1). For example,to achieve a target heating time of less than 1 sec, a heat flux of 50W=cm2 is requiredfor thermally un-isolated case versus only 15W=cm2 for thermally isolated cavities.It should be noted that this computation assumes the heater itself has a negligiblethermal mass compared to the liquid-filled reactor.

The equal volume, pillar-free designs of A1, C1, and D1, bearing isolation gapwidths ranging from 0.1mm�G� 0.5mm, were modeled applying the previouslydescribed proportional controller scheme (see section 2.4.). During transientoperation, the average liquid temperature in the reactor is rapidly heated from334K to 371K in less than 100ms (for design A1, see Figure 3a). The temperaturedispersion, r, rapidly increases during this initial heating stage as seen in Figure 7.Once SP is reached and the average temperature is maintained constant by theproportional controller, thermal diffusion leads to a gradual decrease in r.

Figure 5. Steady-state histograms of the reactor temperature including values of r. a) Different gap widths

(G), and b) different designs with and without pillars.


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It is evident from Figure 7 that increasing the gap width only slightly enhancesthe temperature uniformity within the cavity. The maximum value of the standarddeviation of the liquid temperature, rmax, during the heating cycle ranged from24 to 24.4K for designs A1 and D1, respectively. This means that a 5X increasein G from 0.1mm (design D1) to 0.5mm (design A1) resulted in a limited reductionin rmax of only 2%. On the other hand, it should be noted that the steady-stateresults reveal a stronger influence of the gap width: a 23% decrease in r wascalculated for the same 5X increase in G during steady-state conditions. It is alsoimportant to consider that increasing the width of the isolation gap has the draw-back of increasing the total device footprint for the microreactor. To summarize,thermal isolation of the microreactor is necessary to enable rapid thermal cycling;increasing the isolation gap size, however, has limited benefits for rapid cycling micro-PCR applications.

Figure 7. Evolution of the standard deviation (r) with time for reactor designs with different isolation

gap widths (G).

Figure 6. Time required to increase the average liquid temperature in the reactor from 333K to 371K

as a function of constant input heat flux for the case with thermal isolation (A1, C1, and D1) and

without (E1).


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3.2.2. Effect of pillars. To assess the role of pillars during transientoperation, simulations were conducted utilizing the proportional controllerdescribed in section 2.4. for designs with micropillars (A2, A3, and A4) and withoutpillars (A1 and B). Histograms of the liquid temperature are presented in Figures 8aand 8b at instants of 100ms and 500ms, respectively. Figure 8a reveals improvedtemperature uniformity for the designs with pillars (A2, A3, and A4) compared toA1 and B (without pillars). After 500ms (see Figure 8b), the temperature uniformityhas improved; yet it is still apparent that the designs without pillars have a greatertemperature nonuniformity than the designs with pillars.

Further substantiation of these findings is observable in the calculatedstandard deviation of the liquid temperature, r, as a function of time, shown inFigure 9. Considerably higher values of rmax are attained for cavities without pillars(A1 and B) compared to those with (A2, A3, and A4). For the pillar-free designs, A1and B, rmax is 24K and 22.8K, respectively. Recall that the reactor volume for A1 isslightly larger than B (see Table 1). The small difference in rmax (5%) can thus beattributed to the variance in the physical dimension Wi (3.2mm for A1 comparedto 2.8mm for B). For pillars designs A2, A3, and A4, a rmax of only 3.8, 5.7, and

Figure 8. Temperature histograms at different times. a) 100ms, and b) 500ms.


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9.1K, respectively, is obtained. Therefore, an array of 15 by 15 pillars (design A2)has an 84% lower rmax than the pillar-free cavity A1.

The notable benefits of adding the pillars during a thermal transient are theresult of a reduction in thermal diffusion time provided by the silicon micropillars.The thermal diffusion time (td) can be calculated as follows.

td ¼ l2da¼ l2d

k=qCpð10Þ

Where ld is the thermal diffusion distance and a is the thermal diffusivity. It shouldbe noted that the thermal diffusivity of water (a¼ 0.138mm2=s) is significantly lowerthan the thermal diffusivity of silicon (a¼ 73.1mm2=s). For the purposes of thefollowing discussion, it will therefore be assumed that the heat diffuses throughthe silicon instantaneously and only the slower thermal diffusion through the liquid(water) is considered. Thus, for a cavity without pillars, thermal diffusion occursfrom the bottom of the heated liquid-filled cavity to the top. For ld¼ 300 mm (thecavity depth), Eq. 10 yields a thermal diffusion time (td) around 650ms, which issizeable compared to the thermal transit time (about 100ms) observed in thisstudy. However, for a cavity with pillars, the dominant thermal diffusion distanceis governed by the space in between the pillars. An effective diffusion length, lE,can be defined as follows.

lE ¼ 1

2

4Aps

Pps¼ 2

S2 � p4D

2p

p Dp þ 4 ðS �DpÞð11Þ

Referring to the inset of Figure 1a, Aps is the shaded area between the pillars and Pps

is the dashed perimeter. The thermal diffusion times for the designs with pillars rangefrom 50ms for design A2 to 190ms for design A4 (see Table 3), which are in theorder of the thermal transit time (about 100ms) and significantly lower than the ther-mal diffusion time of the designs without pillars.

The temperature gradient along the Z-direction was studied in further detail.The area-averaged liquid temperature in a cross-sectional XY plane through thereactor cavity is plotted against the vertical (Z) coordinate in Figure 10. Substantially

Figure 9. Standard deviation (r) as a function of time for different modeled reactor designs.


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improved temperature uniformity along the Z direction is readily noted for the casewith pillars versus without pillars. For pillar-free designs A1 and B, the temperaturedifference at 200ms was 19.6K compared to a difference ranging from 1 to 3K forpillar designs A2, A3, and A4 (see Figure 10a). By 500ms, the range of temperatureshas markedly decreased as seen in Figure 10b. Figure 11 shows the time evolution oftemperature contours for pillars and pillars-free designs A1 and A2, respectively, atlocations of Z¼�50 mm and �250 mm. A sizeable difference in temperature is readilyseen between the plane at Z¼�50 mm and Z¼�250 mm for the case without pillars(A1); for the case with pillars (A2), the Z-axis temperature uniformity is markedlybetter at all time-steps. For the pillar-free design A1, at Z¼�50 mm and t¼ 200ms,ms, the temperature ranged from 352 to 384K (a difference of 32K) with an averageof 360K. This temperature difference is more than 6 times its value at steady-state.Across the same planes and at the same instant, the temperature range is only 10Kfor the pillar design A2. This difference is less than twice its steady-state value.

4. AMPLIFICATION EXPERIMENT

In the previous section, micropillars were demonstrated to substantiallyimprove temperature uniformity within the microreactor during transient operation.However, the downside to adding pillars is an accompanying increase in surfacearea to volume ratio (SVR) (see Table 3) [27]. For silicon microreactor surfaces,this SVR increase was previously reported to reduce the PCR efficiency [28, 29].

Figure 10. Temperature distribution for the different designs along the depth of the microreactor.

a) At 200ms, and b) at 500ms.

Table 3. Calculated values for diffusion times for different pillar design, as well as the value for SVR

Design Wi (mm) Dp (mm) S (mm) Np SVR (mm�1) lE (mm) td (s)

A2 3.2 115 200 225 18.57 84.49 0.05

A3 3.2 157 266 121 15.84 110.67 0.09

A4 3.2 246 400 49 13.07 162.05 0.19


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Therefore, micro-PCR experiments are performed as a gross reality check forwhether detectable PCR amplification can be obtained for a high SVR microreactorcontaining pillars.

A micro-PCR test chip of the A2 design (see Table 1) was manufactured andemployed for this study. Recall that design A2 has the highest SVR of the reactordesigns reported in this study. A test facility was constructed to hold and align thetest chip with the micro-thermal cycler (see Figure 12). The experimental setupand test sample is similar to the one reported in reference [6]. The micro-thermalcycler consists of a small, microfabricated thermoelectric module (TEM), a copperheat spreader, a heat sink and a fan. A small type-K thermocouple with 25 mmdiameter wire is placed between the TEM and the silicon micro-cavity for tempera-ture measurement. A PID temperature controller is used to control the powerinput to the TEM. After filling the microreactor with the PCR mixture, the inletand outlet ports were effectively sealed using a strong adhesive tape to preventevaporation within the microreactor (a particular problem previously reportedin past studies [30, 31]).

The amplification of a 148 base-pair (bp) fragment directly from blood wasdemonstrated in the micro-PCR test facility. Thermococcus kodakaraensis (KOD)polymerase was used for the PCR amplification test. A clean micro-PCR test sample

Figure 11. Temporal and spatial variation in the temperature contours for designs A1 and A2.


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was mounted on the setup. For a 10 mL reaction, the following sample mixture wasprepared: 0.6 ml deionized water, 5 ml PCR buffer, 1 ml of 10 mM forward (50-CGTTTCAAATTACAGGGTCAACTGCT) and 1 ml of 10 mM reverse (50-GGTCCCACACTCACAGTTTTCAC) primers, 1 ml (2mM) dNTPs, 0.4 ml KODpolymerase (1U=mL) and 1 ml whole blood. Approximately 2.5 mL of the mixturewas loaded into the micro-PCR test device using a syringe. The temperature cycleconsisted of a 4 minute polymerase activation step at 371K followed by 30 cyclesof the following sequence: 371K for denaturation, 333K to anneal the primers

Figure 12. Experimental setup used for performing PCR with inset showing the fabricated chip (PID

temperature controller not shown).

Figure 13. Gel electrophoresis result for the amplified samples. Lanes are 1) 50 bp DNA ladder, 2) positive

control sample amplified in conventional tool, and 3) successful amplification in fabricated microreactor.


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and 341K for extension of the primers. Each temperature step was performed with a30 second dwell time at the target temperature. A 10 ml sample was also amplified ina conventional, commercially-available PCR tool to serve as a control.

After PCR amplification, the sample was extracted from the micro-PCRreactor and the products were analyzed using slab gel electrophoresis (see Figure 13).The figure demonstrates the successful amplification of the target fragment in themicro-PCR. The target fragment can clearly be seen on the gel for both the micro-PCR(lane 3) and conventional tool (lane 2) near the 150bp marker of the 50bp ladder(lane 1).

5. CONCLUSION

Both steady-state and time-dependent finite element method simulations wereconducted. For the transient study, a rather simple proportional control schemewas developed and implemented numerically. The influence of the thermal isolationgap and micropillars contained within the PCR chamber were studied in detail.The thermal isolation gap is demonstrated as essential for achieving rapidthermal transients (<1 s). However, the precise dimension of this gap is of a lesserimportance. Although micropillars are of limited benefit for reducing thetemperature dispersion during steady-state operation, a notable improvement intemperature uniformity is apparent during rapid thermal transients. For example,during transient operation, an 84% decrease in rmax was computed for the case ofa 15� 15 micropillar array compared to a case without pillars. The implication ofthis study is that transient simulations are necessary for the performanceevaluation of rapid thermal cycling micro-PCR applications while the steady-statesimulation are still applicable to scenarios with a longer temperature dwelltime. Finally, a target DNA fragment from blood was successfully amplifiedinside a fabricated cavity with a 15 by 15 micropillar array, demonstratingthat successful PCR amplification is readily achievable in a silicon reactor witha SVR of 18mm�1.

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Documents

Three-Dimensional Transient Thermal Analysis for a Silicon PCR Microreactor