DNA PDMS/ A Study on integrated Microbiochip fabricated with PDMS/glass for DNA analysis

2008 2

DNA PDMS/ A Study on integrated Microbiochip fabricated with PDMS/glass for DNA analysis

. 2008 2

.

2008 2

() () () () ()

MEMS(Micro Electro Mechanical System) (cell lysis), DNA (DNA purification) (polymerase chain reaction, PCR) PDMS(Polydimethylsiloxane) (pyrex7740, Dow Corning, U.S.A) , (microbiochip) . , DNA , . DNA PDMS pillar filter . (passive check valve) Cell lysis, DNA filtering cell DNA PCR . (silicon) PDMS , , . PDMS (, hybrid type) . CFD-ACE+(ESI group, France) . PDMS SU-8(Microchem, U.S.A) (micro molding) . ~ . (bonding) . LabVIEW(National Instrument, USA) , , .

iv

DNA , DNA , , . 3 1 . .

v

iv Nomenclature ix List of Figure x List of Table xiv 1 15 1.1 1.2 1.3 1.4 1.4.1 15 19 27 28 28 28 (PCR) : DNA PCR 29 Cell lysis, DNA purification 31 PDMS Passive micro check-valve 31 31 One-step Cell lysis, DNA purification, PCR 1.4.1.1 1.4.1.2 1.4.1.3 1.4.2 1.4.2.1 1.4.2.2 1.4.2.3 1.4.2.4 2

28 29

integrated 31 33 2.1 2.1.1 2.1.2 2.1.3 33 PDMS(polydimethylsiloxane) 33 SU-8 35 Pyrex glass 36

vi

2.2 2.2.1 2.2.2 2.2.3

PDMS 38 38 DNA 39 41

2.2.3.1 Microfluidic mixing theory 42 2.2.3.2 43 2.2.3.3 44 2.2.4 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 PCR 49 50 50 51 52 54 54 , TCR 54 55 55 , RTD 58 2.4.1.1 2.4.1.2 2.4.1.3 2.4.1.4 2.4.2 2.5 3 3.1 3.1.1 3.1.2 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3 3.3.1 3.3.2

60 68 70 PDMS 71 73 PDMS 75 76 SU-8 76 , 77 PDMS replica 79 81 81 81

70

vii

3.3.3 3.3.4 3.3.5 3.4 3.5 3.5.1 3.5.2 3.6 4 4.1 4.1.1 4.2 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 4.4.7

82 83 Cr/Au 83 84 84 86 90 91 93 95 96 DNA 98 DNA (Cell lysis and DNA purification) 98 DNA 100 100 DNA 101 DNA 102 102 PCR 104 PCR 104 PCR 107 PCR 108 PCR 110 PCR 110 Y PCR 111 DNA PCR 112

93

4.4.7.1 4.4.7.2 4.5 4.6 5

Integrated DNA 115 118

119

121 ABSTRACT 125

viii

Nomenclature

P D c Ii R T CT RT

pressure density coefficient of viscosity kinematic viscosity diffusivity concentration intensity value resistance temperature thermal capacitor thermal resistance

ix

List of FigureFig. 1 - 1 Miniaturizing and integrating laboratory processes onto a microchip Commercial Lab-on-a-system: (a) LabChip 90 Automated devices: concept of lab-on-a-chip .................................................................... 16 Fig. 1 - 2 Electrophoresis System(Caliper, U.S.A), (b) 2100 Bioanalyzer(Agilent, U.S.A) ............................................................................................................... 17 Fig. 1 - 3 Fig. 1 - 4 Fig. 1 - 5 Fig. 1 - 6 Fig. 1 - 7 Fig. 1 - 8 Fig. 1 - 9 Fig. 1 - 10 Fig. 1 - 11 Fig. 1 - 12 Fig. 2 - 1 Fig. 2 - 2 Fig. 2 - 3 Fig. 2 - 4 Fig. 2 - 5 Fig. 2 - 6 Fig. 2 - 7 Fig. 2 - 8 Fig. 2 - 9 Fig. 2 - 10 Fig. 2 - 11 Forecast of microbiochip market scale ............................................... 18 Mechanical type DNA filter .................................................................... 21 Parylene cantilever type membrane valve ............................................ 23 Properties of main materials for integrated microbiochip ...................... 24 Single step cell lysis/PCR microchip ..................................................... 24 Continuous flow microfluidic device for cell separation, cell lysis and Integrated RT-PCR system for virus detection ...................................... 26 Schematic diagram of integrate system for sample preparation and Research system of MEMS fabrication and Bio analysis .................... 30 Step process of integrated microbiochip development ........................ 30 PDMS molecule structure formula ......................................................... 33 High aspect ratio micro structure fabricated by SU-8 (Microchem, Basic material properties of Pyrex7740 ................................................. 37 Thermal expansion coefficient of silicon and pyrex glass(7740) ........... 37 PDMS channel for cell lysis ................................................................... 38 Pillars and microbeads in PDMS channel for DNA filtration .................. 40 Schematic diagram of filterable size in channel filled with microbead .. 41 Pillars in PDMS channel for mixing of DNA and PCR reagents ............ 42 Simulation model for micro-mixer .......................................................... 46 Simulation results of micro-mixer :(a)pillar diameter size:100, ........ 47 Comparison of mixing efficiency .......................................................... 48[3]

DNA purification ................................................................................................ 25

PCR .................................................................................................................. 27

U.S.A) ............................................................................................................... 36

x

Fig. 2 - 12 Fig. 2 - 13 Fig. 2 - 14 Fig. 2 - 16 Fig. 2 - 17 Fig. 2 - 18 Fig. 2 - 20 Fig. 2 - 21 Fig. 2 - 22 Fig. 2 - 23 Fig. 2 - 24 Fig. 2 - 25 Fig. 2 - 26 Fig. 3 - 1 Fig. 3 - 2 Fig. 3 - 3 Fig. 3 - 4 Fig. 3 - 5 Fig. 3 - 6 Fig. 3 - 7 Fig. 3 - 8 Fig. 3 - 9 Fig. 3 - 10 Fig. 3 - 11 Fig. 3 - 12 Fig. 3 - 13 Fig. 3 - 14

Serpentine micro reactor for PCR ....................................................... 49 Schematic diagram of passive check valve ......................................... 51 Schematic of integrated microchip ...................................................... 52 Forward and backward flow rate ......................................................... 53 Joule heating from metal line by external electric source.................... 55 Circuit model for the joule heating of a resistor driven from a voltage 3D model of micro reactor for heat transfer analysis........................... 61 Thermal profile of microbiochip after 2 sec.......................................... 63 Thermal profile of microbiochip after 2 sec.......................................... 64 Analysis direction for heat planarity ..................................................... 65 Heat planarity in A-B direction ............................................................. 66 Heat planarity in C-D direction ............................................................. 66 Surface temperature of heater and reactor ......................................... 67 Photo mask for micro mold fabrication (First layer) ............................... 72 Photo mask for micro mold fabrication (Second layer).......................... 72 Film photo mask .................................................................................... 73 Photo mask for micro heater and sensor fabrication ............................. 74 Glass photo mask .................................................................................. 74 PDMS chip fabrication process ............................................................. 75 Spin speed vs. thickness curves for selected SU-8 resist (Microchem) 77 Fabricated micro mold for PDMS chip ................................................... 79 PDMS chip replica ................................................................................. 80 Assembly process of PDMS/glass microbiochip ................................. 80 Glass chip fabrication process ............................................................. 81 Schematic diagram of integrated microchip: (a) united chip and (b) Photograph of Separable PDMS/glass microbiochip for biochemical Simulated thermal profile at inner surface of (a)united chip after 2sec,

Fig. 2 - 15 Schematic diagram of experimental instruments setup ......................... 53

source ............................................................................................................... 56

separable chip .................................................................................................. 85 reaction ............................................................................................................. 86 and temperature distribution of (b) in A-B direction of (a) ................................ 88

xi

Fig. 3 - 15 Fig. 3 - 16 Fig. 3 - 17 Fig. 4 - 1 Fig. 4 - 2 Fig. 4 - 3 Fig. 4 - 4 Fig. 4 - 5 Fig. 4 - 6 Fig. 4 - 7 Fig. 4 - 8 Fig. 4 - 9 reaction Fig. 4 - 10 Fig. 4 - 11

Simulated thermal profile at inner surface of (a) separable chip after Experienced temperature at reactor in united chip and separable Comparison of chip production cost: united chip and separable chip . 92 Schematic diagram of temperature control system ............................... 94 Constructed temperature control system............................................... 94 LabVIEW programming ......................................................................... 95 Virtual machine for temperature control by LabVIEW ........................... 96 Calibration curve for the RTD ................................................................ 97 Optical microscope image of human buccal cell ................................. 100 Results of cell lysis and DNA purification in conventional method: Results of cell lysis and DNA purification in microbiochip: (a)DNA Schematic diagram of DNA amplification by polymerase chain[35]

2sec, and temperature distribution of (b) in A-B direction of (a)....................... 89 chip ................................................................................................................... 90

(a)DNA concentration, (b)DNA purity ............................................................. 101 concentration, (b)DNA purity .......................................................................... 102 ....................................................................................................... 103

No additive micro PCR with SRY gene from man: Lane 1 ................ 106 SRY gene PCR results using micro reactor with two additives, Lane

M; 100bp marker, Lane P1; 0.3 PVP, Lane P2; 0.6 PVP, Lane P3; 0.9 PVP, Lane P4; 1.2 PVP, Lane B1; 0.3 BSA, Lane B2; 0.6 BSA, Lane B3; 0.9 BSA, Lane B4; 1.2 BSA ............................................................ 106 Fig. 4 - 12 Micro reactor setup for PCR .............................................................. 109 Thermal cycling of fabricated microbiochip using LabVIEW Fig. 4 - 13 Fig. 4 - 14 Fig. 4 - 15 Fig. 4 - 16

temperature control system and temperature precision on each section ...... 109 AZF micro deletion STS .................................................................... 112 Gel results of PCR results (blood cell gene DNA): Lane M; 100bp Gel results of PCR results(blood cell gene DNA): Lane M; 100bp

marker, Lane A1, A2; conventinal PCR, Lane B1, B2; chip PCR ................... 114 marker, Lane A; (5.2 ng/), Lane B; (10.4 ng/), Lane C; (20.7 ng/), Lane D; (31.1 ng/), Lane E; (41.4 ng/), Lane F; (51.8 ng/), Lane G; negative control ............................................................................................................. 114

xii

Fig. 4 - 17 Fig. 4 - 18

Gel results of PCR results(buccal cell gene DNA): Gel results of PCR results(buccal cell gene DNA):

Lane M; 100bp Lane M; 100bp

marker, Lane A1, A2; conventinal PCR, Lane B1; chip PCR ......................... 117 marker, Lane A1, A2; conventinal PCR, Lane B1; chip PCR ......................... 117

xiii

List of TableTable 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Table 11 Table 12 Table 13 Comparison of micromold fabrication method.......................................... 35 Properties of working fluid at 20 ........................................................... 44 Comparison of temperature sensors ........................................................ 60 Thermal conductivity of materials ............................................................. 62 PR (SU-8 3035) Coating and Softbake condition .................................... 76 PR (SU-8 3035) Exposure and Development condition........................... 78 PR (AZ1512) Coating condition ............................................................... 82 PR (AZ1512) Exposure and Development condition ............................... 83 Cr/Au Etching condition ............................................................................ 83 Comparison of chip fabrication cost: United chip and Separable chip ... 91 Thermal cycle for chip PCR and conventional PCR ............................. 110 Sample reparation for SY158 gene PCR using proposed integrated DNA concentration(ng/) and purity(260/280) before and after ......... 116

microbiochip and conventional PCR machine (unit: ) ................................ 113

xiv

1 1.1 (Lab-on-a-chip, LOC) , , (lab-) (-a-chip) (-on-) . . , polydimethylsiloxane (PDMS) [1]

. PDSM casting, PMMA hot embossing . .

. , , , target sample . . 1990 Manz (sample pretreatment), (reaction & separation),[1]

(detection)

. , , , , , , , . ,

15

. Fig. 1-1 . (microbiochip), (peripheral instruments), (computer), .[1]

Fig. 1 - 1 Miniaturizing and integrating laboratory processes onto a microchip devices: concept of lab-on-a-chip Caliper Life Sciences (U.S.A) LabChip 90 Automated Electrophoresis System (Fig. 1-2(a)) Agilent 2100 Bioanalyzer (Fig. 1-2(b)) , , (device) .

16

(a)

(b)

Fig. 1 - 2 Commercial Lab-on-a-system: (a) LabChip 90 Automated Electrophoresis System(Caliper, U.S.A), (b) 2100 Bioanalyzer(Agilent, U.S.A)

. () . , one-step

. .

l

(IT) , IT IT . 1990 IBM, Motorola, Compaq, Hitachi IT BT ITNT . (Bioinformatics), (Biochip) IT-BT [2]

17

, (genome) . BT, IT, NT . . 2003 25% 2008 8 7 . . , , . , . Frost & Sullivan 2003 5 , 30% , 2010 50 .[3]

Fig. 1 - 3 Forecast of microbiochip market scale

[3]

, , , . , , , , ,

18

. , , , . , , . , , . . , MEMS, , CAD, , . .

1.2 post genomics , . DNA DNA , DNA (polymerase chain reaction, PCR) , (electrophoresis) . , cell lysis , PCR , (capillary electrophoresis, CE) (micro CE chip) DNA . , . . MEMS

19

, integrated . PCR integrated . DNA , , integrated .

l

(sample preparation)

, , , .

(micro total analysis system, TAS) . DNA , . , . , . integrated . DNA . DNA PCR . . DNA . DNA DNA . , , . (wastes) ,

20

(wastes washing process) integrated . . Cathy Keo [22]

94 C . DNA , , .[4-6]

DNA DNA (wastes) (washing) DNA . (wastes washing process) integrated . Fig.1-4 .[4-5]

MEMS

. , .

Fig. 1 - 4 Mechanical type DNA filter

DNA

21

PDMS integrated .

l

[7-20]

(microfluidic system)

. , / , , , , . , dead volume, , , , , . . . (active micro valve)[7-14]

(passive micro valve)

[15-20]

. , , [7-10] [20]

,

[11-13]

,

, diffuser , .

. (portable) . . Cantilever , , , Zengler , Feng Kim[19] [17]

Fig 1-5

parylene cantilever . , ,

22

, Li

[20]

10MPa

, Hu 90 SOI , 35.6 /min 65.5kPa , 600kPa 0.01 /min .

.

Fig. 1 - 5 Parylene cantilever type membrane valve PDMS , PDMS layer intregrated .

l

Integrated Integrated (cell

separation), (cell lysis) , PCR , , optical .

23

. (silicon), (polymer) Fig. 1-6 [42]

.

Fig. 1 - 6 Properties of main materials for integrated microbiochip

. Fig. 1-7 Cathy Ke[22]

cell lysis/PCR .

Fig. 1 - 7 Single step cell lysis/PCR microchip

24

. cell lysis PCR chamber . cell lysis PCR . . Fig. 1-8 Xing Chen[23]

continuous flow microfuidic chip cell separation, cell lysis, DNA purification , . cell PCR PCR . . .

Fig. 1 - 8

Continuous flow microfluidic device for cell separation, cell lysis and DNA purification

25

Fig. 1 - 9 Integrated RT-PCR system for virus detection

, Kang-Yi Lien[24] [25]

. Fig. 1-9

integrated microchip cell

lysis, DNA purification, RT-PCR . , . PDMS/glass , . integrated microchip . , . (passive check valve) , one-step (cell lysis), DNA (purification), (PCR) .

26

1.3 , DNA DNA (polymerase chain reaction, PCR) , . . PCR . , , PCR .

Fig. 1 - 10 Schematic diagram of integrate system for sample preparation and PCR

. , .

27

DNA PCR PDMS passive micro check valve . Fig. 1-10 one-step integrated chip .

1.4

1.4.1 DNA DNA PCR one-step , . .

1.4.1.1 : DNA filtering DNA , PDMS/glass chip (channel type) (cell lysis) PDMS pillar DNA filter , . : , . LabVIEW . heating .

1.4.1.2 (PCR) : DNA PCR

28

Y PCR : Y Yp, AZFa, AZFb, AZFc PCR PCR . : PCR integrated chip . PCR : . PCR . . . .

1.4.1.3 : (passive) (micro check valve) (cell lysis), DNA (purification), PCR one-step PDMS/glass , . Cell lysis, PCR : one-step .

1.4.2 MEMS .

29

, , , , (cell lysis, DNA purification), DNA (PCR) . integrated . .

Fig. 1 - 11 Research system of MEMS fabrication and Bio analysis

Fig. 1 - 12 Step process of integrated microbiochip development

30

1.4.2.1 Cell lysis, DNA purification Biochip /: Cell lysis, DNA purification - Cell lysis - PDMS pillar microbead DNA purification Bio : Cell lysis DNA purification - lysis - Purification DNA conventional PCR

1.4.2.2 PDMS Passive micro check-valve Biochip /: chip integration PDMS check-valve - Passive check-valve - PDMS check-valve - Check valve

1.4.2.3 Biochip /: PCR PDMS/glass chip Bio : PCR PDMS/glass PCR - PCR PDMS/glass chip , - PCR - PCR product quality 1.4.2.4 One-step Cell lysis, DNA purification, PCR integrated

31

Biochip /: Check-valve integrate

- Cell lysis DNA check-valve PCR integrate - Integrate check-valve Bio : One-step - One-step cell lysis, DNA purification, PCR ,

32

2

2.1 2.1.1 PDMS(polydimethylsiloxane) PDMS

. , . . . Fig. 2-1 polydimethylsiloxane .

CH3 CH3 Si CH3 O

CH3 Si CH3 n O

CH3 Si CH3 CH3

Fig. 2 - 1 PDMS molecule structure formula PDMS .

l

. .

l

PDMS (interfacial free energy) . , PDMS polymer molding , .

33

l

PDMS homogeneous, isotropic, 300nm . .

l

PDMS

elastomer

.

molding PDMS stamp , degradation . l PDMS surface property SAM (self-assembly monolayer) plasma , interfacial energy . l Molding PDMS .

.

PDMS

SYLGARD

184

silicone

elastomer

Dow Corning . PDMS . PDMS (hydrophobic) PDMS . O2 Plasma (hydrophilic) . PDMS O2 Plasma . O2 plasma PDMS OH PDMS . PDMS . O2 Plasma biochip glass, Si, PDMS .

34

2.1.2 SU-8PDMS (, mold) PDMS . [26]

Table 1

.

Table 1 Comparison of micromold fabrication method

DUV(deep UV) . DUV thick deep UV-sensitive polyimide, AZ-4000 SU-8 . SU-8 (negative photoresist) (micromachining) . IBM Microchem (www.microchem.com) Sotec Microsystems (www.somisys.ch) IBM , [26]

. SU-8 (Glass), (Ceramic) ,

1~1000

.

UV aligner (expose) (Plasma Ion Etching Process) . 200 . UV aligner (expose) synchrotron X-Ray LIGA(Lithographie, Galvano-formung, Abformung) LIGA-like . SU-8 LIGA-like LIGA(poor mans LIGA) .

35

Fig. 2 - 2 High aspect ratio micro structure fabricated by SU-8 (Microchem, U.S.A)

2.1.3 Pyrex glass20 (Corning Glass Works) (Pyrex) . , . , , (sodalime silica) 90~100 x 10 / . (boron) 32~35 x 10 / 1/3 . , Fig. 2-3 Fig. 2-4 MEMS . 500 4 pyrex 7740 glass wafer .-7 -7

36

Fig. 2 - 3 Basic material properties of Pyrex7740

Fig. 2 - 4 Thermal expansion coefficient of silicon and pyrex glass(7740)

37

2.2 PDMS

2.2.1 . (micro channel) . PDMS 48 . [27-29]

. PDMS

BSA, PVP . . [30]

.

Fig. 2 - 5 PDMS channel for cell lysis

38

cell lysis PCR PDMS serpentine . 150, 600 cell lysis 15. inlet 1mm syringe pump . cell lysis .

2.2.2 DNA Cell lysis DNA . DNA . DNA . DNA . DNA DNA . filtering DNA DNA washing DNA DNA . PDMS . DNA DNA integrated chip . Integrated microchip DNA .

39

Fig. 2 - 6 Pillars and microbeads in PDMS channel for DNA filtration PDMS (pillar) 50 DNA filtering filter . 40~70 . DNA bp 1bp 0.34nm[31]

1000bp DNA 1

. DNA . 600 PDMS pillar 100, pillar 50 . 50 Fig. 2-7 7.7 . DNA .

40

Fig. 2 - 7 Schematic diagram of filterable size in channel filled with microbead

2.2.3 Microfluidic system Laminar . Scale down inertia force . (Reynolds number) macroscale 1000 microscale 100 laminar flow . macroscale convective turbulence . (passive) [32-34]

.

[35-37]

(active)

.

perturbation . stretch and folding laminar chaotic advection . . integrated chip

41

pillar DNA template PCR reagents . ESIGroup CFD-ACE+ pillar , .

Fig. 2 - 8 Pillars in PDMS channel for mixing of DNA and PCR reagents

DNA template PCR reagents 4pillar .

2.2.3.1 Microfluidic mixing theory (continuum flow regime) . Navier stokes Continuity .

r

dV + rV V = - p + m 2V dt V = 0

V , p , r , m

42

. Reynolds(inertial forces to viscous forces) Peclet(convection time/molecular diffusion time) .

Re =

ru l u l = m v

,

Pe =

ul D

,

r , u , m , l , v D .

,

.

c + V c = D 2 c + R t

c , V , D , R

. CFD-ACE+ .

2.2.3.2 pillar pillar CFD-ACE+ . 4 pillar 200,300 . . , 20 (steady state) . 20 Table.2 . .

43

. , . (flow module) (user scalar module) . 3 (3-dimensional unstructured grid) 2 (second order upwind scheme) conjugate gradient squared and preconditioning (CGS+Pre) algebraic multigrid (AMG) . Table 2 Properties of working fluid at 20

Fluid Water Ethanol

Viscosity Diffusivity (Kg-1s-1) (2s-1) 9.010-10 1.210-9 1.2103 1.2103

Density (Kg-3) 9.99810-16 7.8910-16

2.2.3.3 modeling Fig.2-9 600 4 pillar pillar chaotic advection

. syringe pump 200/min(fixed velocity) 100000 N/m (fixed pressure) . (no-slip condition) . , . Paint shop pro version 10 (Jasc software, Inc.) pgm(portable gray map) . pgm , 0 2552

44

. 50

(pixel) . (standard) (measurement) 0~1 (Ii) [39].

Intensity value

I

i

=

measurement - blue s tan dard red s tan dard - blue s tan dard

.

efficiency (%) = 1 N Io

1 N 1 N

(IN i

i

- I iPer .mix -I

)

2

(IN i

o i

Per .mix 2 i

)

* 100

Per.mix

I .

45

Fig. 2 - 9 Simulation model for micro-mixer Fig.2-10 . (a) mixing pillar (b), (c) pillar 200, 300 . 10 Fig.2-11 .

46

(a)

(b)

(c) Fig. 2 - 10 Simulation results of micro-mixer : (a)no pillar, (b)pillar diameter size:200, (C)pillar diameter size:300

47

Fig.2-10 (a) pillar . (laminar flow) . 200 pillar . 300 pillar . pillar . 300 pillar 15% 300 pillar .

Fig. 2 - 11 Comparison of mixing efficiency

PCR inlet . , PCR denaturing 95 C PCR . . 300 pillar 95 C 30 , CFD o o

48

. Fig.2-11 90% . PCR .

2.2.4 PCR PCR [30]

.

PCR serpentine . .

Fig. 2 - 12 Serpentine micro reactor for PCR

49

2.3

2.3.1 Cell lysis, DNA filtering cell DNA PCR . . . . . (passive check valve)

. integrated . . membrane . membrane . . . PDMS , , PDMS (flexible) .

50

Fig. 2 - 13 Schematic diagram of passive check valve

2.3.2 . PCR DNA template PCR reagents

. DNA PCR reagent . . , 3mm, 4mm, 50 membrane PDMS 300.

51

Fig. 2 - 14 Passive check valve in integrated microbiochip

2.3.3 Fig.2-15 ho forward , backward . (water) , 1kPa 20kPa . forward 2kPa 3kPa 5 /min . . Backward 1kPa 20kPa . PDMS .

52

Fig. 2 - 15 Schematic diagram of experimental instruments setup

Fig. 2 - 16 The flow rates as a function of the pressure

53

2.4

2.4.1 MEMS (thin film) . (strain, piezoresistance effect ), (temperature, intrinsic temperature dependence of the resistor ) [23]

.

. (joules heat: ) . .

2.4.1.1 , TCR

. .

R = R0 1 + a R (TR - T0 )

, R0 T0 R TR . a R 10-4 / K . a R - . .

54

2.4.1.2 (current-driven heater) (voltage-driven heater) . (fuse) . . , Fig. 2-17 . .

Voltage or Current Input

Metal line Joule heatingVoltage driven method: Toast machine Current driven method: Fuse

Power Voltage2/Resistance

Current2

Power Resistance

Fig. 2 - 17 Joule heating from metal line by external electric source 2.4.1.3 (joule heating) lumpedelement thermal circuit Fig. 2-18 [40]

.

55

Fig. 2 - 18 Circuit model for the joule heating of a resistor driven from a voltage source

: (power) (voltage source)

V 2 / R , (heat capacity) (thermal capacitor) CT , T0 thermal reservoir (thermal resistance) RT . T0 0 . , PDMS, , , , PDMS, , . . , .

qi , qo [cal / sec] T (o C ) , Ct (cal / o C ) .

Ct

dT = qi - qo dt

,

dT Q = CT (cal ), q = C dt (cal / s )

Rs [o C sec/ cal ] qo = T / Rs ( PDMS . (

56

:

R

total

= Rs + R pyrex + RPDMS ))

Rs Ct

dT + T = Rqi dt

qi

qi = V 2 / RH

V

RH

. , micro reactor .

Rs Ct

dT dT RH T + T = RsV 2 / RH RH Ct + =V2 dt dt Rs

Laplace .

Rs T (s) = U ( s ) RH ( sRCt + 1)

( where, V

2

(t ) = u (t )

)

dT V2 T = , dt R0Ct (1 + a T ) Rs Ct

where RH = R0 (1 + a T )

T0 0 .

V2 V 2 (1 - a T ) Q a < 0, a 2