Modeling and Design Diaphragm Micropump

University of South Florida - March 17, 2008

Diaphragm micropump with passive check-valves

Destination

Inlet valve

Outlet valve

Pump chamber

Pump chamber

Pump chamber

p1

p2

s s

1 1 2 2

d d

Diaphragm

Source

1

2 2

Valve discs

z

Vdead

p2*

p1*

p(t)

p(t)

ΔV

22

1 1

1

Pump chamber: mathematical model

outoutinin QQdt

dV

dt

dp

K

V

dt

dwAQQ

whA

K

dt

dpoutin

ppQin 11 22 ppQout

whAV

Pump chamber: Simulink model

Qin

Qout

1/3

zeta

0.8

h

TriangleWave Scope: w

Scope: p

Scope: Qacc

Scope: Q

Product3

Product2

Product1

Product

110000

P2

92000

P1

Outlet valve

2.23e9

K

1s

Integrator1

1s

Integrator

Inlet valve

Divide

du/dt

Derivative

1/57

C2

1/57

C1

Add1

78.54

A

ppH

pRQin

1

1

22

ppH

pRQout

Pump chamber: simulation results

Typical actuators

Thermopneumatic micropump

Diaphragm deflection

action membraneby resisted load

3

sprestresseby resisted load

0

action bendingby resisted load

3

2 13

84

13

16

a

w

a

E

a

w

aa

w

a

Eppa

321 wBwBppa

20

4

3

214

13

16

aa

EB

42 13

8

a

EB

AwwaV 2deflection

1

0

2 du

Temperature–deflection relationship

aa h

w

p

wBwBTT 11

0

321

0

44

33

2210 1 wCwCwCwCTTa

aaa hp

BC

p

BC

hp

BC

hp

BC

0

24

0

23

0

12

0

11 ,,,

Temperature vs. deflection

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100 120Temperature rise, K

Def

lect

ion,

µm

Measured (Wego et al., 2001)

ζ = 1/2 (Wego et al., 2001)

ζ = 0.458 (s. s. edge model)

ζ = 1/3 (clamped edge model)

ζ = 0.396 (average model)

Actuation chamber: math. model

easass

sps WTTGdt

dTcm ,

dt

dwApTTGTTG

dt

dTcm afafaasas

aava ,

eaa WTTDdt

dTD 021

3

42

32101

44

33

22102

432 wCwCwCCTD

wCwCwCwCTDW

dt

dw e

Actuation chamber: Simulink model

wInput: Heating Power

-C-

zeta

-C-

p0

0.8

h_a

308

T0

MATLABFunction

T(w)/T0

MATLABFunction

T'(w)/T0

Scope: w

Scope: W'e

Pulse

Product4

Product3

Product2

Product1

1s

Integrator

Divide3

Divide2

Divide1

Divide

-K-

D2

-K-

D1

-C-

B2

-C-

B1

Add

Actuation chamber: simulation results

Experimental data

Thermopneumatic micropump: Simulink modelw

Input: Heating Power

Qin

Qout

1/3

zeta1

1/3

zeta

0.8

h_a

0.8

h

308

T0

MATLABFunction

T(w)/T0

MATLABFunction

T'(w)/T0

Scope: w1

Scope: w

Scope: p

Scope: W'e

Scope: Qacc

Scope: Q

Pulse

Product7

Product6

Product5

Product4

Product3

Product2

Product1

Product

110000

P2

92000

P1

Outlet valve

2.23e9

K

1s

Integrator2

1s

Integrator1

1s

Integrator

Inlet valve

Divide4

Divide3

Divide2

Divide1

Divide

du/dt

Derivative

-K-

D2

-K-

D1

1/57

C2

1/57

C1

-C-

B2

-C-

B1

Add1

Add

78.54

A

Thermopneumatic micropump: simulation results

PCB Thermopneumatic micropump

PCB design (boards 1 & 2)

TOP

BOTTOM

1 2

PCB design (boards 3 & 4)

TOP

BOTTOM

3 4

Pneumatic micropump

Pneumatic micropump: math. model

321 wBwBppa

dt

dwAQQ

whA

K

dt

dpoutin

ppQin 11

22 ppQout

42 13

8

a

EB

20

4

3

214

13

16

aa

EB

3

32

210

2211

d

d

wCwCwCCA

ppppK

t

w

10 hBKC 11 BC 22 3hBC 23 3 BC

Pneumatic micropump: Simulink model

Q_in

Q_out

w

p

p_v

0.4

zeta

1.92e5

sigma_0

6900

p_a

0

p_2

0

p_1

0.5

nu

2

h

0.14

delta

MATLABFunction

a to A

4

a

Scope

Pulse Generator

Outlet valve

2.23e9

K

1s

Integrator (0-T)

1s

Integrator

Inlet valve

13.94

13.94

G (volume pumped/cycle)

0.51e6

E

0.033

D2

0.033

D1

715

MATLABFunction

C3 Coeff.

MATLABFunction

C2 Coeff.

MATLABFunction

C1 Coeff.MATLABFunction

C0+C1*w+C2*w^2+C3*w^3

MATLABFunction

C0 Coeff.

MATLABFunction

B3 Coeff.

MATLABFunction

B1*w+B3*w^3

MATLABFunction

B1 Coeff.

50.27

A (base area)

0

100

200

300

400

500

600

700

0 5000 10000 15000 20000Pressure (Pa)

Flo

w r

ate

(m L

/s)

Experiment (Meng et al., 2000)

Linear regression

715H715033.0 ppp

Pneumatic micropump: results

Pneumatic micropump: volume pumped per cycle vs. frequency

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50Frequency (Hz)

Vo

lum

e p

um

pe

d p

er

cycl

e (m L

) Experiment (Meng et al., 2000)

Simulation

Pneumatic micropump: flow rate vs. frequency

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50Frequency (Hz)

Flo

w r

ate

(m L

/s)

Experiment (Meng et al., 2000)

Simulation

Pneumatic micropump: flow rate vs. back pressure

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6

Back pressure (kPa)

Flo

w r

ate

(mL/

s)

Experiment (Meng et al., 2000)

Simulation