Investigation of transport phenomena in nanochannelsInvestigation of transport phenomena in nanochannels and its applications in energy conversion using COMSOL Multiphysics

S k Ch h Ch Ch 張志彰

CO SO u tip ysics

Speaker: Chih‐Chang Chang (張志彰)ResearcherGreen Energy and Environment Research Laboratoriesgy

2013 COMSOL User Conference, Taipei, Taiwan

Outline

Nanaofluidics: fluid/ion transport

El ki i l i l d bl l Electrokinetics: electrical double layer

M d li i COMSOLM lti h iModeling using COMSOL Multiphysics

Physical problems Physical problems

Conclusions Conclusions

What is “Nanofluidics” ? Aquaporins (AQP)

• Slippage• Electrostatic gateElectrostatic gate 

P t i h lPotassium channel Kidney

El t t ti l i f t iGlomerular proteinuriaElectrostatic repulsion of proteins

Engineered Nanofluidicsnanofluidics

Tsukahara et al., Chem. Soc. Rev. 39, 1000 (2010).

New nanofluidics (engineered nanofluidics):1. Well‐designed and controlled nanochannels are ideal physical modeling  systems to  

study fluidics in a precise manner

AAOSili PET

study fluidics in a precise manner.

2. Learning new science using controlled regular nanospaces.

AAOSilica PET

ElectrokineticsElectrokinetics refers to transport phenomena related to the non‐electroneutral EDL, which is created to neutralize the surface charges produced on surface. 

Surface charges are produced by the dissociation of surface functional groups: HAAH

Reactions:

EDL thickness (i.e., Debye length) is

HAHAH2Reactions:

0 1RTf

EDL thickness (i.e., Debye length) is dependent on salt concentration c0 :

0022

0 12 ccFz

fD

KCl solution (mM) )nm(DKCl solution (mM) )nm(D

10

1.0

3

10Diffuse layer

DI water: 300nm0.1 300.01 100

Diffuse layer

6Electro‐osmosis

Electro‐osmosis refers to the movement of liquid relative to a stationary charged surface under an external electric field. 

Electrical body force (Coulomb force) is produced within EDL:

c a ged su ace u de a e te a e ect ic ie d.

EF ee is produced within EDL:

Liquid motion outside of EDL is driven by viscous diffusion

E Plug‐like flow

E

net charge density:

El i fl (EOF) i hi EDL i h l

ccFze

Electro‐osmotic flow (EOF) in a thin EDL microchannel

7Nanochannel: ion selectivity

Microscale: Nanoscale: D~μm 1 aDμm 1 a

D

2a

lwc

lwhKn

22 Silica nanochannels zFlln

(1) bulk conductance (2) Surface conductance (nS)nK ( )n

(1)(2)

• ion‐transport/ion‐current control• electrical sensing

tc

c

( )(2)• separators: energy conversion 

8Nanofluidic transistor02 Dgg VVV 0 gV

dielectric layer

gate (metal)

0gV

dielectric layer

gate (metal)

0gV

gate (metal)0DVgate (metal)0DV

Its function looks like a metal‐oxide‐semiconductor field‐effect i (MOSFET)

D 0gV0DV 0gV

transistor (MOSFET).Negatively charged dye: exclusion effect 

Thin EDL Thick EDL

R. Karnik et al., Nano Lett. 5, 943 (2005)

Mathematical Model (cont.)

Flow field: incompressible Navier‐Stokes equation (continuum theory)2 F

0

2

uFuuu ep

eeFwhere

Poisson‐Nernst‐Planck model

Electric field: Poisson equation (electrostatics)

2

0

2

f

e i

iie CzFwhere

I i i fi ldIonic concentration field:

i i i i i i iz Fc D c c j u : Nernst‐Planck equation

0 ij : Species transport  equation

Mathematical ModelGeometry:

Boundary condition:000c

n unn 0u

000c

n unn

Boundary condition:

or 0L

L

p p n

R

R

p p

0

0

0s f

un

n j

0cn

0c c 0c c

Symmetric boundary condition

s

0 n uy y00c

nn

COMSOL Modeling using PDE Mode

Navier‐Stokes eq.  Poisson eq. Nernst‐Planck eq.

Validation with PB modelMESH: 28000‐32000 quadrilateral elements

Results: compared with analytical solution of PB modelResults: compared with analytical solution of PB model

2mC/m1s 2mC/m3s 2mC/m5s

13Streaming current Under a hydrostatic pressure (∆p), the pressure‐driven liquid flow carries the charges within EDL towards the downstream end and results in an electricalconvection current, namely the streaming current. 

pu

u

p

strI1p 2ppu

12 ppp

A pestrstr dAupSI Streaming current: A

14Streaming current in silica nanochannels

140 nm silica nanochannel

1011

89

A/b

ar)

67

p(p

A

van der Heyden et al. [2]

self consistent PB model [1]

345

I/-p

present modelpresent model

self-consistent PB model [1]

(b = 0)Stern

(b = 0.8b )Stern K+

10-5 10-4 10-3 10-2 10-123

( )

(b = 0.8b )Stern K+

( )self-consistent PNP model [1]

C.‐C. Chang and R.‐J. Yang, J. Colloid Interface Sci. 339, 517 (2009).

C (M)0

15Streaming potentialAt open‐circuit condition (i.e., zero‐current condition), the charges accumulate at the downstream end and then an electrical potential difference called the t i t ti l (i i i l OCV) i d dstreaming potential (i.e., open‐circuit voltage, OCV) is produced.

t

pu eoustrI

str

0Ipu

puepuu

eou

1p 2p

lE

epueou

I

1p 2p

strstrcstr

pSIII 0Streaming potential:

lE strstr cI

cstrcstr Kea i g po e ia

Electrokinetic energy conversion

Electro‐kinetic battery refers to the external electronic load driven by the electric power from streaming current/potential.e ect ic powe o st ea i g cu e t/pote tia .

e e

slip length

Open circuit voltage verus Short‐circuit current

Open‐circuit voltage

Short‐circuit current

Short‐circuit condition: Concentration polarizationp

0 0

0.01MPapI i h

0.05MPapIon enrichment

0.1MPap

0 2MP

0.5MPap

0.2MPap Ion depletion

0.5MPap

Numerical results: I‐P curve

Over limiting currentOhmic current Over‐limiting currentregionLimiting current

region

O ic cu e tregion

Numerical results: I‐V curve0.05MPap

2mC/m1s 2mC/m3s 2mC/m5s

0.1MPap

2mC/m1s 2mC/m3s 2mC/m5s

Numerical results: I‐V curve0.5MPap

2mC/m1s 2mC/m3s 2mC/m5s

1.0MPap

2mC/m1s 2mC/m3s 2mC/m5s

Conversion efficiency30

6

7

8)

dashed-linesolid-line

previous modelpresent model

symbol numerical results6

7

8

)

dashed-linesolid-line

previous modelpresent model

symbol numerical results

30 nm 60 nm

3

4

5

6

max

pow

er(%

)

s-1mC/m2

-3mC/m2

-5mC/m2

3

4

5

6

max

pow

er(%

)

s-1mC/m2

-3mC/m2

1

2

3 m -10mC/m2

5mC/m

1

2

3 m -5mC/m2

0.1MPa 0.1MPa

10-6 10-5 10-4 10-3 10-2 10-1 1000C (M)0

10-6 10-5 10-4 10-3 10-2 10-1 1000C (M)0

6dashed-line

lid liprevious model

t d l

7dashed-line

lid liprevious model

t d l

4

5

pow

er(%

)

solid-linesymbol numerical results

present model

p-

0.05MPa0.1MPa 4

5

6

pow

er(%

)

solid-linesymbol numerical results

present model

p-

0.05MPa

1

2

3

m

axp

1.0MPa

0.1MPa

0.2MPa0.5MPa

1

2

3

max

p 0.1MPa

0.5MPa

0.2MPa

10-6 10-5 10-4 10-3 10-2 10-1 1000

1

C0(M)10-6 10-5 10-4 10-3 10-2 10-1 1000

1

C0(M)

Conversion efficiency‐slippage

Isub

load Electronic Navier slip velocity:

s

0

b

b

a2r zubus

ppL L 0R

0Rpb

lbwhere       is the slip length

y

25

30 b=75nm

b=30nm

p g

15

20

max

(%)

b=15nm

b=30nm

No-slip Partial slip Perfect slip

5

10

b=0

b0b b0 b

100 101 102 103

p (kPa)

24Ion concentration polarization (ICP)‐ nonequilibrium phenomenon at interfaceq p f

nanospacemarcospace marcospace

electromigration flux electromigration flux

nJ

mJ

J J

mJ

JmJ nJmJ

cnc c

ion depletion ion enrichment c

cConcentration gradient

nc c

J Concentration gradient diffusion fluxdiffusionJ

diffusionJ

25Ion depletion and enrichment

~ 60 nm nanochannel

microchannelnanochannel- - GNDGND

glass

+ +VH VH

g

Simulation using COMSOL

26Nanofluidic sample preconcentration/desalination

V Vnet flowEO

VH VL

EK trapping EN

ET

EO + EP = 0 

EPVH VL

GNDVH

V

GND GND

VL

buffer zone depletionzone

desalted zonezone

1. bio‐sample preconcentration1. bio sample preconcentrationApplications: 2. species separation

3. sea water desalination

Simulation using COMSOL

27Electroosmotic pump using a conical‐nanopore membrane (cont.)p

Electro‐osmosis

(membrane)

pressure

Electric power hydraulic power

A single conical shaped nanoporeTrack etched PET membrane A single conical‐shaped nanoporeTrack‐etched PET membrane

zr

28Electro‐osmotic pump using a conical‐nanopore membraneg p

biVforward bias

250 8

Current rectification Flow rectification

ta bazrbiasV

pA) 150

200

250forward biasrevrese bias

c0=10-3M=-3mC/m2

fL/s

)

4

6

8forward biasrevrese bias

c0=10-3M=-3mC/m2

lreverse bias

|I|(p

50

100 |Q|(

f

2

4

• Forward bias: ion‐enrichment resistance is decreased. decreased electric field

|Vbias|0 2 4 6 8 10

0

|Vbias|0 2 4 6 8 10

0

1.2for ard bias

1.5f d bi decreased electric field.

lower pumping efficiency.

• Reverse bias: ion‐depletion x(%

)

0.6

0.8

1forward biasreverse bias

x(%

) 1

forward biasreverse bias

c0=10-3M=-3mC/m2

p resistance is increased. increased electric field. amplified EK flow

max

0

0.2

0.4

0.6

=-3 mC/m2

|Vbias|=1 volt

max

0

0.5

amplified EK flow.   better pumping efficiency. c0 (M)

10-5 10-4 10-3 10-20

|Vbias|0 2 4 6 8 10

0

Reverse electro‐dialysis (RED)

Electrodialysis RED

Gibb f f i iEl i i Gibbs free energy of mixing  Electricity

Electricity    Gibbs free energy of mixing

Diffusion current/potential

RED in a conical‐shaped nanopore5nmta

titip base

55nmba 110nmba 55nmba 110nmba

ConclusionsCOMSOL Multiphysics

User friendly

Flexibility: PDE mode

A quick simulation tool for continuum nanofluidics and multiphysics p y

A very good tool for researchers and graduatedy g gstudents to speed up their research works.