and its applications in energy using comsol · investigation of transport phenomena inphenomena in...
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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COMSOL Modeling using PDE Mode
Navier‐Stokes eq. Poisson eq. Nernst‐Planck eq.
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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
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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
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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
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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
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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
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Open circuit voltage verus Short‐circuit current
Open‐circuit voltage
Short‐circuit current
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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
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Numerical results: I‐P curve
Over limiting currentOhmic current Over‐limiting currentregionLimiting current
region
O ic cu e tregion
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Numerical results: I‐V curve0.05MPap
2mC/m1s 2mC/m3s 2mC/m5s
0.1MPap
2mC/m1s 2mC/m3s 2mC/m5s
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Numerical results: I‐V curve0.5MPap
2mC/m1s 2mC/m3s 2mC/m5s
1.0MPap
2mC/m1s 2mC/m3s 2mC/m5s
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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)
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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)
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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
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25Ion depletion and enrichment
~ 60 nm nanochannel
microchannelnanochannel- - GNDGND
glass
+ +VH VH
g
Simulation using COMSOL
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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
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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
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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
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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
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RED in a conical‐shaped nanopore5nmta
titip base
55nmba 110nmba 55nmba 110nmba
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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.