Transport of ions, colloids and water
in porous media and membranes
with special attention to
water desalination by capacitive deionization
ion
ion
water
ion
Maarten Biesheuvel
Overview
•
•
•
•
Capacitive Deionization (CDI)
Porous electrode theory
Modeling ion electrokinetics (combined flow of water, ions, colloids)
Sedimentation of colloidal particles
2
Carbon Electrode +
+ Porous
Current
Collector
-
_
Current
Collector
Capacitive
Deionization
+
+ +
+
+
cations
Porous Carbon Electrode
+
+
electrical
current
Electrical
Feed Water
current
Freshwater
Porous Carbon Electrode
_
+
+
-
_
+
+
+
+
+
Feed
Water-
Freshwater
-
--
-
-
+
+
+
Current Collector
Current Collector
+ cations
- anions
cations
anions
- anions
cations
+
+
-
-
-
+
-
Curren
-
Curre
cations
Porous Car
-
-
Porous Car
Porous Carbon
Electrode
+ Porous Carbon Electrode
electrical
current
_
+
-
Feed Water
V
VVcell
cell
Current Collector
Vcell
+
+
_
anions
-
3
Membrane Capacitive Deionization
with ion-exchange
membranes
4
Membrane Capacitive Deionization
5
6
CDI testing
7
Water
out
What does CDI look like?
current collector
carbon electrode
cation exchange
membrane
Water in
anion exchange
membrane
carbon electrode
current collector
8
Ion-exchange
membrane
Carbon
electrode
Carbon
Electrode
Carbon
electrode
Graphite
rod
CDI designs using cylinders (wires)
Electrode composition:
90 wt % active carbon
10 wt % polymeric binder
9
10
2
11
2
Transport in porous electrodes
electron-conducting matrix
12
2
Transport in porous electrodes
“RC Transmission Line Theory”, or “De Levie Theory”
13
2
Bob (Robert)
de Levie
ISE, Prague, 2012
14
RC transmission line theory
pore
pore
pore is potential in aqueous pore
relative to conducting matrix (metal, carbon)
15
2
Generalized porous electrode theory
Prof. Martin Bazant
MIT, USA
16
2
Generalized porous electrode theory
From abstract:
Todd Squires
17
2
Transport in porous electrodes
Transport equation
in mAcropores
ci
   JNP,i  ji,mAmi
t
“Electrical double layer” model
in micropores
St
carbon
matrix
diffuse layer
d
ji,mAmi
(x)
JNP,i
,ci,mA  V ,ci,mi
JNP,i  Di ci  zici
18
2
Porous electrode transport theory
+
e-
+
-
+
+
-
+
Brackish
water
Potable
water
-
+
+
-
+
+
19
Potable
water
Porous electrode transport theory
-
+
-
+
-
+
+
-
Ion transport in the
mAcropores
+
-
Brackish
water
+
+
+
Ion adsorption in the
micropores
20
21
Including acid/base reactions
In NP-transport modeling in porous media
• Water not just contains a salt like NaCl which can be assumed
fully dissociated
• Instead, more realistically there are many ions that can undergo
acid/base reactions, such as NH3, NH4+, HCO3• Of special relevance the reactions with and between H+ and OH• All these species must be considered !
F.G. Helfferich
(1922-2005)
22
Helfferich-approach
ci
   JNP,i  Ri
t
RA  RB  RC
JNP,i  Di ci  zici
AB C
RA  k [ A][B]  k [C ]
[ A][B]
Ki 
[C ]

CO  H 
K 
HCO 
2
3
i


3
F.G. Helfferich
23
Advantages Helfferich-approach
• By addition of balances, for each “group” such as CO2/HCO3-/CO32-,
only one balance per group remains (expressed in one chosen “master
species”)
• All dummy parameters R disappear !
• Very elegant now to include electrochemical reactions at electrodes, or
evaporation
F.G. Helfferich
24
Steady-state diffusion of “acid/base ions”
0.350
4
H2CO3
0.300
Na+
H+
OH-
ion flux
bulk
Cl-
Ion flux
CO32-
fr current by OH curr +2
flux H2CO3
flux CO3^2-
1
flux OH
0
OH-
-1
HCO3-
-2
CO32-
-3
0.250
“2H+ +2e-  H2 (g)”
HCO3
fr current by OH curr +4
flux HCO3
2
current_by_OH/total_current
H2CO3
-
fr current by OH curr +3
3
0.200
increas
current
0.150
0.100
0.050
0.000
-4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
x-coordinate
position
It’s not the proton that flows,
and it is not the source of the formed H2-gas !!!
25
Current-induced membrane discharge
water in membrane pores
membrane discharge
SDL: stagnant diffusion layer
Membrane: water-filled structure with very high
concentration of fixed charge, such as RH+, e.g. 5 M
26
Current-induced membrane discharge
charge parameter

RH 

RH  R


27
Ion electrokinetics incl. flow of water
ion
ion
water
ion
• Same approach for ions as for colloids, protein and larger particles
• The ion (with its hydrated water molecules) is a dispersed particle
• Water is the continuum fluidum in between – described very
differently from the ions !!
• Extension of two-fluid model to “colloidal regime”
28
Two-fluid model
ion
ion
water
ion
29
Two-fluid model for colloidal mixtures
vi  v water  Di i
i  lnci   zi  excess  Vi P total  migh
total = Phydr - osm
PNernst-Planck
“Two fluid Navier-Stokes Equation”
ci
total
2
P   waterg   v water   vi  v water 
i Di
P hydr  avgg  2 v water  elecE
30
Paradox in sedimentation
(Theoretical) physicist: at equilibrium, the gravitational
force a colloidal particle feels is its mass density minus
that of the solvent (the liquid in between)”
(Chemical) engineer: in a mixed system, a particle feels
the average, suspension density (*)
(*): and for non-colloidal (larger) particles always
31
Sedimentation of colloidal particles
Solvent/supernatant
• Three types of colloidal particles
(< 1 micron size) with different colors
• All heavier than the solvent
• Purple is mixture
• Not a “solid” sediment that is formed
32
Thank you for your attention !