Transport of ions, colloids and water
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Transport of ions, colloids and water in porous media and membranes with special attention to water desalination by capacitive deionization. water. ion. ion. ion. Maarten Biesheuvel. Overview Capacitive Deionization (CDI) Porous electrode theory

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Transport of ions colloids and water in porous media and membranes with special attention to

Transport of ions, colloids and water

in porous media and membranes

with special attention to

water desalination by capacitive deionization

water

ion

ion

ion

Maarten Biesheuvel


Transport of ions colloids and water in porous media and membranes with special attention to

  • Overview

  • Capacitive Deionization (CDI)

  • Porous electrode theory

  • Modeling ion electrokinetics (combined flow of water, ions, colloids)

  • Sedimentation of colloidal particles


Transport of ions colloids and water in porous media and membranes with special attention to

Capacitive Deionization


Transport of ions colloids and water in porous media and membranes with special attention to

Membrane Capacitive Deionization

with ion-exchange membranes


Transport of ions colloids and water in porous media and membranes with special attention to

Membrane Capacitive Deionization


Transport of ions colloids and water in porous media and membranes with special attention to

CDI testing


Transport of ions colloids and water in porous media and membranes with special attention to

Whatdoes CDI look like?

Water out

current collector

carbon electrode

cation exchange membrane

spacer

Water in

anion exchange membrane

carbon electrode

current collector


Transport of ions colloids and water in porous media and membranes with special attention to

CDI designs using cylinders (wires)

Electrode composition:

90wt% active carbon

10 wt % polymeric binder

1

Graphite rod

Ion-exchange membrane

Carbon

Electrode

Carbon electrode

Carbon electrode


Transport of ions colloids and water in porous media and membranes with special attention to

2

That brings me to the porous electrodes

Here I focus on storage of ions, but the electrodes can also be electrochemically active, and convert one ion into another, a “redox” reaction but that I don’t discuss today


Transport of ions colloids and water in porous media and membranes with special attention to

2


Transport of ions colloids and water in porous media and membranes with special attention to

Transport in porous electrodes

electron-conducting matrix

e-

micropores

micropores

ions

ions

mAcropores

mAcropores

2

Three interpenetrating phases. We don’t have adsorption on the “walls’ of the mAcropores. There are no walls. It is swiss cheese

  • mAcropores charge-neutral

  • EDLs formed in micropores where electronic charge and ionic charge compensate


Transport of ions colloids and water in porous media and membranes with special attention to

Transport in porous electrodes

“RC Transmission Line Theory”, or “De Levie Theory”

2


Transport of ions colloids and water in porous media and membranes with special attention to

Bob (Robert)

de Levie

ISE, Prague, 2012


Transport of ions colloids and water in porous media and membranes with special attention to

RC transmission line theory

pore

pore

pore is potential in aqueous pore

relative to conducting matrix (metal, carbon)

2

Many problems:

Only valid for constant R and C, neither valid except for experiments at say 1 M.

No means to model mixtures of salts

Or acid/base reactions


Transport of ions colloids and water in porous media and membranes with special attention to

Generalized porous electrode theory

Prof. Martin Bazant

MIT, USA

2


Transport of ions colloids and water in porous media and membranes with special attention to

Generalized porous electrode theory

From abstract:

Todd Squires

2


Transport of ions colloids and water in porous media and membranes with special attention to

Transport in porous electrodes

“Electrical double layer” model

in micropores

Transport equation

in mAcropores

2

In limit of no resistance to transfer mA  no explicit relation for j_{i,mAmi}


Transport of ions colloids and water in porous media and membranes with special attention to

Porous electrode transport theory

+

-

+

-

e-

+

-

+

-

+

Brackish

water

Potable

water

-

+

-

+

-

+

-

+

-


Transport of ions colloids and water in porous media and membranes with special attention to

Porous electrode transport theory

Potable

water

-

Ion transport in the mAcropores

-

+

+

+

-

+

-

-

+

-

+

+

Ion adsorption in the micropores

-

+

Brackish

water

-


Transport of ions colloids and water in porous media and membranes with special attention to

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)


Transport of ions colloids and water in porous media and membranes with special attention to

Helfferich-approach

F.G. Helfferich

Many technical advantages in modeling, too many to list them here


Transport of ions colloids and water in porous media and membranes with special attention to

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


Steady state diffusion of acid base ions

Steady-state diffusion of “acid/base ions”

H2CO3

HCO3-

CO32-

Na+

Cl-

H+

OH-

Ion flux

“2H+ +2e-  H2(g)”

bulk

position

It’s not the proton that flows,

and it is not the source of the formed H2-gas !!!


Current induced membrane discharge

Current-induced membrane discharge

membrane discharge

water in membrane pores

SDL: stagnant diffusion layer

Membrane: water-filled structure with very high concentration of fixed charge, such as RH+, e.g. 5 M


Current induced membrane discharge1

Current-induced membrane discharge

charge parameter


Transport of ions colloids and water in porous media and membranes with special attention to

Ion electrokinetics incl. flow of water

water

  • 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”

ion

ion

ion

28


Transport of ions colloids and water in porous media and membranes with special attention to

Two-fluid model

water

ion

ion

ion

29


Transport of ions colloids and water in porous media and membranes with special attention to

Two-fluid model for colloidal mixtures

Ptotal = Phydr - osm

Nernst-Planck

“Two fluid Navier-Stokes Equation”

30

Velocities within own phase, “interstitial velocity”

Many interesting things to be said here, how to apply this to a porous medium, via Brinkman-style approach, where this .. Is replaced by friction of fluid with porous medium

And what amazing result is obtained when we insert this in here.


Transport of ions colloids and water in porous media and membranes with special attention to

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


Transport of ions colloids and water in porous media and membranes with special attention to

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

Theoretical calculation, but is experimentally possible


Transport of ions colloids and water in porous media and membranes with special attention to

Thank you for your attention !


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