Transport of ions, colloids and water Transport of ions, colloids and water in porous media and membranes with special attention to water desalination by capacitive deionization Maarten Biesheuvel ion water

Overview Capacitive Deionization (CDI) Porous electrode theory Modeling ion electrokinetics (combined flow of water, ions, colloids) Sedimentation of colloidal particles 2

Capacitive Deionization 3

with ion-exchange membranes Membrane Capacitive Deionization 4

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CDI testing 7

What does CDI look like? Water in Water out current collector carbon electrode cation exchange membrane anion exchange membrane carbon electrode 8

CDI designs using cylinders (wires) 1 Graphite rod Carbon Electrode Carbon electrode Ion-exchange membrane 9 Electrode composition: 90 wt % active carbon 10 wt % polymeric binder

2 10 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

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2 Transport in porous electrodes mAcropores mAcropores charge-neutral EDLs formed in micropores where electronic charge and ionic charge compensate ions e-e- micropores Three interpenetrating phases. We don’t have adsorption on the “walls’ of the mAcropores. There are no walls. It is swiss cheese 12 electron-conducting matrix

2 Transport in porous electrodes “RC Transmission Line Theory”, or “De Levie Theory” 13

Bob (Robert) de Levie ISE, Prague,

2 RC transmission line theory  pore is potential in aqueous pore relative to conducting matrix (metal, carbon) 15 pore 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

2 Generalized porous electrode theory 16 Prof. Martin Bazant MIT, USA

2 Generalized porous electrode theory 17 From abstract: Todd Squires

2 Transport in porous electrodes Transport equation in mAcropores “Electrical double layer” model in micropores 18 In limit of no resistance to transfer mA   no explicit relation for j_{i,mA  mi}

Potable water Brackish water e-e- Porous electrode transport theory

Potable water Brackish water Porous electrode transport theory Ion transport in the mAcropores Ion adsorption in the m i cropores

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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 NH 3, NH 4 +, HCO 3 - Of special relevance the reactions with and between H + and OH - All these species must be considered ! 22 Including acid/base reactions In NP-transport modeling in porous media F.G. Helfferich ( )

23 Helfferich-approach F.G. Helfferich Many technical advantages in modeling, too many to list them here

By addition of balances, for each “ group ” such as CO 2 /HCO 3 - /CO 3 2-, 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 24 F.G. Helfferich Advantages Helfferich-approach

Ion flux position H 2 CO 3 HCO 3 - CO 3 2- Na + Cl - H + OH - “2  H + +2  e -  H 2 (g)” bulk It’s not the proton that flows, and it is not the source of the formed H 2 -gas !!! 25 Steady-state diffusion of “acid/base ions”

Current-induced membrane discharge water in membrane poresmembrane discharge 26 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 discharge 27 charge parameter

28 Ion electrokinetics incl. flow of 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 water

29 Two-fluid model ion water

P total = P hydr -  osm 30 Two-fluid model for colloidal mixtures 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. Nernst-Planck “Two fluid Navier-Stokes Equation”

31 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

32 Sedimentation of colloidal particles 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 Solvent/supernatant Theoretical calculation, but is experimentally possible

Thank you for your attention !