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

1. 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

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

3. Capacitive Deionization

4. Membrane Capacitive Deionization with ion-exchange membranes

5. Membrane Capacitive Deionization

7. CDI testing

8. Whatdoes CDI look like? Water out current collector carbon electrode cation exchange membrane spacer Water in anion exchange membrane carbon electrode current collector

9. 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

10. 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

11. 2

12. 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

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

14. Bob (Robert) de Levie ISE, Prague, 2012

15. 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

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

17. Generalized porous electrode theory From abstract: Todd Squires 2

18. 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}

19. Porous electrode transport theory + - + - e- + - + - + Brackish water Potable water - + - + - + - + -

20. Porous electrode transport theory Potable water - Ion transport in the mAcropores - + + + - + - - + - + + Ion adsorption in the micropores - + Brackish water -

22. 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)

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

24. 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

25. 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 !!!

26. 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

27. Current-induced membrane discharge charge parameter

28. 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

29. Two-fluid model water ion ion ion 29

30. 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.

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 31

32. 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

33. Thank you for your attention !