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Transport of ions, colloids and water in porous media and membraneswith special attention to water desalination by capacitive deionizationMaarten Biesheuvel

ionionionwater1Overview

Capacitive Deionization (CDI)Porous electrode theoryModeling ion electrokinetics (combined flow of water, ions, colloids)Sedimentation of colloidal particles2

2Capacitive Deionization3

3with ion-exchange membranesMembrane Capacitive Deionization4

Membrane Capacitive Deionization5

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CDI testing7

7What does CDI look like?Water inWater outcurrent collectorcurrent collectorcarbon electrodecation exchange membraneanion exchange membranecarbon electrodespacer8

CDI designs using cylinders (wires)1Graphite rodCarbonElectrode

Carbon electrodeCarbon electrode

Ion-exchange membrane

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Electrode composition:90 wt % active carbon10 wt % polymeric binder

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That brings me to the porous electrodesHere 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 dont discuss today10211

112Transport in porous electrodesmAcroporesmAcroporesmAcropores charge-neutralEDLs formed in micropores where electronic charge and ionic charge compensateionse-ionsmicroporesmicroporesThree interpenetrating phases. We dont have adsorption on the walls of the mAcropores. There are no walls. It is swiss cheese12electron-conducting matrix122Transport in porous electrodesRC Transmission Line Theory, or De Levie Theory13

13Bob (Robert) de LevieISE, Prague, 201214

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

poreporeMany problems:Only valid for constant R and C, neither valid except for experiments at say 1 M.No means to model mixtures of saltsOr acid/base reactions152Generalized porous electrode theory16

Prof. Martin BazantMIT, USA162Generalized porous electrode theory

17From abstract:Todd Squires172Transport in porous electrodes

Transport equationin mAcroporesElectrical double layer modelin micropores18

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

1819-+-+-+-+-+Potable waterBrackishwater+--++- -+e-

Porous electrode transport theory19

--+-+-+Potable waterBrackishwater+-+- -+-++20Porous electrode transport theoryIon transport in the mAcroporesIon adsorption in the micropores2021

Water not just contains a salt like NaCl which can be assumed fully dissociatedInstead, 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 !22Including acid/base reactionsIn NP-transport modeling in porous media F.G. Helfferich(1922-2005)

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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 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

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F.G. HelfferichAdvantages Helfferich-approach

Ion fluxpositionH2CO3HCO3-CO32-Na+Cl-H+OH-2H+ +2e- H2 (g)bulkIts not the proton that flows,and it is not the source of the formed H2-gas !!!25Steady-state diffusion of acid/base ionsCurrent-induced membrane dischargewater in membrane poresmembrane discharge26

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

Current-induced membrane discharge27charge parameter

28Ion electrokinetics incl. flow of waterSame approach for ions as for colloids, protein and larger particlesThe ion (with its hydrated water molecules) is a dispersed particleWater is the continuum fluidum in between described very differently from the ions !!Extension of two-fluid model to colloidal regimeionionionwater

29Two-fluid modelionionionwater

Ptotal = Phydr - osm30Two-fluid model for colloidal mixtures

Velocities within own phase, interstitial velocityMany 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 mediumAnd what amazing result is obtained when we insert this in here.Nernst-Planck

Two fluid Navier-Stokes Equation31Paradox 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 always32

Sedimentation of colloidal particlesThree types of colloidal particles (< 1 micron size) with different colorsAll heavier than the solventPurple is mixtureNot a solid sediment that is formed

Solvent/supernatantTheoretical calculation, but is experimentally possibleThank you for your attention !