1. Electrodialysis Cell A Tutorial Model

2. Introduction Electrodialysis –A separation process for electrolytes based on the use of electric fields and ion selective membranes Applications –Desalination of process streams, effluents, and drinking water –pH regulation in order to remove acids from, for examples fruit juices and wines (when you cannot add caustic) –Metal winning (precious metals) Electrodialysis cell. Image courtesy: Argonne National Laboratory Bench-scale electrodialysis stack with ~10 to100 unit cells

3. Model Definition, the Electrodialysis Stack Schematic picture with 3 desalination units (in reality 10 - 20) Cathode: Negative Electrode Anode: Positive Electrode Diluate Concentrate Electrode Stream Electrode Stream Electrode Stream Electrode Stream OH - SO 4 2- Na + Cl - Na + Cl - Na + Cl - SO 4 2- Na + H + Cathode reaction: 2H 2 O +2e - -> H 2 + 2OH - Anode reaction: H 2 O -> 1/2O 2 + 2H + + 2e -

4. Model Definition, the Model Geometry Na + Cl - Na + Cl - The repetitive unit cell with one desalination unit

5. Model Definition, a First Approximation Parallel free channels with planar structure –In reality, cells are equipped with spacers for mechanical stability and increased mass transport in the direction perpendicular to the main flow Variations in composition and potential along height and width are relatively large while they are small along the depth –2D simplification of the 3D geometry Na + Cl - Na + Cl - 3D 2D Approximation Depth Model Geometry

6. Model Definition, Equations Transport using the Nernst-Planck equations –Flux = diff. + conv. + migration –Conservation of species –Predefined flow field Charge separation controlled through Poisson’s equation –Membrane charge is included in the charge density –Other species can be included as supporting electrolyte in the channels Diluate channel Cation selective membrane Anion selective membrane ½ concentrate channel 1 mm 0.5 mm 0.25 mm 0.2 m

7. Model Definition, Boundary Conditions Separate species balances for the channels and the membranes –Donnan equilibrium and flux continuity for species at channel/membrane boundaries –Given inlet fluxes and convective flux at outlets –Periodic boundary conditions at the boundaries running along the middle of the concentrate channels Ionic potential set at the middle of the concentrate channels and continuity at the channel/membrane boundaries All other conditions are insulating conditions Diluate channel Cation selective membrane Anion selective membrane ½ concentrate channel 1 mm 0.5 mm 0.25 mm 0.2 m

8. Model Results Diluate concentration, Na + Concentrate concentration, Na + Diffusion Migration Net x-flux ≈ 0 Diffusion Migration

9. Model Results Diluate concentration, Cl - Concentrate concentration, Cl - Diffusion Migration Net x-flux ≈ 0 Diffusion Migration

10. Model Results, Cross Section along the Middle of the Cell Concentration profile, Na + Concentration profile, Cl - Cation Selective Membrane Anion Selective Membrane Cation Selective Membrane Anion Selective Membrane Donnan Equilibria Donnan Equilibria

11. The Influence of Spacer in the Flow Channels

12. Model Definition Spacers are introduced in the middle of the flow channels –This means that the flow field cannot be predefined as in the previous model, it has to be solved for. Boundary conditions for the spacer walls are insulating conditions except for the flow field where slip conditions are applied Cation selective membrane Anion selective membrane 0.2 m 0.5 mm 0.25 mm 1 mm 0.5 mm Diluate channel ½ concentrate channel Schematic Spacer Geometry

13. Model Results, Flow Field The presence of spacers enhances the convective transport in the x-direction in the channels Low flow rate High flow rate

14. Model Results, Cross Section along the Middle of the Cell Concentration profile, Na + Concentration profile, Cl - Cation Selective Membrane Anion Selective Membrane Cation Selective Membrane Anion Selective Membrane Without spacer With spacer