  Shock electrodialysis (shock ED), an emerging electrokinetic process for
water purification, leverages the new physics of deionization shock waves in
porous media. In previous work, a simple leaky membrane model with surface
conduction can explain the propagation of deionization shocks in a shock ED
system, but it cannot quantitatively predict the deionization and conductance
(which determines the energy consumption), and it cannot explain the selective
removal of ions in experiments. This two-part series of work establishes a more
comprehensive model for shock ED, which applies to multicomponent electrolytes
and any electrical double layer thickness, captures the phenomena of
electroosmosis, diffusioosmosis, and water dissociation, and incorporates more
realistic boundary conditions. In this paper, we will present the model details
and show that hydronium transport and electroosmotic vortices (at the inlet and
outlet) play important roles in determining the deionization and conductance in
shock ED. We also find that the results are quantitatively consistent with
experimental data in the literature. Finally, the model is used to investigate
design strategies for scale up and optimization.
