Figure 3: Basic physics of shock electrodeposition.

(a) Dendritic instability of electrodeposition in free solution upon diffusion limitation in the electrolyte, where the scarce supply of cations focuses onto a protrusion and results in a self-amplifying process. (b) Stability of deionization shock propagation in response to over-limiting current in a leaky membrane, where a lagging part of the shock wave is removed by large Ohmic currents through the depleted region and results a flat, stable shock wave. (c) Stabilization of electrodeposition behind a deionization shock, if the second effect overcomes the first during fast growth at over-limiting current.