Dynamics of microvortices induced by ion concentration polarization

We investigate the coupled dynamics of the local hydrodynamics and global electric response of an electrodialysis system, which consists of an electrolyte solution adjacent to a charge selective membrane under electric forcing. Under a DC electric current, counterions transport through the charged membrane while the passage of co-ions is restricted, thereby developing ion concentration polarization (ICP) or gradients. At sufficiently large currents, simultaneous measurements of voltage drop and flow field reveal several distinct dynamic regimes. Initially, the electrodialysis system displays a steady Ohmic voltage difference ($\Delta V_{ohm}$), followed by a constant voltage jump ($\Delta V_c$). Immediately after this voltage increase, micro-vortices set in and grow both in size and speed with time. After this growth, the resultant voltage levels off around a fixed value. The average vortex size and speed stabilize as well, while the individual vortices become unsteady and dynamic. These quantitative results reveal that micro-vortices set in with an excess voltage drop (above $\Delta V_{ohm} + \Delta V_c$) and sustain an approximately constant electrical conductivity, destroying the initial ICP with significantly low viscous dissipation.