Direct numerical simulation of electroconvection under a uniform magnetic field

The coupling between ion transport and fluid flow near ion-selective surfaces plays a crucial role in various electrohydrodynamic applications. Above a critical voltage threshold, electroconvective vortices emerge inside the liquid electrolyte and enhance ion transport. Applying a magnetic field modifies the ion mobility and electroconvection by inducing a Lorentz force. To investigate this phenomenon, we numerically study the electroconvection under a perpendicular magnetic field by incorporating the Lorentz force into the coupled Poisson-Nernst-Planck-Stokes equation. The magnetic field induces a cross-flow similar to a pressure-driven Poiseuille flow and completely suppresses the electroconvection when the applied voltage is slightly above the critical threshold. At a high voltage, the crossflow reduces the fluctuation of ion flux passing through the ion-selective surfaces and induces net ion flux along the flow direction. The analysis of the spatial spectra of flow kinetic energy and electric energy reveals that the magnetic field reduces the size of the flow structures.