Electroconvective and morphological instabilities in a cross flow*

Ion transport in a cross flow has wide applications in desalination, electrodialysis and flow batteries. At high applied voltage, electroconvection is initiated by ion concentration polarization and formation of space charge layer. Many previous studies observe that applying a cross flow between two ion selective membranes or electrodes can reduce the size of the electroconvection vortices and even fully suppresses convection and dendrite growth. However, a general theoretical understanding of these effects is still missing. In this work, we investigate the electroconvective and morphological instabilities in a cross flow using both analytical and numerical analysis to solve the eigensolutions. The analysis is first performed based on the electroneutral bulk region using the second kind slip velocity developed by Rubinstein et al. Then, we conduct a numerical stability analysis on the full region, including the double layer, space charge layer and the bulk region. Our results show that the applied cross flow reduces the growth rate of perturbations at small wavenumber and a full suppression of convection is achieved at high enough flow velocity.