Linear stability analysis of time-dependent electrodeposition in charged porous media

We study the linear stability analysis of time-dependent electrodeposition in a charged porous medium flanked by a pair of planar metal electrodes. Discretization of the linear stability problem results in a generalized eigenvalue problem that is solved numerically. Analytical approximations obtained from a boundary layer analysis valid at high wavenumbers agree well with the full numerical solutions. Under galvanostatic conditions, in the classical case of zero pore surface charges, the voltage and electric field at the cathode diverge when the cation concentration there vanishes at Sand's time. The same phenomenon happens for positive surface charges but at a time earlier than Sand's time. In contrast, negative surface charges allow the electrochemical system to sustain an overlimiting current via surface conduction past Sand's time, keeping the voltage and electric field bounded. Therefore, at Sand's time, negative surface charges greatly reduce the electrode surface instabilities while zero and positive surface charges magnify them. We also use the stability analysis to analyze how using a pulse current in electroplating and metal battery charging reduces diffusion limitations and electrode surface instabilities at high currents in the presence of negative surface charges.