We propose a theoretical approach to the problem of electroconvection in the vicinity of electrodeposits which are growing in quasi-two-dimensional cells. Charges at the tips of the branches are expected to induce a convective motion of the solution. We show theoretically that, in the steady state, pairs of contrarotative vortices must be expected between neighboring branches. The concentration map is explicitly derived in the limit where diffusion is negligible, as compared to drift and convection. A more realistic concentration map is computed numerically in the case of nonnegligible diffusion. We compare the theoretical predictions to experimental observations of the growth of copper deposits from a solution of copper sulphate. We show that both the convective vortices and the concentration gradient are very well described by the theoretical model. Hence the simple theoretical approach that we present gives a good understanding of the intricate problem of the electroconvective, diffusive, and drift motion of the ions. To our knowledge, an electrodeposition model which incorporates these three aspects has not been published previously.

• Received 8 March 1993

DOI:https://doi.org/10.1103/PhysRevE.48.1279