Electroconvection and Morphological Instabilities in Potentiostatic Electrodeposition across Liquid Electrolytes with Polymer Additives

Electroconvection in electrodeposition results in fast growing ramified deposits undermining the efficacy of the process. Here we examine the effect of polymer additives in the electrolyte on electroconvection and the consequences for morphological instability. The connection between two interrelated problems is studied, one of pure electroconvection at an ion-selective membrane and one where the electroconvection is coupled to morphological growth of a metal surface in electrodeposition. A two-fluid model for the semidilute polymer solution is employed and linear stability analysis is used to study the two problems. We find that the stable-to-unstable transition in the pure electroconvection problem corresponds to a change in growth rate of the morphology, from a slow diffusive growth to a fast convection-driven instability. The polymer exerts a drag resisting the electroconvective flow of the solvent and can suppress the electroconvective instability. The nature of this transition varies with the wavelength of the perturbation with longer modes having a weaker flow and being stabilized first. Increasing the polymer molecular weight and decreasing the permeability which respectively control the mobility of the polymer and the drag it exerts, weaken the electroconvection. Higher polymer volume fractions, which affect both polymer mobility and the drag, also reduce the electroconvection. It is shown that polymer additives can substantially increase the critical voltage for the onset of electroconvective motions with wavelengths larger than the space charge thickness.