Concentration polarization: Electrodeposition and transport phenomena at overlimiting current

Abstract

In the present thesis we study different aspects of concentration polarization, with emphasis on nonlinear transport phenomena and ramified electrode growth. We aim at extracting the essential features which characterize the problems, and to that end we employ a variety of numerical and analytical methods. The initial study concerns a fundamental problem in the study of concentration polarization at overlimiting current, namely the emergence of an extended space-charge region near the ion-selective interface. Based on the so-called quasi-uniform charge density assumption(QCD), we develop an analytical model for the transport in a system with an extended space-charge region. By comparison with numerical simulations, we show that the analytical model captures all of the essential features of the problem. We use the model to derive a range of results characterizing the extended space-charge region. Secondly, we investigate concentration polarization in a microchannel with charged walls. We provide full numerical solutions to the transport problem, including the effects of advection and surface conduction in the electric double layers. We show that in large areas of the relevant parameter space the transport can be understood in terms of a group of simple analytical models. Some of these are generalizations of a previously published analytical model. In addition to the full numerical model, we employ a numerical boundary layer model with a slip velocity. By carefully comparing the full model and the boundary layer model, we reveal a number of issues, which invalidate most previous attempts at modeling microchannel concentration polarization using a slip model. Returning to concentration polarization in a bulk system, we study the effects of watersplitting at a permselective membrane. We investigate this coupled chemical and transport effect using two simple models of the reaction kinetics. The principal investigations are performed using numerical simulations, but in addition we derive an analytical model for the transport in the system. The analytical model reveals an important link between the current of salt ions and the current of water ions. This link seemingly exists independent of the specific reaction kinetics, and could help in furthering the understanding of the water splitting process. A fit of the model to experimental data from the literature shows quite good agreement, and provides some hints about the reaction kinetics in the given experiment. In the final part of the thesis we investigate electrodeposition, and specifically the tendency of a cathode to become morphologically unstable and develop ramified growth.Firstly, we consider the stability of a flat metal electrode during electrodeposition. Using linear perturbation theory, we develop numerical and analytical models for the instability growth rate as a function of the instability wavelength. In contrast to previous work on the stability problem, our models apply at both under- and overlimiting current. Secondly, we develop a numerical sharp-interface model describing the electrode growth.This model differs from the established phase-field models, in that it is applicable at overlimiting current and implements electrode reactions in a consistent way. Comparison of the sharp-interface model to the results of the stability analysis, provides a validation of the model behavior in the initial stages of the growth. Some preliminary results of the numerical simulations indicate that the electrodeposit morphology might be explainable in terms of a few key parameters.