Asymptotic Analysis of Extreme Electrochemical Transport

In the study of electrochemical transport processes, experimental exploration currently outpaces theoretical understanding of new phenomena. Classical electrochemical transport theory is not equipped to explain the behavior of electrochemical systems in the extreme operating conditions required by modern devices. In this thesis, we extend the classical theory to examine the response of two electrochemical systems that form the basis for novel electrochemical devices. We first examine the DC response of an electrochemical thin film, such as the separator in a micro-battery, driven by current applied through reactive electrodes. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer which mediates Faradaic reactions with Butler-Volmer kinetics. Our analysis differs from previous studies in two significant ways. First, we impose the full nonlinear, reactive boundary conditions appropriate for electrolytic/galvanic cells. Since surface effects become important for physically small systems, the use of reactive boundary conditions is critical in order to gain insight into the behavior of actual electrochemical thin films that are sandwiched between reactive electrodes, especially at high current densities. For instance, our analysis shows that reaction rate constants and the Stern-layer capacitance have a strong influence on the response of the thin film. Second, we analyze the system at high current densities (far beyond the classical diffusion-limited current) which may be important for high power-density applications. At high currents, we obtain previously unknown characterizations of two interesting features at the cathode end of the cell: (i) a nested boundary layer structure and (ii) an extended space charge region. Next, we study the response of a metal (i.e., polarizable) colloid sphere in an electrolyte solution over a range of applied electric fields. This problem, which underlies novel electrokinetically driven microfluidic devices, has traditionally been analyzed using circuit models which neglect bulk concentration variations that arise due to double layer charging. Our analysis, in contrast, is based on the Nernst-Planck equations which explicitly allow for bulk concentration gradients. A key feature of our analysis is the use of surface conservation laws to provide effective boundary conditions that couple the double layer charging dynamics, surface transport processes, and bulk transport processes. The formulation and derivation of these surface conservation laws via boundary layer analysis is one of the main contributions of this thesis. For steady applied fields, our analysis shows that bulk concentrations gradients become significant at high applied fields and affect both bulk and double layer transport processes. We also find that surface transport becomes important for strong applied fields as a result of enhanced absorption of ions by the double layer. Unlike existing theoretical studies which focus on weak applied fields (so that both