Toward an Understanding of Nonlinear Electrochemical Transport

Charge transport plays a crucial role in the response of many colloidal, micro-fluidic, micro-electrochemical and biological systems subjected to applied electric fields. As a result, studying the electrochemical transport properties of these systems is an important first step towards understanding their overall response to applied electric fields. To avoid the nonlinear coupling between the electric field and ion concentration fields, analysis of charge transport problems has traditionally relied on simple circuit models which are only valid in the weak field regime. Unfortunately, to understand the behavior of systems in strong applied fields (which are easy achieved at the micro- and nano-scale), we are forced to face the full nonlinear charge transport equations. In this talk, we will discuss recent advances in our theoretical understanding of the nonlinear charge transport equations in the thin double-layer limit. Our main results include a general formulation of of “surface conservation laws” for diffuse boundary layers and characterization of the structure of the electric and ion concentration fields around spherical, metallic (i.e. highly-polarizable) colloid particles. Along the way, we will discuss various practical issues associated with numerical solution of the nonlinear governing equations.