Toward an Understanding of Nonlinear Electrochemical Transport
PDE & Numerical Methods Seminar, PennState University, University Park, PA, November 14, 2005
Charge transport plays a critical role in many colloidal, micro-electrochemical and biological systems subjected to applied voltages or electric fields. Studying the electrochemical transport properties of these systems is an important first step towards understanding their response to applied fields. However, due to the nonlinear coupling between the total electric field and ion concentration fields, analysis of charge transport problems have traditionally relied on simple circuit models which are only valid in highly restricted operating regimes. In this talk, we shall discuss recent advances in our theoretical understanding of the full nonlinear charge transport equations in the thin double layer limit. Our main results include the formalization and derivation of surface conservation laws and characterization of the structure of electric and ion concentration fields around spherical, metallic (i.e. highly-polarizable) colloid particles via numerical solution of the governing equations.