Condensed Matter Seminar
University of Arizona, April 20, 2000
Title: Asymptotic Theory of Diffuse Charge Layers
Abstract:
Electrochemical sytems typically possess at least two grossly disparate
length scales: the macroscopic dimension of the cell L (e.g. the distance
between the electrodes) and the Debye screening length \lambda which sets
the scale for charge fluctuations. Since \lambda is typically smaller than
100nm, there is generally a very small parameter \lambda / L appearing as
a singular perturbation in the governing partial differential equations
(Nernst-Planck, Navier-Stokes, Butler-Volmer-Stern), which leads to
boundary layers of "diffuse charge" surrounding an electrically neutral
interior. Although this scale separation has been understood and exploited
for almost a century in electrochemistry, in this talk several examples
are presented where a careful asymptotic analysis yields new and
unexpected results. For example, the classical theory of "limiting
current" is modified, and a new theoretical framework for time-dependent
electrohydrodynamic coupling is proposed.