Nonlinear Mathematics 2000
Courant Institute, NYU
poster, Wed. May 31, 2000
Asymptotic Analysis of Diffuse Charge Layers in Electrochemistry
Martin Z. Bazant
Electrochemical sytems typically possess at least two grossly
disparate length scales: a macroscopic dimension $L$ (e.g. the
distance between two 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 tiny
parameter $\lambda / L$ appearing as a singular perturbation in the
governing 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 poster 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.