Abstract
Interfacial equations are derived for the species mass balance, the conservation of charge, Gauss law, the quasi-static form of Faraday's law, the balance of linear and angular momentum, and the first and second laws of thermodynamics. The pointwise interfacial equations are derived by localizing integral balance laws. However, the interfacial Faraday's law is obtained by integrating the volume Faraday's law across a thin domain and then taking the limit as the domain thickness goes to zero. Each of these eight physical principles is derived for both a regular (or single) interface and a double interface representing an electric double layer. The standard interfacial variables are augmented with an electric charge, electric potential, electric field, electric polarization, electric displacement, and electric body force, whereas conventional electrostatics includes only interfacial charge. The theory replaces the Gouy-Chapman equation, a three-dimensional theory of the electric double layer, with a two-dimensional theory in which the effects of the double layer are included as boundary conditions for the volume equations. Example solutions are provided for electroosmosis, including electro-Poiseuille flow and electro-Couette flow.
Ambati, Muralidhar S (2002). An interfacial transport theory for electro-chemical phenomena with emphasis on electric double layers. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -2002 -THESIS -A456.