Double layer electrostatics of heterogeneous surfaces with circle phase contours

A model of a gas-liquid (electrolyte solution) system with charged heterogeneous surface is developed. A charged circular line (1D phase) is the substantial element of the surface heterogeneity, dividing the surface into inner and outer (2D) phases. The charge distribution in the bulk, as well as on the surface is in the form of Debye double layers (the Gouy-Chapman model). A generalisation of the classical bulk (3D) double layer theory is made by introducing of a surface (2D) dielectric susceptibility. The solution of the formulated non-trivial 3D-2D-1D problem is carried out by methods related to the linear theory of transmission boundary problems. The surface electric potential and its dependence on certain governing parameters are evaluated and analysed. Special attention is paid on the Maxwell stress (electrostatic surface pressure) acting on the contact line, in a context of (bio-) membrane pore mechanics.