Study of the electric potential inside wavy-rough annuli interface

The electrostatic potential (field) inside an annulus-like electrode or biomembrane with wavy-roughness along the inner and outer surfaces are obtained using an analytical theory. Boundary perturbation techniques are adopted to handle and solve the Poisson equation with corresponding physical boundary conditions which are Robin type. In particular, the effects of the wavy-roughness via the wave number, phase shift and the small amplitude of the roughness element on the electric field distribution inside the selected geometry (of an electrode or biomembrane) are demonstrated and discussed up to the second order of magnitude. Our results are useful to researchers in both electrochemistry and biophysics fields (e.g., charge transfer in biological systems).