Mathematical Solution for the Two-dimensional Electric Field in a Rectangular Channel

The solution for the two-dimensional electric field is developed in this study, caused by a dielectric liquid in a rectangular channel. Diffuse layer of charge is established by adding the three different electric flow phenomena through an elementary surface: diffusion, convection and migration. Then, assuming the same electric valence for all ions species, the non dimensional equations for current density and charge conservation are obtained with aid of referential parameters. Three expressions for the established non dimensional diffuse layer are proposed considering no motion of the dielectric liquid, and independence on time of diffuse layer's parameters. The solution for the principal system is carried out by applying the Green Functions; the expression obtained represents the potential field distribution in the rectangular channel. The evolutions for electric field along both, the central and close to the wall sections, are presented. Finally, the lines of constant electric field, which depend on the rate between the two sides of rectangular section, are also shown.