1. Screening of surface charge at interfaces – the Gouy-Chapman theory
The screening of electrostatic interactions by mobile charges (ions) is commonly described by the Gouy-Chapman theory, which is a particular solution of the Poisson equation combined with the Boltzmann equation for the distribution of mobile charges in an electric potential. Although the Gouy-Chapman theory is derived for a planar, infinite sheet, with a number of approximations to reality, both experiment and more sophisticated calculations show it to be remarkably "robust". In fact, it works unreasonably well for real systems of various and finite geometries.
A membrane surface with a net surface charge density, σ (charges or Coulombs per unit area), will produce an electric field in the surrounding medium and will attract ions of opposite charge (counterions) and repel those of like charge. For a planar surface with smooth charge density, the electric field (and potential) will be a function of distance from the membrane, x, only. Near the surface, there will be a diffuse net charge or space charge density, ρ(x) (charges or Coulombs per unit volume), reflecting the excess of counterions in the solution:

9. Some Consequences of Surface Electrical Phenomena