Transient electrical double layer dynamics in a quiescent fluid

From the moment a liquid is put in contact with a solid, physico-chemical reactions occur at their interface. These reactions have been modeled over the years by preferential adsorption or corrosion. Whatever the model, they lead to a charge distribution called electrical double layer (EDL), formed by a charge layer at the solid wall, and a diffuse charge layer of opposite sign in the liquid. In this work we focus on the formation of the EDL when a plane wall is put in contact with a quiescent fluid. The governing equations and a semi-analytical solution are presented. A simpler solution can be found by assuming the instantaneous formation of the charge density profile. The semi-analytical solution presented in this work is compared to the former at different reaction rates leading to the conclusion that for fast enough wall reactions, the instantaneous charge density profile cannot be assumed.