Model of Electrochemical "Double Layer" Using the Phase Field Method
  We present the first application of phase field modeling to electrochemistry. A free energy functional that includes the electrostatic effect of charged particles leads to rich interactions between concentration, electrostatic potential, and phase stability. The present model, explored for the equilibrium planar interface, properly predicts the charge separation associated with the equilibrium double layer at the electrochemical interface and its extent in the electrolyte as a function of electrolyte concentration, as well as the form expected of surface energy vs. potential ("electrocapillary") curves. 
J. E. Guyer, W. J. Boettinger, J. A. Warren, and G. B. McFadden