where D i is the diffusion coefficient of species i, z i is the charge of species i, R is the gas constant, T is the temperature, φ is the potential, N A is the Avogadro's constant and a i is the effective solvated diameter of the species i. The values of D i and a i used for the solution species in this work are provided in the SI. Equation ( ) is solved simultaneously with the Poisson equation given by: