where Ji is the molar flux relative to the convective transport, and Ri (SI unit: mol/(m3 ·s)) is the reaction term. The velocity, u, is equal to the velocity of the solvent. This implies that the solute’s contribution to the solvent’s velocity, through shear or any other forces, is negligible in comparison to the solvent’s contribution to the solute. Equation 3-87 introduces one variable for the concentration of each of the dissolved species and the electric potential, V.

Apart from the transport equations, the physics interface assumes that the electroneutrality condition holds:

that is that the net charge in every control volume is zero. This means that Q − 1, where Q is the number of species present, can be solved for using Equation 3-87. The remaining species concentration is computed from the electroneutrality condition. This means that boundary conditions for this species cannot be specified, although it takes part in the boundary condition descriptions for the current density. Often, the species chosen to be computed from electroneutrality is the oppositely charged ion, to the electroactive species, from a supporting electrolyte.

To compute the electric potential, taking the transport of every charged species into account, create the following linear combination of the n mass balance equations, where each mass balance equation is weighted with the factor F zi:

The first term in Equation 3-89 is zero, which can be shown by taking the time derivative of the electroneutrality condition. The expression under the divergence operator is the total current density vector, defined by:

It is now possible to rewrite Equation 3-89 as:

Equation 3-87, Equation 3-88, and Equation 3-91 are sufficient for describing the potential and concentration distribution in an electrochemical cell or in an electrolyte subjected to an electric field.

A useful observation from Equation 3-90 is that the ionic conductivity, defined in absence of concentration gradients, is implicitly given by: