where Ji is the molar flux relative to the convective transport, and
Ri (SI unit: mol/(m
3 ·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 3-115 introduces one variable for the concentration of each of the dissolved species and the electric potential,
V.
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 3-115. 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.
The first term in Equation 3-117 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:
Equation 3-115,
Equation 3-116, and
Equation 3-119 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 3-118 is that the ionic conductivity, defined in absence of concentration gradients, is implicitly given by: