The ion migration coefficients can be expressed as: Here, D represents the diffusivity of an ion in a membrane. Z is the signed charge number of the ion. F is Faraday's constant. R is the universal gas constant and T is the absolute temperature. 𝜎 is conductivity of the membrane in the electrolyte. We refer to 𝑃 𝑂𝐻 - + 𝑀 𝐻 + 𝐶𝐸𝑀 𝑗 as the proton exchange terms (through the CEM). The net acid-base crossover flux (𝐽 𝑐𝑟𝑜𝑠𝑠𝑜𝑣𝑒𝑟 ) of the system can be described as in Equation 3.