When there is a concentration gradient in the system, show that the potential gradient is composed of two terms, (i) an Ohm's-law contribution and (ii) a diffusional contribution. State the equation for the current. Now take the divergence of the current and show that the

following Poisson equation holds for the potential field:
\[abla \cdot(\kappa abla \phi)=-F \sum_{i} z_{i} abla \cdot\left(D_{i} abla c_{i}\right)\]
Show the similarity to heat transport with generation with a variable thermal conductivity. What assumption is implicit in the above equation?