User:Seth Bresnett/Sandbox

$$D = \mu_p k_B T$$

$$\mu_p = \mathrm{velocity/force} = \frac{v}{F}$$

Force = charge * field.

Field = E_m / L

Charge = valence * electron charge.

kB = R/avogadro's number.

1 Faraday = avogadro's number * charge of electron.

so

$$v = \frac{D n_A F E_m}{RTL} $$

Presumably flux is just velocity * concentration, so that gives the second term in the relevant equation.

Hopefully that answers what you're actually asking, and isn't what you've done already...