Diffusion in a Nonuniform System

In some systems, the chemical potential depends explicitly on r, not only through c(r). An example is charged colloidal particles in an electric field. Here, we consider diffusion of particles in an external field such as an electric field. We limit the discussion to the low concentration limit. 

When a stationary external field is applied, the chemical potential has an extra term U r) due to the field  

Charged particles will experience UJr) = (charge) X (electrostatic potential at r), for instance. The diffusion equation is rewritten to 

We can immediately obtain the equilibrium distribution Ceq(r) from Vcg, + CeqV(/E/ B7 = Oas 

Problem 3.1 We consider a walk on a cubic lattice. Its ith step motion Ar, in 

---