The Separability of the Diffusion Equation with Drift Term

The paper investigates the diffusion equation with drift term, ∂ C /∂ t = div ( D grad C + + μ C grad U ), in particular the question of its separability in three dimensions. ( D is the diffusion coefficient, μ the mobility, both assumed to be constant scalar quantities; U denotes the potential giving rise to the drift.) The transformation to a new dependent variable f = C exp (μ U /2 D ) transforms the equation into a Schrödinger equation. Using this it is shown that, for appropriate choices of the potentials U , the diffusion‐drift equation is separable with modulation factor in the ellipsoidal coordinates (and its degenerate special cases) but in no other coordinate systems. The conditions to which U has to be subjected in order to lead to separability are stated and shown to have a close relationship to the factorization of the solutions of the original equation.