We may recall from our treatment of the Einstein model of Brownian motion that the concentration C r t( , )

of say, sugar molecules, as solutes in a solvent

like water follows the diffusion equation.

d dt

C r t D C r t( , ) ( , ),2

= ∇


where C r t( , )

is the number of sugar molecules per unit volume within a region r

and r dr

+ and D is the diffusion constant. We now raise the ques-

tion: How is Equation (10.1) modified when we have to deal with diffusion of not just a single species (e.g., sugar particles) but two different molecular species such as oil and water that interact? One important example of such interactions is the situation in which water molecules like each other and oil molecules like each other while water and oil dislike each other.