In fluids, diffusive transport and fluid parameters are determined by the thermally driven movement of molecules, whereas in granular media, thermal effects play no role in transport. Despite this fundamental difference, mixing in fluids and mixing and segregation in granular solids share many similarities. The advection diffusion equation formalism unites the two systems and can be used in both cases to predict and understand how and when mixing occurs, through the use of strategic simplifications. We illustrate this connection with a fluid mixing example (the rotated potential mixer) and a granular segregation example (the segregation of a bidisperse mixture flowing in a chute).