Basic conceptual diffusion problem Suppose that some particles which are suspended in a liquid medium would be pulled down at the constant velocity V by gravity in the absence of diffusion. Taking into account the diffusion, find the equation for the concentration of particles. Assume homogeneity in the horizontal direction X and Y. Let the Z axis point upwards. It seems the question is simply asking for the standard three dimensional diffusion equation, no? What role does the velocity due to gravity play in the diffusion equation?

The solution is as follows:

Ut = KUzz + VUz

Where the lower case letters represent partial derivatives.