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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?

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This is diffusion with drift. If you write down the diffusion equation in this case, you should be able to do something akin to completing the square by a change of variables, and this should enable you to reduce it to the standard diffusion equation. The solution will just have a shifted variable.

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There is no mention in the book or lectures of diffusion with a drift. I'm not sure I understand anything you're suggesting. –  rmh52 Sep 13 '12 at 17:00
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The solution is as follows:

Ut = KUzz + VUz

Where the lower case letters represent partial derivatives.

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