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The boundary conditions given are not realistic. The boundary conditions at the wall, assuming a normal cylindrical test tube, must involve theta (and possibly z), as the walls are not parallel to the radius vector. However, if we consider a wedge shaped cell such that the walls are along the radial lines, and the thickness of the cell is infinite, then this boundary condition may make sense. But then it is better to ignore the boundary condition and consider flow along the radial lines with the assumption that the test tube size is so large that the wall effects are absent (this may be a better assumption).
This condition may be useful in gas centrifuges where the sample is not confined in a cell and we then have an additional problem of thermal convection currents that is distinct from the simple diffusion equation.
The diffusion equation quoted was first derived by Einstein. chami 08:07, 24 July 2011 (UTC) — Preceding unsigned comment added by Ck.mitra (talk • contribs)