Imagine a narrow pipe, filled with fluid, in which the concentration of a certain type of molecule varies only along the length of the pipe (in the x direction). By considering the flux of these particles from both directions into a short segment Δx, derive Fick's second law,
∂t∂n=D∂x2∂2n.
Noting the similarity to the heat equation derived in Problem 1.62, discuss the implications of this equation in some detail.