Transport Equations in Chromatography with a Finite Speed of Signal Propagation

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Abstract
It is known that the diffusion equation used to model transport in a large variety of chromatographic techniques has an infinite speed of signal propagation, i.e., if c(x,t) is the concentration at time t, then c(x,t) > 0 for any t > 0. We generalize and solve the telegraph equation, which is known to have a finite speed of signal propagation, to allow for asymmetric convection, as is appropriate for the theory of chromatographic processes. We derive the telegraph equation from a continuous time random walk picture and examine two sources of convection, an asymmetry in sojourn times in states in which diffusing particles move in one direction or the other, and a corresponding asymmetry in the velocities.

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