Biased continuous time random walks between parallel plates

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Abstract
The generalized scheme of continuous time random walks in moving fluids [A. Compte, Phys. Rev. E 55, 6821 (1997)] is applied to particles diffusing between parallel plates whose jumps are biased by a nonhomogeneous longitudinal velocity field. We observe that when the statistics governing diffusion is Brownian the results are those of Taylor dispersion, i.e., enhanced longitudinal diffusion due to the coupling of the transverse diffusion of the solute and the unidirectional velocity field. However, for Lévy flights with infinite mean waiting time we observe an anomalous dispersion approaching ballistic diffusion. We interpret this behavior as a consequence of the coupling between the flow and the waiting time statistics.

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