Taylor dispersion with absorbing boundaries: a stochastic approach

We solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to closed-form expressions for all the moments of the convective displacement of the dis...

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Bibliographic Details
Published in:Physical review letters 2007-04, Vol.98 (16), p.164501-164501, Article 164501
Main Authors: Biswas, Rudro R, Sen, Pabitra N
Format: Article
Language:English
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Summary:We solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to closed-form expressions for all the moments of the convective displacement of the dispersing particles in terms of the transverse diffusion eigenmodes. We also find that the cumulants grow asymptotically linearly with time, ensuring a Gaussian distribution in the long-time limit. As a demonstration of the technique, the first two longitudinal cumulants (yielding respectively the effective velocity and the Taylor diffusion constant) as well as the skewness (a measure of the deviation from normality) are calculated for fluid flow in the parallel plate geometry. We find that the effective velocity and the skewness are enhanced while Taylor dispersion is suppressed due to absorption at the boundary.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.98.164501