We describe how to solve the problem of Taylor dispersion in the presence ofabsorbing boundaries using an exact stochastic formulation. In addition toproviding a clear stochastic picture of Taylor dispersion, our method leads toclosed-form expressions for all the moments of the convective displacement ofthe dispersing particles in terms of the transverse diffusion eigenmodes. Wealso find that the cumulants grow asymptotically linearly with time, ensuring aGaussian distribution in the long-time limit. As a demonstration of thetechnique, the first two longitudinal cumulants (yielding respectively theeffective velocity and the Taylor diffusion constant) as well as the skewness(a measure of the deviation from normality) are calculated for fluid flow inthe parallel plate geometry. We find that the effective velocity and theskewness (which is negative in this case) are enhanced while Taylor dispersionis suppressed due to absorption at the boundary.
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