Dispersion in an unconsolidated porous medium

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Abstract
The dispersion of passive scalar by Stokes flow through a dilute suspension of solid spheres fixed at random points in space is a basic model of mixing and transport in an unconsolidated porous medium. Earlier investigators have used a general theory of macroscopic transport to calculate the Lagrangian velocity autocorrelation function and the effective diffusivity of this system. If the tracer does not diffuse molecularly then the autocorrelation function has a ‘‘long tail,’’ proportional to t−1. Small molecular diffusivity provides a cutoff at long times and implies an effective diffusivity that increases as the logarithm of the Péclet number. In the present work the same results are obtained including the constants of proportionality, using an elementary Lagrangian argument that avoids the formalism of the macrotransport theory.

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