Dispersion resulting from flow through spatially periodic porous media

Abstract

A rigorous theory of dispersion in both granular and sintered spatially-periodic porous media is presented, utilizing concepts originating from Brownian motion theory. A precise prescription is derived for calculating both the Darcy-scale interstitial velocity vector v* and dispersivity dyadic D* of a tracer particle. These are expressed in terms of the local fluid velocity vector field v at each point within the interstices of a unit cell of the spatially periodic array and, for the dispersivity, the molecular diffusivity of the tracer particle through the fluid. Though the theory is complete, numerical results are not yet available owing to the complex structure of the local interstitial velocity field v. However, as an illustrative exercise, the theory is shown to correctly reduce in an appropriate limiting case to the well-known Taylor-Aris results for dispersion in circular capillaries.