Scaling in Diffusive Transport

             Robert P. Ewing and Robert Horton
    Department of Agronomy, Iowa State University, Ames, IA

    Submitted to the CRC monograph "Methods of scaling in soil physics"
                 Yakov Pachepsky, Editor

Abstract:
Some porous media have sparsely connected porespaces.  We perform Monte Carlo 
simulations using pore network models, in conjunction with percolation theory, 
to examine diffusive transport in such media.  Results indicate that accessible 
porosity, tortuosity, and diffusivity are largely determined by pore 
connectivity.  At the percolation threshold, that point at which the medium is 
just barely traversed by a continuous porespace, these parameters are described 
by equations that scale with time, distance, and/or proximity to the 
percolation threshold.  Slightly above the percolation threshold, a different 
kind of scaling appears, essentially an intrinsic edge effect.  Accessible 
porosity and diffusivity are strongly affected by this edge effect, 
particularly at low connectivity and/or sample size.  From porosity and 
diffusivity a residual tortuosity can be calculated, which also shows both 
kinds of scaling.  Accessible porosity, tortuosity, and diffusivity can all be 
estimated from connectivity considerations, showing the pivotal role of pore 
accessibility for transport in low-connectivity media.