DIFFUSIVE TRANSPORT IN 2-PHASE MEDIA - SPATIALLY PERIODIC MODELS AND MAXWELLS THEORY FOR ISOTROPIC AND ANISOTROPIC SYSTEMS

The problem of diffusion and heat conduction in two-phase systems is u sed to illustrate the utility of approximate solutions for the closure problem associated with the method of volume averaging. Numerical sol utions for spatially periodic models are compared with experimental da ta and with an approximate solution of the closure problem first used by Chang. Chang's unit cell replaces the spatially periodic boundary c onditions in the closure problem with a Dirichlet condition that leads to analytical solutions for the closure variables. These analytical s olutions are identical to the classical solutions of Maxwell and Rayle igh, and the comparison between spatially periodic models and Chang's unit cell indicates only minor differences between the two approaches. In this work we extend the studies of Chang to include both interfaci al resistance and anisotropic systems which are generated by means of ellipsoidal unit cells. The inclusion of interfacial resistance is imp ortant for the study of diffusion in cellular systems, while the use o f ellipsoidal unit cells provides a comparison between theory and expe riment for diffusion in anisotropic porous media.