Micro-inhomogeneous Porous Media and Diffusion Problems

1 Micro-inhomogeneous Porous Media and Diffusion Problems 

As mentioned in Sect. 5.5, in the classical diffusion theory for a porous medium, adsorption is described by a distribution coefficient Kd resulting from the transfer of the species from the fluid phase to the solid phase through the linearized equation of equilibrium adsorption isotherm (5.113). 

We conjecture that the actual adsorption mechanism results in a source term rather than a storage that provides a coefficient to the term dc/dt. This perspective, however, is relevant only if the theory is developed through a formulation that couples the microscale phenomena with the macroscale behavior. This is because in the classical theory, it is simple to evaluate an experimental result macroscopically due to adsorption as Kd. Here we will develop an alternative adsorption/desorption/diffusion theory, which is based on MD (molecular dynamics) and HA (homogenization analysis). 

Let us consider the problem of the diffusion of a multi-component fluid (see e.g.. Drew and Passman 1998) in a non-deformable porous medium which is saturated with the solution. Note that in ensuring adsorption, desorption is also taken into account unless otherwise specified. Referring to (3.246), the mass conservation equation for the multi-component fluid is 

Ichikawa and A.P.S. Selvadurai, Transport Phenomena in Porous Media, 

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