Random walk studies of equilibrium and transport properties of porous materials

Random porous materials play important roles in numerous natural and technological processes. A good understanding of these processes mandates knowledge of the equilibrium and transport properties of these materials, which depend on their microstructure, and, in certain cases, the transport mechanisms involved. Due to the inherent complexity of disordered porous structures, random walk (RW) simulation methods provide the most efficient means to obtain exact solutions to such problems. These methods themselves can be accelerated via incorporation of first-passage time (FPT) probability distributions.; Here the FPT RW technique is used or adapted to compute equilibrium and transport properties of random porous materials as a function of medium geometry. The effective conductivity, the effective reaction rate of diffusion-controlled reactions occurring at the pore-solid interface, and the partition coefficient of dilute bulk polymer solutions in equilibrium with disordered porous structures are determined for one or both of two model porous systems possessing distinctly different pore space morphologies: the penetrable concentric shell (PCS) model and the random pore (RP) model. The convex (PCS) and concave (RP) natures of the pore-solid interfaces of these models lead to a crossover of the results for certain properties. For the PCS model, the key variable in the closely related partitioning and effective reaction rate problems was shown to be the square of the mean pore size, while the effective conductivity exhibits only a slight dependence on pore size. Thus, the mean pore size appears to be determinant when the first encounter with the pore-solid interface is of chief importance. Experimental data for the effective electrical conductivity of artificial rocks are well-described by the PCS model.; A novel FPT RW algorithm is also used to compute the effective diffusivity of Brownian tracers diffusing in a cubic pore network via bulk and surface diffusion mechanisms. An expression demonstrating a linear relationship between the effective diffusivity and the fraction of time spent in a given dimension was derived and is in good agreement with simulation results.