Porosity for the penetrable-concentric-shell model of two-phase disordered media: Computer simulation results

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Abstract
Computer-simulation results are reported for the porosity of a model of two-phase random media composed of identical D-dimensional spheres (D=2 or 3) distributed with an arbitrary degree of impenetrability λ, 0≤λ≤1; λ=0 corresponding to randomly centered or ‘‘fully penetrable’’ particles and λ=1 corresponding to totally impenetrable particles. We specifically consider the D-dimensional penetrable-concentric-shell model in which each sphere of diameter σ is composed of a mutually impenetrable core of diameter λσ, encompassed by a perfectly penetrable concentric shell of thickness (1−λ)σ/2. We develop two independent techniques to sample for the porosity. Simulation results agree with known exact results for the extreme limits of λ=0 and λ=1 up to three significant figures. The results for intermediate λ are new and compare favorably with approximate analytical expressions obtained by Rikvold and Stell.