Diffusion amid random overlapping obstacles: Similarities, invariants, approximations

Efficient and accurate numerical techniques are used to examine similarities of effective diffusion in a void between random overlapping obstacles: essential invariance of effective diffusion coefficients (D_eff) with respect to obstacle shapes and applicability of a two-parameter power law over nearly entire range of excluded volume fractions (ϕ), except for a small vicinity of a percolation threshold. It is shown that while neither of the properties is exact, deviations from them are remarkably small. This allows for quick estimation of void percolation thresholds and approximate reconstruction of D_eff (ϕ) for obstacles of any given shape. In 3D, the similarities of effective diffusion yield a simple multiplication "rule" that provides a fast means of estimating D_eff for a mixture of overlapping obstacles of different shapes with comparable sizes.