TRAPPING AND FLOW AMONG RANDOM ARRAYS OF ORIENTED SPHEROIDAL INCLUSIONS

The effective trapping rate k associated with diffusion-controlled reactions among random distributions of spatially correlated and uncorrelated, oriented spheroidal traps of aspect ratio epsilon is determined from Brownian motion simulations. Data for k are obtained for prolate cases (epsilon = 2, 5, and 10), oblate cases (epsilon = 0.1, 0.2, and 0.5), and spheres (epsilon = 1) over a wide range of trap volume fractions (phi-2) and satisfy recently obtained rigorous lower bounds on k for this statistically anisotropic model. The results for the trapping rate for correlated traps always bounds from above corresponding results for uncorrelated traps. Generally, the trapping rate k, for fixed phi-2, increases with decreasing aspect ratio epsilon, showing a precipitous rise in k as the spheroids become disklike. Using a recent theorem due to Torquato [Phys. Rev. Lett. 64, 2644 (1990)], data for the trapping rate k can be employed to infer information about the fluid permeability tensor K associated with slow viscous flow through porous media composed of the same arrays of oriented spheroidal particles.