Simulation of diffusion and trapping in digitized heterogeneous media

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Abstract
We present an efficient and fast simulation technique to determine the mean survival time τ of a Brownian particle diffusing among a digitized lattice-based domain of traps. Following the first-passage time ideas of Torquato and Kim [Appl. Phys. Lett. 55, 1847 (1989)], the algorithm is based on the known solution for the mean first passage time of a Brownian particle in a cube. The mean survival time, the inverse of the trapping rate, is obtained for a variety of configurations involving digitized spheres. Since the survival time is highly sensitive to the surface area and associated resolution, the results provide a means of determining the relation between the survival time of a real material and its digitized representation. In general, lower resolution images give rise to a diminished mean survival time and, thus, a lower bound on the true mean survival time τ. Digitization can affect other transport properties in which the interface plays a major role, e.g., the fluid permeability associated with flow in porous media. We demonstrate both analytically and computationally that the mean survival time for the digitized medium converges to the continuum value in the high-resolution limit.