Simulation of diffusion and trapping in digitized heterogeneous media

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 flo...

[1]  Graeme W. Milton,et al.  Bounds on the Electromagnetic, Elastic, and Other Properties of Two-Component Composites , 1981 .

[2]  Masao Doi,et al.  A New Variational Approach to the Diffusion and the Flow Problem in Porous Media , 1976 .

[3]  S. Prager,et al.  Improved Variational Bounds on Some Bulk Properties of a Two‐Phase Random Medium , 1969 .

[4]  Salvatore Torquato,et al.  Diffusion‐controlled reactions: Mathematical formulation, variational principles, and rigorous bounds , 1988 .

[5]  Torquato.  Relationship between permeability and diffusion-controlled trapping constant of porous media. , 1990, Physical review letters.

[6]  M. Avellaneda,et al.  Diffusion and reaction in heterogeneous media: Pore size distribution, relaxation times, and mean survival time , 1991 .

[7]  James G. Berryman,et al.  Use of digital image analysis to estimate fluid permeability of porous materials: Application of two-point correlation functions , 1986 .

[8]  S. Torquato,et al.  Porosity for the penetrable-concentric-shell model of two-phase disordered media: Computer simulation results , 1988 .

[9]  Day,et al.  Universal conductivity curve for a plane containing random holes. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[10]  E. Garboczi,et al.  Length scales relating the fluid permeability and electrical conductivity in random two-dimensional model porous media. , 1992, Physical review. B, Condensed matter.

[11]  John M. Deutch,et al.  Diffusion-Controlled Reactions , 1983 .

[12]  G. Binnig,et al.  Scanning tunneling microscopy , 1984 .

[13]  Nicos Martys,et al.  Transport and diffusion in three-dimensional composite media , 1994 .

[14]  Salvatore Torquato,et al.  Efficient simulation technique to compute effective properties of heterogeneous media , 1989 .

[15]  Lee,et al.  Random-walk simulation of diffusion-controlled processes among static traps. , 1989, Physical review. B, Condensed matter.

[16]  M. C. Nichols,et al.  X-Ray Tomographic Microscopy (XTM) Using Synchrotron Radiation , 1992 .

[17]  Mark J. Beran,et al.  Statistical Continuum Theories , 1968 .

[18]  Kim,et al.  First-passage-time calculation of the conductivity of continuum models of multiphase composites. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[19]  H. Borchers.  Local rings and the connection of spin with statistics , 1965 .

[20]  Salvatore Torquato,et al.  Random Heterogeneous Media: Microstructure and Improved Bounds on Effective Properties , 1991 .

[21]  B. U. Felderhof.  Wigner solids and diffusion controlled reactions in a regular array of spheres , 1985 .

[22]  Salvatore Torquato,et al.  Diffusion and reaction among traps: some theoretical and simulation results , 1991 .

[23]  Wilkinson,et al.  Nuclear magnetic relaxation in porous media: The role of the mean lifetime tau ( rho,D). , 1991, Physical review. B, Condensed matter.

[24]  Noam Agmon,et al.  Residence times in diffusion processes , 1984 .

[25]  Y. Chiew,et al.  Computer simulation of diffusion‐controlled reactions in dispersions of spherical sinks , 1989 .

[26]  Karen L. Klomparens,et al.  Scanning and Transmission Electron Microscopy: An Introduction , 1993 .

[27]  R. Siegel,et al.  A new Monte Carlo approach to diffusion in constricted porous geometries , 1986 .