Effective conductivity, dielectric constant, and diffusion coefficient of digitized composite media via first-passage-time equations

Journal Article · Mon Feb 01 04:00:00 EST 1999 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.369287· OSTI ID:295503

Torquato, S; Kim, I C ^[1]; Cule, D ^[2]

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1. Princeton Materials Institute and Department of Civil Engineering Operations Research, Princeton University, Princeton, New Jersey 08544 (United States)
2. Princeton Materials Institute, Princeton University, Princeton, New Jersey 08540-5211 (United States)

We generalize the Brownian motion simulation method of Kim and Torquato [J. Appl. Phys. {bold 68}, 3892 (1990)] to compute the effective conductivity, dielectric constant and diffusion coefficient of digitized composite media. This is accomplished by first generalizing the {ital first-passage-time equations} to treat first-passage regions of arbitrary shape. We then develop the appropriate first-passage-time equations for digitized media: first-passage squares in two dimensions and first-passage cubes in three dimensions. A severe test case to prove the accuracy of the method is the two-phase periodic checkerboard in which conduction, for sufficiently large phase contrasts, is dominated by corners that join two conducting-phase pixels. Conventional numerical techniques (such as finite differences or elements) do not accurately capture the local fields here for reasonable grid resolution and hence lead to inaccurate estimates of the effective conductivity. By contrast, we show that our algorithm yields accurate estimates of the effective conductivity of the periodic checkerboard for widely different phase conductivities. Finally, we illustrate our method by computing the effective conductivity of the random checkerboard for a wide range of volume fractions and several phase contrast ratios. These results always lie within rigorous four-point bounds on the effective conductivity. {copyright} {ital 1999 American Institute of Physics.}

• OSTI ID: 295503
• Journal Information: Journal of Applied Physics, Journal Name: Journal of Applied Physics Journal Issue: 3 Vol. 85; ISSN JAPIAU; ISSN 0021-8979
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGORITHMS
BROWNIAN MOVEMENT
COMPOSITE MATERIALS
DIELECTRIC PROPERTIES
DIFFUSION
DIGITAL SYSTEMS
ELECTRIC CONDUCTIVITY
PERMITTIVITY
RANDOMNESS
SIMULATION
THERMAL CONDUCTIVITY