Determination of the effective conductivity of heterogeneous media by Brownian motion simulation

In Chan Kim, S. Torquato

Research output: Contribution to journalArticlepeer-review

118 Scopus citations

Abstract

A new Brownian motion simulation technique developed by Torquato and Kim [Appl. Phys. Lett. 55, 1847 (1989)] is applied and further developed to compute "exactly" the effective conductivity σe of n-phase heterogeneous media having phase conductivities σ1, σ2,..., σn and volume fractions φ1, φ2,., φn. The appropriate first passage time equations are derived for the first time to treat d-dimensional media (d=1, 2, or 3) having arbitrary microgeometries. For purposes of illustration, the simulation procedure is employed to compute the transverse effective conductivity σe of a two-phase composite composed of a random distribution of infinitely long, oriented, hard cylinders of conductivity σ2 in a matrix of conductivity σ1 for virtually all volume fractions and for several values of the conductivity ratio α=σ21, including perfectly conducting cylinders (α=∞). The method is shown to yield σe accurately with a comparatively fast execution time.

Original languageEnglish (US)
Pages (from-to)3892-3903
Number of pages12
JournalJournal of Applied Physics
Volume68
Issue number8
DOIs
StatePublished - 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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