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=σ2/σ1, including perfectly conducting cylinders (α=∞). The method is shown to yield σe accurately with a comparatively fast execution time.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)