Boundary effects on effective conductivity of random heterogeneous media with spherical inclusions

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Abstract

It is common to determine the effective conductivity of heterogeneous media by assuming stationarity of the random local properties. This assumption is not obeyed in a boundary layer of a body of finite size. The effect of different types of boundaries is examined for a two-phase medium with spherical inclusions of given conductivity distributed randomly in a matrix of a different conductivity. Exact solutions are derived for the apparent conductivity and the boundary layer thickness. The interaction between the spheres and the boundaries is fully incorporated in the solutions using a spherical harmonics expansion and the method of images. As applications, the corrections for the effective conductivity are given for two cases of finite bodies: the Maxwell sphere and a cylinder of flow parallel to the axis.

Original languageEnglish
Article number046601
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume86
Issue number4
DOIs
StatePublished - 3 Oct 2012

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