A HIGHER-ORDER APPROXIMATION TO EFFECTIVE CONDUCTIVITY IN MEDIA OF ANISOTROPIC RANDOM STRUCTURE

Properties of the effective conductivity tensor K(eff) are studied by deriving the second-order terms in its expansion in the variance sigma2 of normally distributed log conductivity. It is shown that for media of anisotropic structure, the components of the effective conductivity tensor are expressed by a functional of the log conductivity covariance; that is, it depends on the shape of the correlation function and not only on anisotropy ratios, variance sigma2 and space dimensions. However, the trace of K(eff) is independent of the log conductivity autocovariance, and for a given mean conductivity depends only on sigma2 The dependence of the effective conductivity on the correlation structure is illustrated for Gaussian and exponential autocovariances of log conductivity and for two- and three-dimensional flows.