Two models for determination of the effective conductivity of concentrated suspensions of ellipsoidal particles with surface phenomena

Abstract

Many multicomponent materials such as rocks or nanofluids are characterized by the presence of conductive surface layers at the interface. These conductive layers can change effective physical properties (for example, effective thermal or electrical conductivities) of such materials. A suspension of ellipsoidal particles with surface conductivity is considered. Two theoretical models are presented for the solution of the so-called one-particle problem that can be used then in any homogenization scheme for determination of the effective conductivity of such suspension. The first model is based on the modification of the boundary conditions for the electric current density (the jump boundary conditions). The second model is based on the confocal ellipsoids. The effect of surface conductivity is obtained for this model by limiting transition to the infinitely thin external ellipsoidal shell.For the calculation of the effective conductivity of the medium containing the ellipsoidal particles with the surface phenomena one of the popular homogenization scheme named by Differential Effective Medium (DEM) method is used. Comparison of numerical results obtained by this method for two different solution of the one-particle problem show that these results are rather close even for very large values of the surface conductivity.