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We describe new effects associated with electrical conduction along phase interfaces for particle reinforced conductors. For particles of general shape we introduce a new quantity β1 called the 'surface to volume dissipation' of a particle. This quantity is a measure of the particle's ability to dissipate energy on its surface relative to the energy dissipated in its interior. It is described mathematically as the minimum value of a suitably defined Rayleigh quotient and is related to an eigenvalue problem posed on the particle surface. We consider the overall conductivity of a particle reinforced conductor when the particle conductivities are less than that of the matrix. It is shown that the overall conductivity will be increased by the presence of a specific particle when the particle's 'surface to volume dissipation' lies above a critical value. We calculate the surface to volume dissipation for a sphere and for starlike particles we provide a lower bound in terms of particle dimensions. These estimates allow for the prediction of new particle size effects. Second, we present a new criterion on the particle size distribution for which the overall conductivity lies below the matrix conductivity. © 1998 The Royal Society.

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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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