Abstract
We present a two-dimensional mathematical model of a composite material with conducting inclusions (fibers) embedded in a matrix. Our main objective is to study how polydispersity (two different sizes of particles) affects the overall conductivity of the composite. If the conductivity of inclusions is higher than the conductivity of the matrix, then previous studies suggest an increase of the effective conductivity due to polydispersity. We show that for high volume fraction when inclusions are not well-separated and percolation effects play a significant role, polydispersity may result in either an increase or decrease of the effective conductivity. Our proof is based on the method of functional equations and it provides sufficient conditions for both the increase and the decrease of the effective conductivity.
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Berlyand, L., Mityushev, V. Increase and Decrease of the Effective Conductivity of Two Phase Composites due to Polydispersity. J Stat Phys 118, 481–509 (2005). https://doi.org/10.1007/s10955-004-8818-0
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DOI: https://doi.org/10.1007/s10955-004-8818-0