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A Method for Determining the Effective Conductivity of Dispersions of Particles

Bonnecaze, R. T. and Brady, J. F. (1990) A Method for Determining the Effective Conductivity of Dispersions of Particles. Proceedings of the Royal Society of London. Series A, Mathematical, Physical and Engineering Sciences, 430 (1879). pp. 285-313. ISSN 0962-8444. https://resolver.caltech.edu/CaltechAUTHORS:20141215-102858372

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Abstract

A general method is developed to predict the effective conductivity of an infinite, statistically homogeneous suspension of particles in an arbitrary (ordered or disordered) configuration. The method follows closely that of 'stokesian dynamics', and captures both far-field and near-field particle interactions accurately with no convergence difficulties. This is accomplished by forming a capacitance matrix, the electrostatic analogue of the low-Reynolds-number resistance matrix, which relates the monopole (charge), dipole and quadrupole of the particles to the potential field of the system. A far-field approximation to the capacitance matrix is formed via a moment expansion of the integral equation for the potential. The capacitance matrix of the infinite system is limited to a finite number of equations by using periodic boundary conditions, and the Ewald method is used to form rapidly converging lattice sums of particle interactions. To include near-field effects, exact two-body interactions are added to the far-field approximation of the capacitance matrix. The particle dipoles are then calculated directly to determine the effective conductivity of the system. The Madelung constant of cohesive energy of ionic crystals is calculated for simple and body-centred cubic lattices as a check on the method formulation. The results are found to be in excellent agreement with the accepted values. Also, the effective conductivities of spherical particles in cubic arrays are calculated for particle to matrix conductivity ratios of infinity, 10 and 0.01.


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http://www.jstor.org/stable/79996JSTORArticle
Additional Information:© 1990 The Royal Society.
Issue or Number:1879
Record Number:CaltechAUTHORS:20141215-102858372
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20141215-102858372
Official Citation:A Method for Determining the Effective Conductivity of Dispersions of Particles R. T. Bonnecaze and J. F. Brady Proceedings: Mathematical and Physical Sciences, Vol. 430, No. 1879 (Aug. 8, 1990), pp. 285-313 Published by: The Royal Society Article Stable URL: http://www.jstor.org/stable/79996
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52808
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 Dec 2014 18:40
Last Modified:03 Oct 2019 07:44

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