Effective conductivity by fluid analogy for a porous insulator filled with a conductor

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Abstract
By combining identities relating effective conductivity to tortuosity and tortuosity to induced mass, a general formula for the effective (electrical or thermal) conductivity of a porous insulator filled with a conductor is obtained. This formula depends on an induced-mass factor which arises by treating the conducting material as an inviscid fluid. This induced-mass factor can be estimated with the use of an effective-medium theory. For random arrays of equal spheres, the estimates of conductivity obtained with the use of this fluid analogy are in good agreement with recent exact values derived for periodic arrays of insulating spheres to closest packing.