ON THE EFFECTIVE CONDUCTIVITY OF A DILUTE SUSPENSION OF SPHERICAL DROPS IN THE LIMIT OF LOW PARTICLE PECLET NUMBER

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Abstract
In this paper we consider the effective conductivity of a dilute suspension of neutrally bouyant spherical drops which is undergoing a simple shear flow. The thermal conductivity, viscosity and specific heat capacity of the drops are assumed to be different from those of the suspending fluid, though it is assumed that the local Peclet and Reynolds numbers are small both inside and outside the drop. The analysis consists of three parts: a derivation of the relationship between bulk heat flux on the one hand and the thermal and momentum fields at the microscale of the suspended particles on the other; a calculation of the local temperature field near a single neutrally buoyant spherical drop in shear flow with an imposed transverse temperature gradient at large distances; and a synthesis of the general relationship for bulk heat flux and the calculated local temperature field to determine an effective conductivity for a dilute suspension of spherical drops.

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