DIFFERENTIAL MULTIPHASE MODELS FOR POLYDISPERSED SUSPENSIONS AND PARTICULATE SOLIDS

We report some novel applications of the differential scheme to constr uct the effective viscosity and moduli of suspensions of spheres of di verse sizes. Exact closed form expression for the effective viscosity of droplets of diverse sizes is derived, which includes the generalise d Einstein formula of Brinkman and Roscoe. Exact closed form solutions for the effective moduli of a particulate solid consisting of rigid s pheres of diverse sizes embedded in an elastic solid shows that the Po isson's ratio of the composite should approach the value 1/5 at high v olume fraction. The effect of a limited range of sizes of the included phase and locally-inhomogeneous distribution of inclusions is taken i nto account by considering a three-component system, with a fictitious inclusion phase made up of the matrix (solvent) material, which limit s the space available for the real inclusions. (C) 1997 Elsevier Scien ce B.V.