We derive rigorous upper and lower bounds on the bulk and shear moduli of suspensions of spheres of variable penetrability distributed throughout a matrix (or fluid), for all possible phase property values, through second order in the sphere volume fraction φ2. The bounds, at the very least, capture the salient qualitative features that come into play when particles overlap, and, in some instances, are shown to be quantitatively very sharp. Among other results, we use these bounds to obtain good estimates of the bulk and expansion viscosities of an incompressible fluid containing spherical air bubbles and thus extend the corresponding results of Taylor in which pair interactions were neglected.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry