Modeling the effective viscosity of suspensions of spheres beyond the dilute limit is a difficult problem that has challenged researchers for nearly a century since Einstein derived an equation for dilute suspensions. Hydrodynamics modeling requires complex mathematical treatments of integral equations describing interactions between spheres, & its solutions have been limited to semi dilute dispersion of monosized hard spheres. Mechanics modeling treats suspensions in a statistical sense & generally provides upper/lower bounds solutions for poly-dispersed suspensions. A closed-form solution for effective viscosity of concentrated suspensions of monosized spheres using both the elastic-viscous analogy & the analogy between the effective dielectric constant of a polarizable medium & the effective viscosity of two-phase flow is derived in this study.
