Analyses of effective viscosity of suspensions with deformable polydispersed spheres

A simple expression is derived for the effective shear viscosity of suspensions with deformable polydispersed spheres in this study. The analyses commence with the modified Eshelby model to derive the elastic stress-strain relation for an elastic composite containing spherical inclusions. Then, using the elastic-viscous analogy, the effective shear viscosity is obtained for suspensions with small volume fractions of deformable mono-sized spheres. Finally, using Bruggeman's differential model, the formula for the effective shear viscosity of suspensions with concentrated deformable polydispersed spheres is obtained. The present formulae are compared with some of the existing solutions and experimental measurements, and good agreement is obtained.