A differential approach to suspensions with power-law matrices

We apply the differential method of Roscoe (1952) to the problem of finding the viscosity of a suspension of non-colloidal spheres in a power-law matrix. The results are compared with other theories and published experiments, and reasonable agreement is found up to moderate concentrations ( ϕ ∼ 0.5) when viscoelasticity and other effects are not important. The Roscoe paper depends on using a “crowding” function in the analysis; here two modified crowding functions are discussed, with a view to explaining the success of the Maron–Pierce formula, which does not reduce to the Einstein form for low concentrations.