The viscosity of a moderately dense, polydisperse suspension of spherical particles

A recently developed formalism for computing the low-frequency, Newtonian viscosity of moderately dense monodisperse suspensions is extended to include polydisperse suspensions. In the form presented here this general theory is applicable to spherical solute particles suspended in a Newtonian solvent. Explicit formulas are obtained for the viscosity virial coefficients associated with first and second order terms in powers of the solute volume fraction. It is proved that the second order term in the viscosity virial series for a polydisperse suspension of solute particles is fully characterized by a single, dimensionless function b2(λ), with 0 λ 1. Numerical values are presented for the second order (Huggins) coefficient specific to hard-sphere particles with general stick-slip solute–solvent boundary conditions and for “spherical surfactant particles” as well. Calculations are included also for suspensions with log-normal particle-size distributions.