The viscosity of suspensions of rigid spheres

An explanation is given of the dependence of the relative viscosity on the size distribution of the suspended spheres, an effect recently observed by Ward and Whitmore.(1) It is shown theoretically that if the spheres are of very diverse sizes, the relative viscosity is (1 - c)-2.5 for all values of the volume concentration c. For spheres of equal size, the validity of the Einstein expression for the relative viscosity (1 + 2.5c) is restricted to concentrations well below c = 0.05; while for medium and high concentrations the relative viscosity is given by the theoretical expression (1 - 1.35c)-2.5. The use of the latter formula in interpreting measurements on the viscosity of solutions is briefly indicated.