The Einstein Relation between Relative Viscosity and Volume Concentration of Suspensions of Spheres

Abstract

IN 1906, Einstein1 deduced that the relative viscosity ηr of a very dilute suspension of spheres of volume concentration c could be expressed by ηr = 1 + c. This expression was derived from three equations by elimination, omitting higher-order terms in c. The three equations used by Einstein give directly the expression: ηr = (1 − c)/(1 − 2c), which can be expanded to ηr = 1 + c + 2c 2 + 4c 3 …, simplifying tO ηr = 1 + c at great dilution.