Viscosity of Suspensions of Uniform Spheres

A mathematical development of the viscosity of suspensions is presented based on the steady-state Stokes-Navier equations of motion omitting inertia terms. The disturbance due to each sphere is assumed to be confined to a frictionless envelope surrounding it similar to the stream tube for flow inside ducts. The relationship obtained between relative viscosity and solids concentration is in good agreement with existing data over a wide concentration range without the necessity of introducing empirical constants. It is thus thought that it may be a suitable model for further theoretical study as well as furnishing a basis for empirical correlation equations of rheological properties. In very dilute systems it does not agree with the well-known Einstein formula, and possible reasons for this variation are advanced.