in a suspension of solid particles (e.g. micron-size spheres suspended in oil), an effective viscosity formula_112 can be defined in terms of stress and strain components which are averaged over a volume large compared with the distance between the suspended particles, but small with respect to macroscopic dimensions. such suspensions generally exhibit non-newtonian behavior. however, for dilute systems in steady flows, the behavior is newtonian and expressions for formula_112 can be derived directly from the particle dynamics. in a very dilute system, with volume fraction formula_114, interactions between the suspended particles can be ignored. in such a case one can explicitly calculate the flow field around each particle independently, and combine the results to obtain formula_115. for spheres, this results in the einstein equation: