Hydrodynamic theory of suspensions

In the first decade of the 20 century, Einstein [27] gave his attention to the prediction of the viscosity of a dilute suspension of spheres. Einstein began with the creeping flow Navier-Stokes equation of Newtonian fluid hydrodynamics  

Here v is velocity, p is pressure, t] is viscosity, and R is the radius of the sphere. 

Stokes [28] had earlier used Eq. 2.5 for analyzing the flow aroimd a sphere. Einstein argued that the viscosity of the suspension could be determined by the increase of the energy dissipated, 5, by the presence of the sphere, i.e.. 

In 1945 Guth [29] noted the similarity of the mathematical formulations of the theory of linear elasticity with those of Newtonian fluid hydrodynamics. He saw that if the elastic solid were incompressible that the presence of rigid spheres would similarly increase the modulus G according to elastic energy arguments, specifically. 

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