The viscosity of a suspension of spheres

Publisher Website
Google Scholar
Abstract
It is shown that in Stokes's flow the perturbation field, due to the addition of one more sphere to a shear flow of a fluid containing a number of non-interacting spheres, has the property that the total additional shearing force, acting on any plane normal to the direction of velocity change, is zero. However, the perturbation velocity, integrated over such a plane, takes a constant value, positive if the plane lies on one side of the sphere and negative if it lies on the other side. It follows that the effect of all the spheres is not to alter the shearing stress at all, but to reduce the mean shear by a factor 1 – 2·5c, where c is the concentration. This suggests that Einstein's viscosity law should be altered to η = η0/(1 – 2·5c) when c is not small.

This publication has 4 references indexed in Scilit: