A theoretical research to effective viscosity of colloidal dispersions

Colloidal dispersions are common in nature with wide industrial applications. One of the central theoretical problems in the field is to determine the rheological properties of the colloidal dispersion from the microstructures of the systems. Because of the difficulties associated with the boundary_value problems of the many_particle system, existing theories for colloidal suspensions are limited to low particle concentrations. In this work, a method of transformation field is developed by which one can calculate the effective viscosity of an incompressible viscous fluid containing colloidal particles (either solid particles or liquid drops). The predictions of our theory are in good agreement with the Einstein's formula for suspensions and the Taylor's formula for emulsions at low particle concentrations. At higher particle concentrations, the results of Nunan and Keller are produced. The method is also applicable to the viscosity of colloidal systems with non_spherical particles.