A Treatment of the Viscosity of Concentrated Suspensions

In current theories of the concentration dependence the solute molecules are treated as point centers of disturbance. The finite size that produces a shielding of two interacting particles in the presence of intervening ones reduces the interaction calculated in the point approximation and thus reduces the discrepancy between experiment and theory. An approximate treatment for a spherical solute based on the cage model, and hence more adequate at high concentrations, is presented. It operates with a spherical enclosure around a central particle. The position of this shell reflects the relative extent to which particles beyond nearest neighbors can hydrodynamically interact with the central molecule. Thus, a parameter f appears in the theory which increases slowly with concentration and approaches a limit corresponding to the coincidence of the shell with the wall of the nearest neighbor cage at high concentrations. In the framework of the present theory, f must be regarded as a semiempirical quantity. The hydrodynamic problem can be handled rigorously. The relative viscosity calculated is in satisfactory agreement over a range of concentrations with empirical expressions successfully applied to pertinent systems. The initial value of f derived from the observed coefficient of the quadratic term is also reasonable.