Comparison of Stokesian Dynamics Method based on Additivity of Velocities with Additivity of Forces.

Abstract

The characteristics and differences in the two approximations. i.e., the additivity of forces and the additivity of velocities, on which Stokesian dynamics methods are based, have been investigated. To do so, Stokesian dynamics simulations of a ferromagnetic colloidal dispersion have been carried out for a simple shear flow, and the aggregate structures and the averaged viscosities have been evaluated, From the results of aggregate structures in equilibrium, the results obtained by the additivity of forces are quantaively different from those by the approximation of ignoring hydrodynamic interactions, although a qualitative agreement is recognized. The results obtained by the additivity of velocities give medium characteristics between the two above approximations. This difference in characeristics between the two additivity approximations and that of ignoring hydrodynamics becomes clearer as the influences of the shear flow dominate those of magnetic forces more significantly. From the results of transient characteristics from an initial state, the results of the additivity of velocities agree well with those of the additivity of forces. In contrast, the results without hydrodynamic interactions deviate from those of the two additivity approximations at a time step when a nearly particle particle touching situation starts to appear.