Hindered settling of a suspension at low Reynolds number

The purpose of this paper is to analyze how the settling velocity of a dispersion of spherical particles (that is, drops of arbitrary viscosity) depends on concentration. The procedure used entirely avoids the divergent integrals which previous workers in this field have been forced to deal with and yields explicit formulas for the sedimentation velocity. These formulas, accurate to first order in the particle volume fraction, depend on both the physical characteristics of the particles (size, buoyant density, viscosity ratio) as well as on any long range forces (for example, electrical double layer repulsions or van der Waals attraction) which may exist between particles. Sample calculations are given for globular proteins subject to double layer repulsions and for micron size colloids which experience van der Waals attractions in addition to the electrostatics. In the latter case, it is shown how the Hamaker constant can be extracted from sedimentation data. The analysis is extended to more concentrated suspensions by assuming that the hydrodynamic interactions among particles are pairwise additive; comparison with published data shows this analysis to be reasonably accurate, even for dense suspensions, without any adjustable parameters.