Sedimentation of dilute suspensions in creeping motion

Abstract

AbstractSolutions to the creeping motion equations for a cylinder and particles in an infinite media were superimposed to calculate the first‐order correction to the Stokes settling velocity for a particle inside a cylindrical container and for various models used to approximate the settling characteristics of dilute suspensions. The models were based on an assumed disribution of translating particles subject only to the hydrodynamic forces produced by their motion. Particle interactions and wall effects for ordered and random arrangements of spherical particles in a cylinder were calculated on a digital computer and used to devlop equations for settling velocity as a function of concentration.The equations developed for the models containing spherical particles were modified to apply to nonspherical particles by considering each particle as a point force with regard to the fluid motion it produces at neighboring particles. As an application of these equations, a model of a dilute fiber suspension was studied in which prolate spheroide settle perpendicular to their symmetry axes.The correction to Stokes' law for ordered arrangements of spheres is close to that obtained by earlier investigators working with similar models. However this correction leads to lower settling rates than the bulk of reported experimental data at any given particle concentration in the dilute range of less than 5% solids. The authors have shown that this discrepancy may be eliminated by assuming an alternate model composed of doublets in place of uniformly distributed particles. It may be concluded that in the dilute concentration range a model of a sedimenting suspension must include terms which reflect its tendency toward cluster formation and the consequent effect on settling rate. In order to accomplish this, forces other than hydrodynamic may have to be considered, for example, electrostatic forces.