An Application of Mixture Theory to Particulate Sedimentation

Abstract

Equations for two-phase flow are used to analyze the one-dimensional sedimentation of solid particles in a stationary container of liquid. A derivation of the equations of motion is presented which is based upon Hamilton’s extended variational principle. The resulting equations contain diffusivity terms, which are linear in the gradient of the particle concentration. It is shown that the solution of the equations for steady sedimentation is stable under small perturbations. Finally, finite-difference solutions of the equations are compared to the data of Whelan, Huang, and Copley for blood sedimentation.