Simulations and Models for Sedimentation at Small Reynolds Numbers

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

This award supports simultaneous mathematical and numerical study of various low Reynolds number sedimentation flows. These systems are complicated by the long range nature of the fluid flows generated by individual solid particles as they fall, requiring efficient algorithms for particle simulations, introducing variable nonlinear coefficients of different dependencies into model continuum partial differential equations, and leading to nontrivial distributions in the statistical mechanics of the interacting particles. In this work, efficient algorithms specialized to dilute wall-bounded sedimentation, previously developed to investigate the scaling of velocity fluctuations in monodisperse sedimentation, will be used to provide quantitative data for comparison with existing and newly-developed kinetic and fluid models. The simulations will be generalized to include effects due to inclined channels, polydispersity, non-spherical particles, and small non-zero Reynolds numbers. Interactions between solid particles sedimenting in a fluid are important in many natural and industrial processes, including the settling motions of silt in rivers and dust in the air, and in applications which use centrifugal or gravitational separation such as those for proteins, minerals, waste water, and recyclable plastics. While the mathematics describing the interactions between individual particles and the suspending fluid are well known, simulations of large scale flows based on these rules are computationally prohibitive. It would be far preferable to use macroscopic models which are less costly to solve because they neglect the detailed motion of individual particles. Unfortunately, existing macroscopic models for sedimentation have very limited ranges of validity. This work will consider restricted classes of sedimentation systems in which efficient computation of the interactions between large numbers of particles remains possible because of simplified geometries and limits for the mathematical rules describing particle motion. Results will be used to help identify improved macroscopic models to describe both these restricted classes and more general sedimentation flows. Ultimately, this work will lead to improved equations for modeling sedimentation flows in nature and for better design of separation processes based on sedimentation.