An analytical study on settling of non‐spherical particles

The clarification of the unsteady falling movement of immersed bodies in fluids occurs in several natural situations and many manufacturing processes, e.g. particulate processing and two‐phase solid–liquid applications. In this paper, the acceleration motion of a spherical particle in an incompressible Newtonian environment has been studied for a wide range of Reynolds numbers using a drag coefficient as defined by Chien [S.F. Chien. SPE Drill. Complet., 1994; 9, 281]. The governing equation is strongly nonlinear due to nonlinear nature of the drag coefficient. An analytical mathematical procedure is performed to express an expression for velocity of the particle during the acceleration motion using variational iteration method. Therefore, both the acceleration and position of the particle were easily obtained. The equation of motion was solved in a general form and also for some realistic solid–liquid combinations. The effects of particle sphericity and continuous‐phase viscosity were investigated for different practical situations, where the results satisfactorily describe the settling behavior of the particle. The results were compared with a numerical method and very good agreement was obtained. This work demonstrates the effectiveness of the current mathematical method and presents a simple approach for this type of problem, where the derived expression can be used in different numerical and analytical surveys. Copyright © 2010 Curtin University of Technology and John Wiley & Sons, Ltd.