Analytical solution for settling of non-spherical particles in incompressible Newtonian media

In this paper, the acceleration motion of a vertically falling non-spherical particle in incompressible Newtonian media was investigated. The instantaneous velocity and acceleration were carried out by using the differential transformation method (DTM) which is an analytical solution technique. The current results were also compared with those derived from the variational iteration method (VIM) and the established fourth-fifth order Runge–Kutta–Fehlberg method in order to verify the accuracy of the proposed method. The analytic solution was found to be in good agreement with the direct numerical solution. After such verifications, the effects of parameters such as sphericity, ϕ, and the integrated added mass coefficient, CA, on the velocity and acceleration profiles of a falling non-sphere particle in different Newtonian fluids are illustrated and explained. An infinity medium of water, glycerin or ethylene-glycol was considered as liquid phase. Moreover, the results demonstrate that the DTM is very effective in generating analytical solutions for even highly nonlinear problems.

This figure clearly shows that the Basset History force has a pronounced effect on the velocity profile of the particle.Figure optionsDownload as PowerPoint slideHighlights
► Nonlinear differential equation solved analytically by the DTM.
► It is found that the DTM can achieve more suitable results compared with the VIM.
► Acceleration duration is increased by reduction of liquid viscosity.
► The Basset History force has a pronounced effect on the velocity profile.