Analytical investigation on acceleration motion of a vertically falling spherical particle in incompressible Newtonian media

The settling behavior of solid particles is of fundamental importance in natural and artificial applications. In current study, the unsteady motion of a spherical particle falling in a Newtonian fluid was analyzed using a drag of the form given by Oseen/Ferreira, for a range of Reynolds numbers. Particle equation of motion involved added-mass term and neglected the Basset term. Using the homotopy perturbation method (HPM) analytical expressions for the instantaneous velocity, acceleration and position of the particle were derived. The practical applications of the results were discussed. The presented investigation showed the effectiveness of HPM.