Analytical study on accelerating falling of non-spherical particle in viscous fluid

Unsteady motion of a vertically falling non-spherical particle has attracted considerable attention due to its frequent applications in nature and industry. A series of semi-analytical methods have been used to raise the results' accuracy as well as widening the region of convergence. The current study pursued a new analytical solution for the unsteady motion of a rigid non-spherical particle in a quiescent Newtonian fluid, based on the Optimal Homotopy Analysis Method. With a view towards obtaining the highest level of accuracy and ensuring the convergence of the analytical results, the averaged residual errors were obtained and minimized. In addition to flexibility, it was also proven that the proposed method can lead to completely reliable and precisely accurate results. Based on the series solution, the effects of physical parameters on the terminal settling velocity (i.e. the greatest velocity that a falling body may reach) and the acceleration time (i.e. the time that a particle reaches the settling velocity) are investigated.