Application of the Laplace Decomposition Method for Motion of Spherical/Non-Spherical Particles within a Highly Viscous Fluid

Abstract

Downward movement of solid particles within a fluid in the presence of a gravitational field occurs in many industrial and engineering processes, e.g. particulate processing and two phase solid-liquid applications. Three highly viscous liquids including water, glycerin and ethylene-glycol were selected to study the motion of spherical/non-spherical solid particles for a wide range of Reynolds numbers employing a drag coefficient as defined by Chien [10]. The governing equation of the motion is strongly nonlinear due to the nonlinear nature of the drag force exerted on the solid body during falling. In this paper, a numerical technique, namely the Laplace Decomposition Method (LDM), is applied to solve the governing equation. This method applies the Laplace transform to the differential equation whereas the nonlinear term is decomposed in terms of Adomian polynomials. A good agreement was achieved when compared with a famous numerical method, then the effects of solid sphericity were tested for the different liquids. This study demonstrates the effectiveness of the present mathematical technique and illustrates a simple application for this type of problem which may be used for a large class of nonlinear differential equations