A semi-Analytical technique for non-linear settling particle equation of Motion

Reliable knowledge of a free falling solid particle in a quiescent liquid is necessary for a range of chemical, mineral and process engineering applications. A recent series-integral-based mathematical method, called the variational iteration method, is used, and a semi-exact solution is derived for the instantaneous velocity of the particle versus time. The equation is solved for its general form and for a realistic combination of solid–liquid systems, and the convergence of the methods is examined for a special case. The results obtained are compared with previous analytical results and the finite difference method. The outcomes clearly demonstrate the falling behavior of a particle settling in an incompressible fluid and show the effectiveness and simplicity of the current mathematical method.