• solid spherical particle;
  • acceleration motion;
  • solid–liquid systems;
  • sedimentation;
  • non-linear differential equation;
  • differential transformation method (DTM);
  • experimental data


In this paper, the acceleration motion of a vertically falling spherical particle in incompressible Newtonian media was investigated. The instantaneous velocity and acceleration were carried out using analytical solution technique i.e. the differential transformation method (DTM). Using the DTM, the non-linear constrained governing equations were reduced to recurrence relations and related initial conditions were transformed into a set of algebraic equations. The solutions were subsequently solved by a process of inverse transformation. The results were also compared with those derived from the homotopy perturbation method (HPM), closed-form solution, the established fourth order Runge–Kutta method and experimental data in order to verify the accuracy of the proposed method. It was found that this method can achieve more accurate results compared with the HPM. © 2012 Canadian Society for Chemical Engineering