Unsteady sedimentation analysis of spherical particles in Newtonian fluid media using analytical methods

Unsteady settling behavior of solid spherical particles falling in water as a Newtonian fluid is investigated using a drag coefficient of the form given by Ferreira et al. Differential transformation method (DTM), Galerkin method (GM), collocation method (CM), and numerical methods are applied to analyze the characteristics of particles motion. The influence of physical parameters on terminal velocity is discussed and moreover, comparing the techniques, it is showed that GM and CM are very efficient for solving the governing equation and DTM with Padé approximation has the best agreement with numerical results. The novelty of this work is introducing three simple and exact analytical method for solving the nonlinear equation of sedimentation and applied it in many industrial and chemical applications.