A series exact solution for one-dimensional non-linear particle equation of motion

Considerable industrial interest has been shown in fluid/solid-particle system such as those for hydraulic transportation of particulate material in pipes. The current paper aims to present a strong analytical method for nonlinear particle equation of motion. A series-based method, so-called homotopy analysis method is used and the flexibility of the technique is shown. The proposed method is valid for both spherical and non-spherical particles. It is demonstrated that by using an appropriate initial guess and auxiliary parameter, homotopy analysis method is very accurate and reliable.