Analysis of nano droplet dynamics with various sphericities using efficient computational techniques

Motion of a vertically falling nano droplet in incompressible Newtonian media with initial velocity is investigated. The instantaneous velocity and acceleration are carried out by using the variational iteration method (VIM) and homotopy perturbation method (HPM), which are analytical solution techniques. The obtained results are compared with Runge–Kutta method in order to verify the accuracy of the proposed methods. The results show that, the analytical solutions are in good agreement with each other and with the numerical solution. Also, the effects of sphericity (φ) on the velocity and acceleration profiles of the nano droplet are explained. Moreover, the results demonstrate that the VIM-Padé and HPM-Padé are very effective in generating analytical solutions for even highly nonlinear problems.