Velocity analysis of a single vertically falling non-spherical particle in Newtonian and non-Newtonian fluids

Abstract

An analytical investigation is applied for the velocity of a vertically falling non-spherical particle in Newtonian and non-Newtonian fluid. The velocity of vertically falling non-spherical particle can be described by the force balance equation (Basset-Boussinesq-Ossen equation). Variational Iterations Method (VIM) and Runge-Kutta 4th order method are used to solve the existing problem. The results were compared those obtained from VIM by R-K 4th order method. We obtained that VIM which was used to solve such non-linear differential equation with fractional power is simpler and more accurate than other methods. Analytical results indicate that the velocity in a falling procedure is significantly increased and more in Newtonian fluid. Also particle’s velocity in Newtonian fluid reaches early at terminal velocity as compare to non-Newtonian fluid. To obtain the results for all different methods, the symbolic calculus software MATLAB is used.