On unsteady rolling motion of spheres in inclined tubes filled with incompressible Newtonian fluids

The characterization of the motion of immersed bodies in fluids is existent in several manufacturing operations. In the current study, the unsteady motion of a spherical particle rolling down an inclined tube submerged in an incompressible Newtonian environment has been studied using experimental data of Chhabra et al., for a wide range of Reynolds numbers. An analytical expression for instantaneous particle velocity was gained using a non-perturbation series based technique so-called homotopy perturbation method first proposed by J.H. He. Therefore, acceleration and position of the particle are derived simply. Equation of motion was solved generally and for some realistic combinations of solid–liquid. The rolling behavior of the particle was studied clearly with the analytical method and had shown for different physical conditions. The effects of particle diameter (size), continues phase viscosity and inclination angle was studied. As an important result it was found that the inclination angle does not affect the acceleration duration. Present research shows the capability and effectiveness of HPM and exhibits a new application of this method for non-linear problems. Moreover, the limited studies for particles motion in contact with a solid boundary are extended.