An analytical study on unsteady motion of vertically falling spherical particles in quiescent power-law shear-thinning fluids

Unsteady motion of a rigid spherical particle in a quiescent shear-thinning power-law fluid was investigated analytically. The accurate series solution was found by coupling the homotopy-perturbation method (HPM) and the variational iteration method (VIM). The results were compared with those obtained from VIM and the established finite difference scheme. It was shown that both methods (VIM and HPM-VIM) gave accurate results; however, the amount of calculations required for HPM-VIM was significantly reduced. In addition to improved efficiency, it was revealed that HPM-VIM leads to completely reliable and precise results. The terminal settling velocity-that is the velocity at which the net forces on a falling particle eliminate-for three different spherical particles (made of plastic, glass and steel) and three flow behavior index n, in two sets of power-law non-Newtonian fluids was investigated, based on the series solution. Analytical results obtained indicated that the time of reaching the terminal velocity in a falling procedure is significantly declined with growing the particle size. Further, with approaching flow behavior to Newtonian behavior from shear-thinning properties of flow (n -> 1), the transient time to achieving the terminal settling velocity is decreased. (C) 2013 Elsevier B.V. All rights reserved.