Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids

Abstract

Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids are investigated by direct numerical simulation. Previous works on this topic for Newtonian fluids show that the two-dimensional channel can be divided into alternating regions defined by the stability of the particle’s equilibrium. We observe stability regions with the same pattern in flows of shear thinning fluids and study the effects of shear thinning properties on the distribution of the stability regions. Joseph and Ocando [J. Fluid Mech. 454, 263 (2002)] analyzed the role of the slip velocity Us=Uf−Up and the angular slip velocity Ωs=Ωp−Ωf on migration and lift in plane Poiseuille flow of Newtonian fluids. They concluded that the discrepancy Ωs−Ωse, where Ωse is the angular slip velocity at equilibrium, changes sign across the equilibrium position. In this paper we verify that this conclusion holds in shear thinning fluids. Correlations for lift forces may be constructed by analogy with the classical lift formula L=CUΓ of aerodynamics and the proper analogs of U and Γ in the present context are Us and Ωs−Ωse. Using dimensionless parameters, the correlation is a power law near the wall and a linear relation (which can be taken as a power law with the power of one) near the centerline. The correlations are compared to analytical expressions for lift forces in the literature and we believe that the correlations capture the essence of the mechanism of the lift force. Our correlations for lift forces can be made completely explicit provided that the correlations relating Us and Ωs to prescribed parameters are obtained.