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

J. Wang and D.D. Joseph

Department of Aerospace Engineering and Mechanics
University of Minnesota Minneapolis, MN 55455

Abstract

Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids is investigated by direct numerical simulation. Previous works on this topic for Newtonian fluids show that the 2D 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 omega_s = omega_p - omega_f on migration and lift in plane Poiseuille flow of Newtonian fluids. They concluded that the discrepancy omega_s - omega_se, where omega_se 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 = CUGamma of aerodynamics and the proper analogs of U and Gamma in the present context are Us and omega_s - omega_se. 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 force 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 correlations relating Us and omega_s to prescribed parameters are obtained.

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