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Simple shear flow round a rigid sphere: inertial effects and suspension rheology

Published online by Cambridge University Press:  29 March 2006

Chen-Jung Lin ,
James H. Peery  and
W. R. Schowalter
Chen-Jung Lin
Affiliation:
Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08540 Present address: Esso Production Research Company, Houston, Texas.
James H. Peery
Affiliation:
Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08540 Present address: Humble Oil & Refining Company, Houston, Texas.
W. R. Schowalter
Affiliation:
Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08540
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Abstract

An analysis is presented of the flow field near a neutrally-buoyant rigid spherical particle immersed in an in compressible Newtonian fluid which, at large distances from the particle, is undergoing simple shear flow. Subject to conditions of continuity of stress at the particle surface and to conditions of zero net torque and zero net force on the sphere, the effect of fluid inertia on the velocity and pressure fields in the vicinity of the particle has been computed to $O(R^{\frac{3}{2}})$, where R = a2G/ν is a shear Reynolds number, a being the sphere radius, G the velocity gradient in the free stream (taken to be a positive number), and ν the kinematic viscosity.

Some streamlines have been computed and plotted. These illustrate how the fore–aft symmetry of the creeping-motion solution is destroyed when one includes inertial effects.

Knowledge of the velocity and pressure fields enables one to compute the effect of inertial forces in suspension rheology. The results include a correction to the Einstein viscosity law to $O(R^{\frac{3}{2}})$ for a dilute (non-interacting) suspension of spheres. In addition it is found that inertial effects give rise to a non-isotropic normal stress.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 44 , Issue 1 , 21 October 1970 , pp. 1 - 17
Copyright
© 1970 Cambridge University Press

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