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Nonlinear effects in the rheology of dilute suspensions

Published online by Cambridge University Press:  28 March 2006

J. D. Goddard  and
Chester Miller
J. D. Goddard
Affiliation:
Department of Chemical and Metallurgical Engineering, The University of Michigan
Chester Miller
Affiliation:
Department of Chemical and Metallurgical Engineering, The University of Michigan
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Abstract

An analysis is presented of the deformation of a solid-like, viscoelastic sphere suspended in the infinite Stokesian flow field of a Newtonian fluid undergoing an arbitrary time-dependent homogeneous deformation far from the particle. The results of the analysis are then used to deduce the macroscopic rheological behaviour of a dilute monodisperse suspension of slightly deformable spheres.

Even though inertial effects and second-order terms in the particle deformation are neglected, it is found that non-linear rheological effects can arise, because of the interaction between the deformed particle and the flow. As a consequence, the rheological relation obtained here differs from those presented earlier by Fröhlich & Sack (1946) and by Oldroyd (1955) through the appearance of certain terms which are non-linear in the deformation rate.

When the suspended particles are purely elastic in their behaviour the rheological equation presented here reduces for certain flows to a special case of Oldroyd's (1958) phenomenological model, with material constants which can be directly related to suspension properties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 4 , 22 June 1967 , pp. 657 - 673
Copyright
© 1967 Cambridge University Press

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