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Modelling of concentrated suspensions using a continuum constitutive equation

Published online by Cambridge University Press:  25 October 1998

SAMUEL R. SUBIA ,
MARC S. INGBER ,
LISA A. MONDY ,
STEVE A. ALTOBELLI  and
ALAN L. GRAHAM
SAMUEL R. SUBIA
Affiliation:
Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, USA Present address: Energetic and Multiphase Processes Department, Sandia National Laboratories, Albuquerque, NM 87185, USA.
MARC S. INGBER
Affiliation:
Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, USA
LISA A. MONDY
Affiliation:
Energetic and Multiphase Processes Department, Sandia National Laboratories, Albuquerque, NM 87185, USA
STEVE A. ALTOBELLI
Affiliation:
The Lovelace Institutes, 2345 Ridgecrest Drive SE, Albuquerque, NM 87108, USA Present address: New Mexico Resonance, 2425 Ridgecrest Drive SE, Albuquerque, NM 87108, USA.
ALAN L. GRAHAM
Affiliation:
Los Alamos National Laboratory, ESA-EPE, Los Alamos, NM 87545, USA
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Abstract

We simulate the behaviour of suspensions of large-particle, non-Brownian, neutrally-buoyant spheres in a Newtonian liquid with a Galerkin, finite element, Navier–Stokes solver into which is incorporated a continuum constitutive relationship described by Phillips et al. (1992). This constitutive description couples a Newtonian stress/shear-rate relationship (where the local viscosity of the suspension is dependent on the local volume fraction of solids) with a shear-induced migration model of the suspended particles. The two-dimensional and three-dimensional (axisymmetric) model is benchmarked with a variety of single-phase and two-phase analytic solutions and experimental results. We describe new experimental results using nuclear magnetic resonance imaging to determine non-invasively the evolution of the solids-concentration profiles of initially well-mixed suspensions as they separate when subjected to slow flow between counter-rotating eccentric cylinders and to piston-driven flow in a pipe. We show good qualitative and quantitative agreement of the numerical predictions and the experimental measurements. These flows result in complex final distributions of the solids, causing rheological behaviour that cannot be accurately described with typical single-phase constitutive equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 373 , 25 October 1998 , pp. 193 - 219
Copyright
© 1998 Cambridge University Press

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