An Eulerian-Eulerian formulation of suspension rheology using the finite volume method

•An Euler-Euler two phase model for particles in a Newtonian liquid.•Mixture constitutive model of Morris and Boulay is reformulated by splitting the stress.•Successfully predicts correct particle volume fractions and velocity profiles of NMR experiments.•Discussion of anisotropic normal stress diff...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics 2017-07, Vol.245, p.38-48
Main Authors: Inkson, N.J., Papoulias, D., Tandon, M., Reddy, V., Lo, S.
Format: Article
Language:English
Subjects:
Bifurcations
Buoyancy
Computational fluid dynamics
Concentration (composition)
Continuity (mathematics)
Drag
Finite volume method
Fluid flow
Low Reynolds number
Mathematical models
Newtonian liquids
NMR
Non-Newtonian fluids
Nuclear magnetic resonance
Pipes
Rheological properties
Rheology
Shear flow
Stresses
Three dimensional flow
Two dimensional flow
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Summary:•An Euler-Euler two phase model for particles in a Newtonian liquid.•Mixture constitutive model of Morris and Boulay is reformulated by splitting the stress.•Successfully predicts correct particle volume fractions and velocity profiles of NMR experiments.•Discussion of anisotropic normal stress difference effects. We have adapted a well-known constitutive model formulated by Morris and Boulay (1999) that describes the stress tensor for a mixture of particles in a Newtonian liquid into a two-phase finite-volume solver. The two-phase model treats each phase with a separate continuity and momentum equation that splits the stress of the constitutive model between the two phases, with the particle pressure applied only to the particle phase in addition to source terms related to the drag of particles in the fluid. We compare the resulting model using a variety of NMR experiments, considering the flow of neutrally buoyant monodisperse particles at low Reynolds number in the following geometries: 2D simple shear flow in a Couette device, axisymmetric and 3D pressure driven flow down a pipe and in a 2D and 3D asymmetric channel bifurcation. We find excellent agreement with velocity and volume fraction profiles in all of the comparisons with experimental data without much further numerical fitting beyond the original suspension stress model.
ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2017.05.002