Truby, J.M. and Mueller, S.P. and Llewellin, E.W. and Mader, H.M. (2015) 'The rheology of three-phase suspensions at low bubble capillary number.', Proceedings of the Royal Society A : mathematical, physical and engineering sciences., 471 (2173). p. 20140557.
We develop a model for the rheology of a three-phase suspension of bubbles and particles in a Newtonian liquid undergoing steady flow. We adopt an ‘effective-medium’ approach in which the bubbly liquid is treated as a continuous medium which suspends the particles. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and particle suspension rheology, which are taken from the literature. The model is validated against new experimental data for three-phase suspensions of bubbles and spherical particles, collected in the low bubble capillary number regime. Good agreement is found across the experimental range of particle volume fraction (0≤ϕp≲0.5) and bubble volume fraction (0≤ϕb≲0.3). Consistent with model predictions, experimental results demonstrate that adding bubbles to a dilute particle suspension at low capillarity increases its viscosity, while adding bubbles to a concentrated particle suspension decreases its viscosity. The model accounts for particle anisometry and is easily extended to account for variable capillarity, but has not been experimentally validated for these cases.
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|Publisher Web site:||http://dx.doi.org/10.1098/rspa.2014.0557|
|Publisher statement:||© 2014 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.|
|Date accepted:||28 October 2014|
|Date deposited:||22 January 2015|
|Date of first online publication:||08 January 2015|
|Date first made open access:||No date available|
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