title: The rheology of three-phase suspensions at low bubble capillary number.
abstract: 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 ([Formula: see text]) and bubble volume fraction ([Formula: see text]). 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.
authors.affiliation: Department of Earth Sciences , Durham University , Durham DH1 3LE, UK.
authors.forename: J M
authors.initials: JM
authors.lastname: Truby
authors.affiliation: Institute of Geosciences, Johannes Gutenberg University Mainz , 55099 Mainz, Germany.
authors.forename: S P
authors.initials: SP
authors.lastname: Mueller
authors.affiliation: Department of Earth Sciences , Durham University , Durham DH1 3LE, UK.
authors.forename: E W
authors.initials: EW
authors.lastname: Llewellin
authors.affiliation: School of Earth Sciences, University of Bristol , Bristol BS8 1RJ, UK.
authors.forename: H M
authors.initials: HM
authors.lastname: Mader
keywords: analogue experiments; bubble suspension; particle suspension; rheology; three phase