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Truby JM, Mueller SP, Llewellin EW, et al. The rheology of three-phase suspensions at low bubble capillary number. Proc Math Phys Eng Sci. 2015;471(2173):20140557doi: 10.1098/rspa.2014.0557.
Truby, J. M., Mueller, S. P., Llewellin, E. W., & Mader, H. M. (2015). The rheology of three-phase suspensions at low bubble capillary number. Proceedings. Mathematical, physical, and engineering sciences, 471(2173), 20140557. https://doi.org/10.1098/rspa.2014.0557
Truby, J M, et al. "The rheology of three-phase suspensions at low bubble capillary number." Proceedings. Mathematical, physical, and engineering sciences vol. 471,2173 (2015): 20140557. doi: https://doi.org/10.1098/rspa.2014.0557
Truby JM, Mueller SP, Llewellin EW, Mader HM. The rheology of three-phase suspensions at low bubble capillary number. Proc Math Phys Eng Sci. 2015 Jan 08;471(2173):20140557. doi: 10.1098/rspa.2014.0557. PMID: 25568617; PMCID: PMC4277193.
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Proc Math Phys Eng Sci. 2015 Jan 08;471(2173):20140557. doi: 10.1098/rspa.2014.0557.

The rheology of three-phase suspensions at low bubble capillary number.

Proceedings. Mathematical, physical, and engineering sciences

J M Truby, S P Mueller, E W Llewellin, H M Mader

Affiliations

  1. Department of Earth Sciences , Durham University , Durham DH1 3LE, UK.
  2. Institute of Geosciences, Johannes Gutenberg University Mainz , 55099 Mainz, Germany.
  3. School of Earth Sciences, University of Bristol , Bristol BS8 1RJ, UK.

PMID: 25568617 PMCID: PMC4277193 DOI: 10.1098/rspa.2014.0557

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.

Keywords: analogue experiments; bubble suspension; particle suspension; rheology; three phase

References

  1. Science. 2004 Feb 13;303(5660):990-3 - PubMed
  2. J Geophys Res. 2008 Jan 1;113:null - PubMed
  3. Phys Rev Lett. 2013 Sep 6;111(10):108301 - PubMed

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