Journal
JOURNAL OF FLUID MECHANICS
Volume 696, Issue -, Pages 175-214Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2012.26
Keywords
gravity currents; lubrication theory; multiphase flow
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Funding
- NSERC
- Schlumberger through CRD [354717-07]
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We study buoyant displacement flows with two miscible fluids of equal viscosity in the regime of low Atwood number and in ducts that are inclined close to horizontal. Using a combination of experimental, computational and analytical methods, we characterize the transitions in the flow regimes between inertial- and viscous-dominated regimes, and as the displacement flow rate is gradually increased. Three dimensionless groups largely describe these flows: densimetric Froude number Fr, Reynolds number Re and duct inclination beta. Our results show that the flow regimes collapse into regions in a two-dimensional (Fr, Re cos beta/Fr) plane. These regions are qualitatively similar between pipes and plane channels, although viscous effects are more extensive in pipes. In each regime, we are able to give a leading-order estimate for the velocity of the leading displacement front, which is effectively a measure of displacement efficiency.
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