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Buoyant miscible displacement flows in rectangular channels

Published online by Cambridge University Press:  10 August 2017

S. M. Taghavi Open the ORCID record for S. M. Taghavi [Opens in a new window] ,
R. Mollaabbasi  and
Y. St-Hilaire
S. M. Taghavi*
Affiliation:
Department of Chemical Engineering, Université Laval, Québec, QC G1V 0A6, Canada
R. Mollaabbasi
Affiliation:
Department of Chemical Engineering, Université Laval, Québec, QC G1V 0A6, Canada
Y. St-Hilaire
Affiliation:
Department of Chemical Engineering, Université Laval, Québec, QC G1V 0A6, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Buoyant displacement flows of two miscible fluids in rectangular channels are studied, theoretically and experimentally. The scenario considered involves the displacement of a fluid by a slightly heavier one at nearly horizontal channel inclinations, where inertial effects are weak and laminar stratified flows may be expected. In the theoretical part, a lubrication approximation model is developed to simplify the displacement flow governing equations and furnish a semi-analytical solution for the heavy and light fluid flux functions. Three key dimensionless parameters govern the fluid flow motion, i.e. a buoyancy number, the viscosity ratio and the channel cross-section aspect ratio. When these parameters are specified, the reduced model can deliver the interface propagation in time, leading and trailing front heights, shapes and speeds, cross-sectional velocity fields, etc. In addition, the model can be exploited to provide various classifications such as single or multiple fronts as well as main displacement flow regimes at long times such as no sustained backflows, stationary interface flows and sustained backflows. Focusing on the variation of the buoyancy number, a large number of iso-viscous displacement experiments are performed in a square duct and the results are compared with those of the lubrication model. Qualitative displacement flow features observed in the theory and experiments are in good agreement, in particular, in terms of the main displacement flow regimes. The quantitative comparisons are also reasonable for small and moderate imposed displacement flow velocities. However, at large flow rates, a deviation of the experimental results from the model results is observed, which may be due to the presence of non-negligible inertial effects.

JFM classification

Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , pp. 676 - 713
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Copyright
© 2017 Cambridge University Press 

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