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Miscible displacement flows in near-horizontal ducts at low Atwood number

Published online by Cambridge University Press:  27 February 2012

S. M. Taghavi ,
K. Alba ,
T. Seon ,
K. Wielage-Burchard ,
D. M. Martinez  and
I. A. Frigaard
S. M. Taghavi
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, British Columbia, V6T 1Z3, Canada
K. Alba
Affiliation:
Department of Mechanical Engineering, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, British Columbia, V6T 1Z4, Canada
T. Seon
Affiliation:
Université Pierre et Marie Curie, Institut d’Alembert, 4 place Jussieu, 75005 Paris, France
K. Wielage-Burchard
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, V6T 1Z2, Canada
D. M. Martinez
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, British Columbia, V6T 1Z3, Canada
I. A. Frigaard*
Affiliation:
Department of Mechanical Engineering, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, British Columbia, V6T 1Z4, Canada Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, V6T 1Z2, Canada
*
†Email address for correspondence: frigaard@math.ubc.ca
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Abstract

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 , Reynolds number and duct inclination . Our results show that the flow regimes collapse into regions in a two-dimensional 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.

JFM classification

Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Lubrication theory Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 696 , 10 April 2012 , pp. 175 - 214
Copyright
Copyright © Cambridge University Press 2012

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