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An experimental study of laminar displacement flows in narrow vertical eccentric annuli

Published online by Cambridge University Press:  13 April 2010

S. MALEKMOHAMMADI ,
M. CARRASCO-TEJA ,
S. STOREY ,
I. A. FRIGAARD  and
D. M. MARTINEZ
S. MALEKMOHAMMADI
Affiliation:
Department of Mechanical Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, BC, Canada, V6T 1Z4
M. CARRASCO-TEJA
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada, V6T 1Z2
S. STOREY
Affiliation:
Department of Mechanical Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, BC, Canada, V6T 1Z4
I. A. FRIGAARD*
Affiliation:
Department of Mechanical Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, BC, Canada, V6T 1Z4 Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada, V6T 1Z2
D. M. MARTINEZ
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, BC, Canada, V6T 1Z3
*
†Email address for correspondence: frigaard@math.ubc.ca
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Abstract

We present an experimental study of slow laminar miscible displacement flows in vertical narrow eccentric annuli. We demonstrate that for suitable choices of viscosity ratio, density ratio and flow rate, we are able to find steady travelling wave displacements along the length of the annulus, even when strongly eccentric. Small eccentricity, increased viscosity ratio, increased density ratio and slower flow rates all appear to favour a steady displacement for Newtonian fluids. Qualitatively similar effects are found for non-Newtonian fluids, although the role of flow rate is less clear. These results are largely in line with predictions of a Hele-Shaw style of displacement model (Bittleston et al., J. Engng Math., vol. 43, 2002, pp. 229–253). The experiments also reveal interesting phenomena caused largely by secondary flows and dispersion. In the steady displacements, eccentricity drives a strong azimuthal counter-current flow above/below the advancing interface. This advects displacing fluid to the wide side of the annulus, where it focuses in the form of an advancing spike. On the narrow side we have also observed a spike, but only in Newtonian fluid displacements. For unsteady displacements, the azimuthal currents diminish as the interface elongates. With a strong enough yield stress and with a large enough eccentricity, unyielded fluid remains behind on the narrow side of the annulus.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 649 , 25 April 2010 , pp. 371 - 398
Copyright
Copyright © Cambridge University Press 2010

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