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Gravity-driven flow in a horizontal annulus

Published online by Cambridge University Press:  02 October 2017

Marcus C. Horsley Open the ORCID record for Marcus C. Horsley [Opens in a new window]  and
Andrew W. Woods Open the ORCID record for Andrew W. Woods [Opens in a new window]
Marcus C. Horsley
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
Andrew W. Woods*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

A theory for the low-Reynolds-number gravity-driven flow of two Newtonian fluids separated by a density interface in a two-dimensional annular geometry is developed. Solutions for the governing time-dependent equations of motion, in the limit that the radius of the inner and outer boundaries are similar, and in the case that the interface is initially inclined to the horizontal, are analysed numerically. We focus on the case in which the fluid is arranged symmetrically about a vertical line through the centre of the annulus. These solutions are successfully compared with asymptotic solutions in the limits that (i) a thin film of dense fluid drains down the outer boundary of the annulus, and (ii) a thin layer of less dense fluid is squeezed out of the narrow gap between the base of the inner annulus and dense fluid. Application of the results to the problem of mud displacement by cement in a horizontal well is briefly discussed.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 830 , 10 November 2017 , pp. 479 - 493
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Copyright
© 2017 Cambridge University Press 

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