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Flow of viscoelastic jet with moderate inertia near channel exit

Published online by Cambridge University Press:  07 October 2009

AMIR SAFFARI  and
ROGER E. KHAYAT
AMIR SAFFARI
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, CanadaN6A 5B9
ROGER E. KHAYAT*
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, CanadaN6A 5B9
*
†Email address for correspondence: rkhayat@uwo.ca
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Abstract

The steady-state moderately inertial jet flow of a viscoelastic liquid of the Oldroyd-B type, emerging from a two-dimensional channel, is examined theoretically in this study. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow and stress fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface and the flow in the core region. The influence of elasticity on the shape of the free surface, the profiles of velocity and stress and the interplay between inertia and elasticity are explored. It is found that even for a jet with moderate inertia, elastic effects play a significant role, especially close to the channel exit near the free surface. It is also found that similar to the Newtonian case, the viscoelastic jet contracts downstream from the channel exit. However, in contrast to Newtonian jet, a viscoelastic jet is preceded by a flat region very close to the channel exit at which elastic and inertial effects are in balance. The extent of this region increases with elasticity. A momentum integral balance is applied to validate the theory and obtain the jet contraction ratio explicitly in terms of the Deborah number, viscosity ratio and Reynolds number.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 639 , 25 November 2009 , pp. 65 - 100
Copyright
Copyright © Cambridge University Press 2009

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References

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