NDLI: On rimming flows with shocks

Content Provider	Springer Nature Link
Author	Benilov, E. S. Lapin, V. N. O’Brien, S. B. G.
Copyright Year	2011
Abstract	We examine rimming flows, i.e. flows of a liquid film on the inside of a horizontal rotating cylinder. So far this problem has mostly been explored using the so-called lubrication approximation (LA). It was shown that, if the volume of the liquid in the cylinder exceeds a certain threshold, then a shock similar to a tidal bore appears in the lower half of the cylinder on its rising side. The position of the shock can be characterized by the polar angle θ s, with a value between θ s = −90° (the bottom of the cylinder) and θ s = 0° (the horizontal direction). In this study, we examine rimming flows without the LA, by solving numerically the exact Stokes equations. It is shown that a steady solution describing a (smoothed) shock exists only if $${-60^{\circ}\lesssim\theta_{\rm s} <0 ^{\circ}}$$ . Shocks with lower locations overturn, so no steady solution exists. It is also shown that smoothed-shock solutions have an oscillating structure upstream from the shock. If, however, capillary effects are taken into account, the range of θ s where solutions overturn contracts, and if surface tension is sufficiently strong, solutions exist for all values of θ s.
Starting Page	49
Ending Page	62
Page Count	14
File Format	PDF
ISSN	00220833
Journal	Journal of Engineering Mathematics
Volume Number	75
Issue Number	1
e-ISSN	15732703
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-11-22
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Liquid films Rimming flows Wave overturning Numeric Computing Mathematical Modeling and Industrial Mathematics Analysis Applications of Mathematics Mechanics
Content Type	Text
Resource Type	Article
Subject	Mathematics Engineering

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