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Two-dimensional cusped interfaces

Published online by Cambridge University Press:  26 April 2006

Daniel D. Joseph ,
John Nelson ,
Michael Renardy  and
Yuriko Renardy
Daniel D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union Street SE, Minneapolis, MN 55455, USA
John Nelson
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union Street SE, Minneapolis, MN 55455, USA
Michael Renardy
Affiliation:
Department of Mathematics and ICAM, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA
Yuriko Renardy
Affiliation:
Department of Mathematics and ICAM, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA
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Abstract

Two-dimensional cusped interfaces are line singularities of curvature. We create such cusps by rotating a cylinder half immersed in liquid. A liquid film is dragged out of the reservoir on one side and is plunged in at the other, where it forms a cusp at finite speeds, if the conditions are right. Both Newtonian and non-Newtonian fluids form cusps, but the transition from a rounded interface to a cusp is gradual in Newtonian liquids and sudden in non-Newtonian liquids. We present an asymptotic analysis near the cusp tip for the case of zero surface tension, and we make some remarks about the effects of a small surface tension. We also present the results of numerical simulations showing the development of a cusp. In those simulations, the fluid is filling an initially rectangular domain with a free surface on top. The fluid enters from both sides and is sucked out through a hole in the bottom.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 383 - 409
Copyright
© 1991 Cambridge University Press

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