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Lubrication in a corner

Published online by Cambridge University Press:  18 November 2005

ROMAN STOCKER and
A. E. HOSOI
ROMAN STOCKER
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA romans@mit.edu
A. E. HOSOI
Affiliation:
Department of Mechanical Engineering, Hatsopoulos Microfluids Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA peko@mit.edu
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Abstract

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A mathematical model for the evolution of a thin film in an interior corner region is presented. The model is based on the idea that the film can be considered thin everywhere in the $\eta$-direction if viewed in the new coordinate system $\xi\,{=}\,x^2\,{-}\,y^2$, $\eta\,{=}\,2xy$. Lubrication theory is applied to the governing equations written in this coordinate system. The exact integration of the mass conservation equation for a no-slip boundary condition yields a single evolution equation, which is integrated numerically. The evolution of a thin film driven by surface tension and gravity is predicted as a function of the Bond number and successfully compared to laboratory experiments.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 544 , 10 December 2005, pp. 353 - 377
Copyright
© 2005 Cambridge University Press