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Buckling instabilities in layers of viscous liquid subjected to shearing

Published online by Cambridge University Press:  21 April 2006

T. Brooke Benjamin  and
T. Mullin
T. Brooke Benjamin
Affiliation:
Mathematical Institute, 24/29 St Giles, Oxford OX1 3LB, UK
T. Mullin
Affiliation:
Mathematical Institute, 24/29 St Giles, Oxford OX1 3LB, UK
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Abstract

A theoretical and experimental investigation is reported dealing with the onset of buckling in a horizontal layer of highly viscous liquid. The layer floats on a heavier liquid with negligible viscosity, and at rest is stabilized by gravity and surface tension. When sheared at a sufficient rate, the flat configuration of the layer becomes unstable; and the aim of the investigation is to establish the relation between critical values of the shearing rate and values of the layer's thickness and other physical parameters.

A primitive theory based on membrane approximations is first reviewed and its deficiencies are appreciated. Then a more reliable theory is developed, providing estimates of values taken by a dimensionless shear stress f at the threshold of instability. The values fc are found to depend primarily on a dimensionless number H proportional to the thickness of the layer.

Experiments on sheared layers of silicone oil with various high viscosities are then described. Measured values of fc plotted against H over a wide range are shown to be in satisfactory agreement with the theory. Finally, discrepancies between previous experimental results and ours are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 195 , October 1988 , pp. 523 - 540
Copyright
© 1988 Cambridge University Press

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