Journal of Fluid Mechanics

Buckling instabilities in layers of viscous liquid subjected to shearing

T. Brooke  Benjamin a1 and T.  Mullin a1
a1 Mathematical Institute, 24/29 St Giles, Oxford OX1 3LB, UK

Article author query
benjamin tb   [Google Scholar] 
mullin t   [Google Scholar] 


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.

(Published Online April 21 2006)
(Received December 11 1987)