Surface tension and buoyancy effects in cellular convection
- 1 July 1964
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 19 (3), 341-352
- https://doi.org/10.1017/s0022112064000763
Abstract
The cells observed by Bénard (1901) when a horizontal layer of fluid is heated from below were explained by Rayleigh (1916) in terms of buoyancy, and by Pearson (1958) in terms of surface tension. These rival theories are now combined. Linear perturbation techniques are used to derive a sixth-order differential equation subject to six boundary conditions. A Fourier series method has been used to obtain the eigenvalue equation for the case where the lower boundary surface is a rigid conductor and the upper free surface is subject to a general thermal condition. Numerical results are presented. It was found that the two agencies causing instability reinforce one another and are tightly coupled. Cells formed by surface tension are approximately the same size as those formed by buoyancy. Bénard's experiments are briefly discussed.Keywords
This publication has 9 references indexed in Scilit:
- On convection cells induced by surface tensionJournal of Fluid Mechanics, 1958
- Some Further Results on the Bénard ProblemPhysics of Fluids, 1958
- Surface Tension as the Cause of Bénard Cells and Surface Deformation in a Liquid FilmNature, 1956
- The stability of viscous fluid flow between rotating cylindersMathematical Proceedings of the Cambridge Philosophical Society, 1937
- The Stability of Viscous Fluid Flow under Pressure between Parallel PlanesMathematical Proceedings of the Cambridge Philosophical Society, 1936
- On the criterion for stability of a layer of viscous fluid heated from belowProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1929
- Some cases of instability in fluid motionProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1928
- LXXVI.The stability of a layer of fluid heated belowThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1926
- LIX. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under sideThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1916