Indian J. Phys. 73B (2), 385-393 (1999)
U P B
— an international journal
Marangoni convection
Kausik S Das and J K Bhattacharjec
Department of Theoretical Physics, Indian Association for the Cultivation of Science,
Jadavpur, Calcutta-700 032, India
Abstract : Aspects of Marangoni convection induced by heating from below are reviewed.
The effect of rotation is discussed with the emphasis on the oscillatory modes of the system
which can be released in a Hopf bifurcation.
Keywords : Convection, rotation, Hopf bifurcation
PACS Nos. : 47 20 Dr, 47.20.ky
1. Introduction
After the rain water has evaporated from hot dusty road, what is left behind is an almost regular
patterns of hexagons traced out by the dust. This is a fairly common observation when the first
rains arrive in most of the tropical countries. The physical phenomenon underlying this
observation is convection [1,2]. Generally one associates convection with buoyancy - the hot
fluid below rises upwards and the cold fluid at the top tumbles down when a container of liquid
is heated from below. The motion takes place with periodicity in the horizontal plane in the
absence of any imperfections. If the fluid layer is very thin as happens when the rain starts
falling on the hot road surface, the driving force which causes convection is not buoyancy but
surface tension. The surface tension driven convection is called Marangoni convection. At
the free surface of the fluid, surface tension forces come into play and for a sufficiently thin
fluid layer, the surface forces can cause convective motion in the bulk. If one carries out this
experiment in a controlled environment, then a quantitative measure can be had of when the
convection begins. The temperature gradient in the fluid has to be large enough before a
convective motion can be sustained. For sufficiently small gradients, any attempted movement
will be damped out by viscosity and thermal conductivity. The gradient has to exceed a critical
value before convection begins. Assuming ideal conditions, the convective pattern will be
periodic in the horizontal plane. What would be the wavelength of the periodicity ? That too
can be answered from controlled experiments. In a laboratory one takes a fluid layer of height
'd' in a metallic container of lateral extension L and heats from the bottom plate. At the surface
of the fluid there is a liquid-air interface. In general L » rfand the system acts like an infinite
system, with wall effects completely absent. The heating of the bottom surface is controlled
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© 19991ACS