an:03911951
Zbl 0571.76036
Cloot, A.; Lebon, G.
A nonlinear stability analysis of the B??nard-Marangoni problem
EN
J. Fluid Mech. 145, 447-469 (1984).
00149751
1984
j
76E15 76E30
thermocapillary; instability; B??nard-Marangoni convection; horizontal fluid layer of infinite extent; Gorkov-Malkus-Veronis technique; buoyancy; temperature-dependent surface-tension effects; band of allowed steady states; onset of convection; Marangoni number; wave number; hexagons; flow patterns
The authors give a nonlinear analysis of B??nard-Marangoni convection in a horizontal fluid layer of infinite extent. The resulting equations are solved by using the Gorkov-Malkus-Veronis technique, which consists of developing the steady solution in terms of a small parameter measuring the deviation from the marginal state. The present work constitutes a generalization of an earlier work of \textit{A. Schl??ter}, \textit{D. Lortz} and \textit{F. Busse} [ibid. 23, 129-144 (1965; Zbl 0134.218)] where only buoyancy-driven instabilities were treated. Here, however, both buoyancy and temperature-dependent surface-tension effects are considered. The authors determine the band of allowed steady states of convection near the onset of convection as a function of the Marangoni number and the wave number, and they display supercritical as well as subcritical zones of instability. As a result, it is found that hexagons are allowable flow patterns.
J.Burbea
Zbl 0134.218