Pattern Selection in Surface Tension Driven Flows
When a motionless liquid layer is heated from below, spontaneous convection appears when the vertical temperature gradient exceeds a critical value. Under slightly supercritical conditions, the liquid organizes into steady regular polygonal patterns, for example rolls or hexagons. If the liquid has an upper free surface open to ambient air, both buoyancy gradients and surface tension gradients may be responsible for these flows. The latter effect is dominating in thin layers and in a micro-gravity environment and in that case usually hexagonal patterns are observed. In this chapter, an introduction is provided into the physics of these flows by giving an (incomplete) overview of theoretical, experimental and numerical results which have been obtained over the last decades. Focus is on the existence of the critical temperature gradient and the selection of steady patterns near critical conditions.
KeywordsSurface Tension Bifurcation Diagram Pattern Selection Marangoni Number Amplitude Equation
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- Bénard, H.: Les tourbillons cellulaires dans une nappe liquide transportant de la chaleur en régime permanent, Ann. Chem. Phys., 23 (1901), 62–144.Google Scholar
- Koschmieder, E.L.: Bénard cells and Taylor Vortices, Cambridge University Press 1993.Google Scholar
- Thompson, J.J.: Phil. Mag., 10 (1855), 330.Google Scholar
- Cerisier, P., Perez-Garcia, C. and R. Occelli: Evolution of induced patterns in surface-tension-driven Bénard convection, Phys. Rev.E., 47 (1993), 3316–3325.Google Scholar
- Aris, R: Vectors, tensors, and the basic equations of fluid mechanics. Dover publications 1962.Google Scholar
- Drazin, P.G. and W.H. Reid: Hydrodynamic Stability, Cambridge University Press 1981.Google Scholar
- Joseph, D.D.: Stability of fluid motions, volumes I and II, Springer-Verlag 1976.Google Scholar
- Kuznetsov, Y.A.: Elements of applied bifurcation theory, Springer Verlag 1995.Google Scholar
- Nayfeh, A.H. and B. Balachandran: Applied nonlinear dynamics, John Wiley 1995.Google Scholar
- Dijkstra, H.A.: Surface tension driven cellular patterns in three-dimensional boxes Linear Stability, Microgravity Science and Technology, VII /4 (1995), 307–312.Google Scholar
- Dijkstra, H.A.: Surface tension driven cellular patterns in three-dimensional boxes The formation of hexagonal patterns, Microgravity Science and Technology, VIII/3, 155–162.Google Scholar
- Dijkstra, H.A.: Surface tension driven cellular patterns in three-dimensional boxes On the preference of hexagonal patterns, in preparation, (1998).Google Scholar