P. Cerisier, B. Billia, S. Rahal
Evolution and Stability Limits of Patterns in Surface-Tension-Driven-Bénard Convection
Experimental results on the evolution of patterns in surface-tension driven Be?nard
convection are reported. Experiments were performed in a hexagonal container with
an aspect ratio ? = 65 for different distances (?) to convection threshold and two
Prandtl numbers (Pr1 = 440 and Pr2 = 880). Regular hexagonal patterns are initially
imposed that are then allowed to relax. A stability diagram of the spatial modes, the
variation of the stable modes band and the selected mean wavenumber were
established as functions of ? and Pr. For the mean wavenumber, an increase followed
by a decrease, is observed for Pr1; and an opposite behavior is observed for Pr2. The
bandwidth of stable modes broadens with ?, the broadening being larger for Pr2 than
for Pr1. Using the phenomenological model of Swift-Hohenberg, developed for roll
patterns and adapted to hexagonal patterns, a potential function is defined, which
allows the study of the time evolution of such arrays. This function is minimized
during the transition of the structure from the initial to the steady (asymptotic) state.
The various wavenumber selection mechanisms are considered: bulk contribution
(wavenumber disparity, cell row bending), topological defects and sidewalls. The
total potential is mainly influenced by the wavenumber variation and by defects.
Owing to the special geometry of the container, sidewall and bulk effects related to
the local wave vector divergence (due to the disalignment and the bending of the cell
rows), play a less important role, at least in such medium size containers. From the
experiment, it follows that the model is valid up to an ? of about 9 for both Pr. Beyond
that limit, the potential fluctuates probably due to the spatiotemporal mobility of the
structure and the nucleation of defects, whose number increases with increasing ?.
Journal of Non-Equilibrium Thermodynamics, Walter de Gruyter
Print ISSN: 0340-0204
Volume: 26, 07/2001
Pages: 99 - 118
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