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Ouvrir l'actualité 17/11/2017 - Nouar Chérif - Univ. Lorraine
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Titre de l'actualité 21/06/2013 : Pattern formation due to the Bénard-Marangoni instability in drying liquid films

21 juin 2013 - 11h salle 259

PIERRE COLINET (Université Libre de Bruxelles)

Pattern formation due to the Bénard-Marangoni instability in drying liquid films

 The spontaneous Bénard-Marangoni (BM) patterns induced by evaporation of a pure liquid layer are studied experimentally and theoretically. A thin volatile liquid layer placed in a cylindrical container is left free to evaporate into air at rest under ambient conditions. The time evolution of the temperature field in the layer, representative of the pattern organization resulting from the BM instability, is visualized using either an infrared (IR) camera, or a Schlieren optical set-up. Due to evaporation, the liquid layer thickness monotonically decreases, at a rate which can be tuned by controlling the global evaporation rate. This continuous quench of the system forces a rapid growth of the number of convection cells, hence leading to an increase of the average pattern wavenumber with time. Surprisingly, both the dimensionless wavenumber and the concentration of defects (mostly chains of pentagons-heptagons) at a given supercriticality do not depend on the speed of change in the pattern. Even though this might seem natural for sufficiently small quenching speed (quasi-static, or adiabatic regime), it is not really clear why this is still the case at the moderate speeds studied here. Moreover, it is shown that the wavenumber adjustment can proceed in two ways: splitting (or nucleation) of new cells, and drift of coherent “islands” of cells from the periphery, resulting in a compression of the pattern. While drift/compression seems to dominate at low quenching speeds, splitting/nucleation is the main mechanism at faster evaporation rates. In addition, inspection of the cells topological arrangements shows that nucleation (and collapse of cells, though it plays a minor role in the pattern genesis) appears more likely at the defects positions (more precisely, the cells splitting most often are heptagons) than in areas consisting of islands of quasi-perfect hexagonal cells. Yet, the proportion of these defects (e.g. number of pentagons and of heptagons divided by the total number of cells) seems independent of the mechanism, splitting or drift, allowing the wavenumber adjustment. On the theoretical point of view, it is first shown that a simple model allows predicting the critical film thickness below which convection patterns disappear (i.e. the BM instability threshold). In addition, ramped long-wave models of convection are numerically investigated in order to gain deeper insight into the dynamics of wavenumber adjustment. Although studied here for Bénard convection, it is believed that these mechanisms of cellular pattern genesis should be generic for many physical systems where the preferred wavenumber is continuously varied by some external constraint.

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