Speaker: Dr. François Gallaire (EPFL, Lausanne, Switzerland)
Title: Dripping down the rivulet
Date: Friday November 15th, 2019
Time: 10:40 a.m.
Place: Mithat Çoruh Amphitheater
Abstract: We consider the Rayleigh-Taylor instability of a thin film coating the underside of a curved or inclined surface. We first focus on the effect of curvature and investigate the Rayleigh-Taylor instability of a thin liquid film coated on the inside of a cylinder whose axis is orthogonal to gravity. We are interested in the effects of geometry on the instability, and contrast our results with the classical case of a thin film coated under a flat substrate. In our problem, gravity is the destabilizing force at the origin of the instability, but also yields the progressive drainage and stretching of the coating along the cylinder’s wall. We find that this flow stabilizes the film, which is asymptotically stable to infinitesimal perturbations. However, the short-time algebraic growth that these perturbations can achieve promotes the formation of different patterns, whose nature depends on the Bond number that prescribes the relative magnitude of gravity and capillary forces. Our experiments indicate that a transverse instability arises and persists over time for moderate Bond numbers. The liquid accumulates in equally spaced rivulets whose dominant wavelength corresponds to the most amplified mode of the classical Rayleigh-Taylor instability.
We then focus on the pattern formation in thin liquid flowing down along the underside an inclined plate. Rivulets parallel to the flow direction are the naturally selected patterns in this geometry too, and we demonstrate that this results from the effect of nonlinearity. Depending on the inclination, a secondary instability sets in which breaks the rivulet in a collection of drops draining or dripping down.
Bio: Born in 1975, François Gallaire obtains in 1998 the engineering degree from Ecole Polytechnique in Paris and in 1999, a master in Liquids Physics at Université Pierre et Marie Curie, still in Paris. He then joins the Laboratoire d’hydrodynamique (LadHyX) at Ecole Polytechnique where he defends a PhD thesis in 2002 on swirling flow instabilities and vortex breakdown under the supervision of Jean-Marrc Chomaz. He is then appointed as CNRS research associate at the Laboratoire J.A. Dieudonné in Université de Nice Sophia-Antipolis where he works for 6 years at the intersection of mathematics and fluid dynamics. In 2009, he joins EPFL to found the Fluid Mechanics and instabilities lab (LFMI), first as assistant professor. Since 2016, he is associate professor and director of the mechanical engineering teaching department since 2018. In 2019 he becomes fellow the American Physical Society in the Division of Fluid dynamics.
His research interests span from hydrodynamic instabilities and flow control to flow of drops and bubbles in microfluidics with recent focus on free surface waves and instabilities. His mission is to provide fundamental contributions to hydrodynamic instability, balanced on the tripod of theory, numerics and experiments, with an emphasis on predictive theoretical understanding of vortex dynamics, droplets, coating flows, and theoretical microfluidics.