Where and when

Speaker: Pier giuseppe Ledda, Università di Cagliari

Abstract: Multiscale phenomena are involved in countless problems in fluid mechanics. Coating flows, known to exhibit a broad variety of patterns, such as wine tears in a glass, are typically modeled assuming that there is a separation of scales between the microscopic variations of the velocity and pressure field along the thin layer and the macroscopic modulations of the free-surface. A different multiscale phenomenon of undeniable interest is the flow around and through porous objects, such as the transport of dandelion seeds thanks to a hairy parachute-like structure, called pappus. This thesis investigates the pattern formation of several coating flows and the wake dynamics past diverse permeable bodies via multiscale models. We initially consider the flow of a thin viscous film underneath an inclined planar substrate. We show the emergence of free- surface structures modulated along the direction transversal to the main flow, called rivulets, which result from a pure equilibrium between hydrostatic gravity and surface tension and may destabilize with the formation of traveling drops. We determine via a linear stability analysis the critical values of the inclination angle and film thickness beyond which rivulets destabilize. The dripping problem is deepened by considering a single drop deposited on a very thin film. Very slight inclinations with respect to the horizontal, of the order of degrees, lead to the formation of a rivulet in the wake of a shrinking drop. Subsequently, we investigate the role of these instabilities in karst draperies formation, by coupling the hydrodynamic model with the deposition of calcium carbonate on the substrate. We implement an algorithm which retrieves the asymptotic properties of the two-dimensional linear impulse response from numerical simulations. The analysis shows the predominance of streamwise structures, reminiscent of draperies, growing on the substrate. The role of modifications of the substrate is then investigated in the cases of dewetting of very thin polymer films, in the context of production of optical metasurfaces, and in the case of three-dimensional spreading of a mass of fluid. The last part of the thesis is devoted to the modifications of wake flows instabilities past bluff bodies when composed of a permeable microstructure, with a focus on the case of a porous iiiAbstract sphere and a cylindrical circular membrane. We develop an inverse procedure to optimize and retrieve the microstructure based on flow objectives. The analysis is concluded by studying the path instability of a freely-falling permeable disk. A complex series of bifurcations occurs but, as the ratio between voids and solid structure increases, all wake and path instabilities are damped.

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