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Personne# Pier Giuseppe Ledda

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Dynamique des fluides

La dynamique des fluides (hydrodynamique ou aérodynamique), est l'étude des mouvements des fluides, qu'ils soient liquides ou gazeux. Elle fait partie de la mécanique des fluides avec l'hydrostatiqu

Instabilité

État de déséquilibre dynamique ou thermique de l'atmosphère, qui détermine les mouvements verticaux ascendants.
-Larrouse
Physique
Électricité

- Instabilité électrotherm

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François Gallaire, Pier Giuseppe Ledda, Giuseppe Antonio Zampogna

A model to describe the transport across membranes of chemical species dissolved in an incompressible flow is developed via homogenization. The asymptotic matching between the microscopic and macroscopic solute concentration fields leads to a solute flux jump across the membrane, quantified through the solution of diffusion problems at the microscale. The predictive model, written in a closed form, covers a wide range of membrane behaviors, in the limit of negligible Reynolds and Peclet numbers inside the membrane. The closure problem at the microscale, found via homogenization, allows one to link the membrane microstructure to its effective macroscopic properties, such as solvent permeability and solute diffusivity. After a validation of the model through comparison with the corresponding full-scale solution, an immediate application is provided, where the membrane behavior is a priori predicted through an analysis of its microscopic properties. The introduced tools and considerations may find applications in the design of thin microstructured membranes. Published under an exclusive license by AIP Publishing.

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The prediction of trajectories of buoyancy-driven objects immersed in a viscous fluid is a key problem in fluid dynamics. Simple-shaped objects, such as disks, present a great variety of trajectories, ranging from zig-zag to tumbling and chaotic motions. Yet, similar studies are lacking when the object is permeable. We perform a linear stability analysis of the steady vertical path of a thin permeable disk, whose flow through the microstructure is modelled via a stress-jump model based on homogenization theory. The relative velocity of the flow associated with the vertical steady path presents a recirculation region detached from the body, which shrinks and eventually disappears as the disk becomes more permeable. In analogy with the solid disk, one non-oscillatory and several oscillatory modes are identified and found to destabilize the fluid-solid coupled system away from its straight trajectory. Permeability progressively filters out the wake dynamics in the instability of the steady vertical path. Modes dominated by wake oscillations are first stabilized, followed by those characterized by weaker, or absent, wake oscillations, in which the wake is typically a tilting induced by the disk inclined trajectory. For sufficiently large permeabilities, the disk first undergoes a non-oscillatory divergence instability, which is expected to lead to a steady oblique path with a constant disk inclination, in the nonlinear regime. A further permeability increase reduces the unstable range of all modes until quenching of all linear instabilities.

Multiscale phenomena are involved in countless problems in fluid mechanics. Coating flows are known to exhibit a broad variety of patterns, such as wine tears in a glass and dripping of fresh paint applied on a wall. Coating flows are typically modeled under the assumption that the thickness of the fluid layer is much smaller than the characteristic length of the free-surface deformations, i.e. 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 in the fluid dynamics community is the flow around and through porous objects. Dandelion seeds are transported by the wind thanks to a hairy structure, called pappus, known to present larger values of the aerodynamic drag and a more stable wake compared to an impervious disk in the same flow conditions.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. These rivulets result from a pure equilibrium between hydrostatic gravity and surface tension effects, 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. We numerically study the linear and non-linear response with respect to a harmonic forcing in the inlet flow rate, determining the diverse lenses' patterns emerging on a steady rivulet. 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 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.