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Publication# From coating flow patterns to porous body wake dynamics via multiscale models

Abstract

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.

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Related concepts (5)

Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

Instability

In dynamical systems instability means that some of the outputs or internal states increase with time, without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior. In structural engineering, a structural beam or column can become unstable when excessive compressive load is applied. Beyond a certain threshold, structural deflections magnify stresses, which in turn increases deflections. This can take the form of buckling or crippling.

Direct numerical simulation

A direct numerical simulation (DNS) is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales (Kolmogorov microscales), up to the integral scale , associated with the motions containing most of the kinetic energy.