Hydrodynamic-driven morphogenesis of karst draperies: spatio-temporal analysis of the two-dimensional impulse response

“…In addition to its scientific interest, this situation is of practical importance in liquid coating, film cooling and some geophysical processes (see e.g. Whitehead 1988;Lister & Kerr 1989;Fermigier et al 1992;Bertagni & Camporeale 2017;Ledda et al 2020Ledda et al , 2021Lerisson et al 2020).…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, it is well-known that the Rayleigh-Taylor instability acts on the film not only in the vertical direction, but also in the spanwise direction, leading to the formation of rivulets from which, in appropriate conditions, droplets can detach. This aspect has been studied both experimentally and theoretically in several papers (Indeikina et al 1997;Lin, Kondic & Filippov 2012;Rietz et al 2017;Charogiannis et al 2018;Ledda et al 2020Ledda et al , 2021Lerisson et al 2020). However, the fact that many of the theoretical studies mentioned before deal with the two-dimensional problem (e.g.…”

Section: Introductionmentioning

confidence: 99%

Dripping instability of a two-dimensional liquid film under an inclined plate

Zhou

Prosperetti

2021

J. Fluid Mech.

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It is known that the dripping of a liquid film on the underside of a plate can be suppressed by tilting the plate so as to cause a sufficiently strong flow. This paper uses two-dimensional numerical simulations in a closed-flow framework to study several aspects of this phenomenon. It is shown that, in quasi-equilibrium conditions, the onset of dripping is closely associated with the curvature of the wave crests approaching a well-defined maximum value. When dynamic effects become significant, this connection between curvature and dripping weakens, although the critical curvature remains a useful reference point as it is intimately related to the short length scales promoted by the Rayleigh–Taylor instability. In the absence of flow, when the film is on the underside of a horizontal plate, the concept of a limit curvature is relevant only for small liquid volumes close to a critical value. Otherwise, the drops that form have a smaller curvature and a large volume. The paper also illustrates the peculiarly strong dependence of the dripping transition on the initial conditions of the simulations. This feature prevents the development of phase maps dependent only on the governing parameters (Reynolds number, Bond number, etc.) similar to those available for film flow on the upper side of an inclined plate.

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“…2005; Camporeale & Ridolfi 2012) and flutings in limestone caves (Camporeale 2015; Bertagni & Camporeale 2017; Ledda et al. 2021) and due to solidification and melting of water (Camporeale 2015), while physical or chemical erosion leads to scallops (Meakin & Jamtveit 2010) or linear karren (Bertagni & Camporeale 2021) patterns. Gravity currents, widely encountered in environmental fluid dynamics, are flows driven by gravity differences typically imputed to the presence of one phase heavier than the other which spreads on a substrate.…”

Section: Introductionmentioning

confidence: 99%

Gravity-driven coatings on curved substrates: a differential geometry approach

et al. 2022

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Drainage and spreading processes in thin liquid films have received considerable attention in the past decades. Yet, our understanding of three-dimensional cases remains sparse, with only a few studies focusing on flat and axisymmetric substrates. Here, we exploit differential geometry to understand the drainage and spreading of thin films on curved substrates, under the assumption of negligible surface tension and hydrostatic gravity effects. We develop a solution for the drainage on a local maximum of a generic substrate. We then investigate the role of geometry in defining the spatial thickness distribution via an asymptotic expansion in the vicinity of the maximum. Spheroids with a much larger (respectively smaller) height than the equatorial radius are characterized by an increasing (respectively decreasing) coating thickness when moving away from the pole. These thickness variations result from a competition between the variations of the substrate's slope and mean curvature. The coating of a torus presents larger thicknesses and a faster spreading on the inner region than on the outer region, owing to the different curvatures in these two regions. In the case of an ellipsoid with three different axes, spatial modulations in the drainage solution are observed as a consequence of a faster drainage along the short principal axis, faithfully reproduced by a three-dimensional asymptotic solution. Leveraging the conservation of mass, an analytical solution for the average spreading front is obtained. The solutions are in agreement with numerical simulations and experimental measurements obtained from the coating of a curing polymer on diverse substrates.

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Hydrodynamic-driven morphogenesis of karst draperies: spatio-temporal analysis of the two-dimensional impulse response

Abstract: Abstract

Cited by 9 publications

References 51 publications

Hydrodynamic-driven morphogenesis of karst draperies: spatio-temporal analysis of the two-dimensional impulse response – CORRIGENDUM

Hydrodynamic-driven morphogenesis of karst draperies: spatio-temporal analysis of the two-dimensional impulse response – CORRIGENDUM

Dripping instability of a two-dimensional liquid film under an inclined plate

Gravity-driven coatings on curved substrates: a differential geometry approach

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