Surface tension and energy conservation in a moving fluid

Bohr, Tomas; Scheichl, Bernhard

doi:10.1103/physrevfluids.6.l052001

Cited by 16 publications

(12 citation statements)

References 21 publications

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“…We observe that In a manner reminiscent of Dupré (1867, 1869), we can write where (kinematic boundary condition at the tip of the film) and . Additionally, following Bohr & Scheichl (2021) and Appendix B, the rate of change of surface energy is given by Using (8.8)–(8.9), and rearranging, we get which is the same as the inertial scaling derived using the force balance (insets of figures 6 a and 7 a ).…”

Section: Taylor–culick Retractions: An Energetics Perspectivementioning

confidence: 88%

“…Energy calculations This appendix explains the motivation and mathematical expressions used in the present study to describe different energy transfers, and their rates, as discussed in § 8. Similar approaches have been used in the literature to study the dynamics of two-phase flows (Bohr & Scheichl 2021; Sanjay, Lohse & Jalaal 2021). Here, we extend these formulations to three-phase flows. The kinetic energies and viscous dissipations associated with the three fluids are given by (Landau & Lifshitz 1987, pp.…”

Section: Figure 12mentioning

confidence: 98%

“…Culick (1960) realized that the correct energy balance entails that the rate of surface energy released should be distributed equally into an increase in kinetic energy of the rim and the viscous dissipation inside the film (A12). Figure 12( c , d ) illustrate the energy balance associated with the classical Taylor–Culick retractions (note that in figure 12 c and in figure 12 d ), where (see Appendix B and Bohr & Scheichl (2021)). Note that the rate of viscous dissipation at any given instant is analogous to the inelastic collision of a tiny fluid parcel in the film with the massive rim.…”

Section: Figure 12mentioning

confidence: 99%

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Taylor–Culick retractions and the influence of the surroundings

et al. 2022

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When a freely suspended liquid film ruptures, it retracts spontaneously under the action of surface tension. If the film is surrounded by air, the retraction velocity is known to approach the constant Taylor–Culick velocity. However, when surrounded by an external viscous medium, the dissipation within that medium dictates the magnitude of the retraction velocity. In the present work, we study the retraction of a liquid (water) film in a viscous oil ambient (two-phase Taylor–Culick retractions), and that sandwiched between air and a viscous oil (three-phase Taylor–Culick retractions). In the latter case, the experimentally measured retraction velocity is observed to have a weaker dependence on the viscosity of the oil phase as compared with the configuration where the water film is surrounded completely by oil. Numerical simulations indicate that this weaker dependence arises from the localization of viscous dissipation near the three-phase contact line. The speed of retraction only depends on the viscosity of the surrounding medium and not on that of the film. From the experiments and the numerical simulations, we reveal unprecedented regimes for the scaling of the Weber number ${We}_{f}$ of the film (based on its retraction velocity) or the capillary number ${Ca}_{s}$ of the surroundings versus the Ohnesorge number ${Oh}_{s}$ of the surroundings in the regime of large viscosity of the surroundings ( ${Oh}_{s} \gg 1$ ), namely ${We}_{f} \sim {Oh}_{s}^{-2}$ and ${Ca}_{s} \sim {Oh}_{s}^{0}$ for the two-phase Taylor–Culick configuration, and ${We}_{f} \sim {Oh}_{s}^{-1}$ and ${Ca}_{s} \sim {Oh}_{s}^{1/2}$ for the three-phase Taylor–Culick configuration.

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Section: Taylor–culick Retractions: An Energetics Perspectivementioning

confidence: 88%

Section: Figure 12mentioning

confidence: 98%

Section: Figure 12mentioning

confidence: 99%

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Taylor–Culick retractions and the influence of the surroundings

et al. 2022

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“…As we have seen, the rich physics characterizing circular hydraulic jumps has attracted researchers for centuries, and the degree to which surface tension controls these jumps remains an active research topic. Duchesne et al [120] and Bohr and Scheichl [121] consider a static control volume and argue that surface tension has a negligible influence as it is fully contained in the Laplace pressure, while Bhagat and Linden [122] come to a different conclusion by an energy-based analysis. Another aspect of hydraulic jumps concerns the influence of different surface coatings on the jump radius and shape, and Walker et al [123] showed that when a water jet impinges on a shear thinning liquid [see §IV A], the radius becomes time dependent.…”

Section: Hydraulic Jumps In the Kitchen Sinkmentioning

confidence: 99%

Culinary fluid mechanics and other currents in food science

Mathijssen¹,

Lisicki²,

Prakash³

et al. 2022

Preprint

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Innovations in fluid mechanics have refined food since ancient history, while creativity in cooking inspires science in return. Here, we review how recent advances in hydrodynamics are changing food science, and we highlight how the surprising phenomena that arise in the kitchen lead to discoveries and technologies across the disciplines, including rheology, soft matter, biophysics and molecular gastronomy. This review is structured like a menu, where each course highlights different aspects of culinary fluid mechanics. Our main themes include multiphase flows, complex fluids, thermal convection, hydrodynamic instabilities, viscous flows, granular matter, porous media, percolation, chaotic advection, interfacial phenomena, and turbulence. For every topic, we first provide an introduction accessible to food professionals and scientists in neighbouring fields. We then assess the state-of-the-art knowledge, the open problems, and likely directions for future research. New gastronomic ideas grow rapidly as the scientific recipes keep improving too.

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“…2018). The latter study was, later, shown to be formally flawed and misinterpreted results (Duchesne, Andersen & Bohr 2019; Bohr & Scheichl 2021; Duchesne & Limat 2022). The destabilisation of the circular to polygonal jump was examined by Bush, Aristoff & Hosoi (2006), Martens, Watanabe & Bohr (2012) and Teymourtash & Mokhlesi (2015).…”

Section: Introductionmentioning

confidence: 99%

The transient spread of a circular liquid jet and hydraulic jump formation

2022

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The transient flow of a circular liquid jet impinging on a horizontal disk, and the hydraulic jump formation, are examined theoretically and numerically. The interplay between inertia and gravity is particularly emphasised. The flow is governed by the thin-film equations, which are solved along with a force balance across the jump. The unsteadiness of the flow is caused by a linearly accelerating jet from an initial to a final steady state. To validate the predicted boundary-layer flow evolution, an analytical development is conducted for small distance from impingement, and for small time. In addition, the predictions of the film profile and jump location are compared against numerical simulation for the transient flow, and are further validated against experiment for steady flow. The evolutions of the film thickness and the wall shear stress in the developing boundary-layer region are found to be similar to those reported for a fluid lying on a stretching surface. The flow responds to the jet acceleration quasi-steadily near impingement but exhibits a long-term transient behaviour near the jump. Analysis of the jump evolution is considered in the range 5 < Fr < 40 for the Froude number (based on the jet radius and velocity). For Fr < 10, the jump reaches the final state instantly when the jet acceleration ceases. At higher Froude number, the jump settles at a later time, exhibiting an overshoot in the thickness due to the dominance of inertia.

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Surface tension and energy conservation in a moving fluid

Cited by 16 publications

References 21 publications

Taylor–Culick retractions and the influence of the surroundings

Taylor–Culick retractions and the influence of the surroundings

Culinary fluid mechanics and other currents in food science

The transient spread of a circular liquid jet and hydraulic jump formation

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