Surface waves along liquid cylinders. Part 1. Stabilising effect of gravity on the Plateau–Rayleigh instability

Pham, Chi-Tuong; Perrard, Stéphane; Doudic, Gabriel Le

doi:10.1017/jfm.2020.114

Cited by 7 publications

(35 citation statements)

References 37 publications

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“…In this section, we present an experimental characterisation of the waves propagating along cylindrical drops (namely, with translational invariance along one direction), when deposited upon superhydrophobic substrates. We will study the dispersive regime, while Pham et al (2020) only focused on the non-dispersive regime.…”

Section: Experimental Set-up and Resultsmentioning

confidence: 99%

“…On either of them, a controlled volume of distilled water is deposited and stretched from one end to the other end of the channel. If the deposited volume is sufficiently large, such long drops can be pinned at both ends of the channel without breaking up (see Pham et al 2020).…”

Section: Experimental Set-upmentioning

confidence: 99%

“…We propose an estimation of σ eff as a cross-sectional averaging of the hydrostatic pressure field, by taking into account the non-uniform profile of curvature of the interface along the transverse section of it, due to the presence of varicose modes. In short, we go one step further than the non-dispersive calculation of Pham et al (2020) and calculate the k 4 contribution in the framework of the Saint-Venant equations. Owing to the length of the derivations, their technical details are deferred to Appendix B, where we first analytically compute the curvature of the interface of the varicose modes using an adiabatic hypothesis on the sections.…”

Section: An Analytical Estimation Of σ Effmentioning

confidence: 99%

“…We then perform an estimation of the averaged pressure gradient that yields σ eff , through a toy model. This toy model is motivated by a few statements on how dispersive effects due to surface tension can be taken into account within the Saint-Venant formalism we used to study the non-dispersive regime of our sessile cylinders (Pham et al 2020). These statements are made in Appendix A.…”

Section: An Analytical Estimation Of σ Effmentioning

confidence: 99%

See 3 more Smart Citations

Surface waves along liquid cylinders. Part 2. Varicose, sinuous, sloshing and nonlinear waves

Doudic

Perrard²,

Pham³

2021

J. Fluid Mech.

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Section: Experimental Set-up and Resultsmentioning

confidence: 99%

Section: Experimental Set-upmentioning

confidence: 99%

Section: An Analytical Estimation Of σ Effmentioning

confidence: 99%

Section: An Analytical Estimation Of σ Effmentioning

confidence: 99%

See 2 more Smart Citations

Surface waves along liquid cylinders. Part 2. Varicose, sinuous, sloshing and nonlinear waves

Doudic

Perrard²,

Pham³

2021

J. Fluid Mech.

Self Cite

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show abstract

“…A cylindrical liquid bridge, for example, will be stable in the absence of gravity if its length L is less than the circumference 2πR (equivalently, if its slenderness S = L/(2R) < π). Gravity, which causes a vertical column to bulge near the bottom, affects these limits [155], as does contact with a solid support or substrate [62,121]. In fact, the growth of the instability may be arrested completely in the interior of a wetted cylindrical tube [37].…”

Section: Strategies For Controlmentioning

confidence: 99%

A review of fluid instabilities and control strategies with applications in microgravity

Porter

Sánchez

Shevtsova

et al. 2021

Math. Model. Nat. Phenom.

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We give a brief review of several prominent fluid instabilities representing transitions driven by gravity, surface tension, thermal energy, and applied motion/acceleration. Strategies for controlling these instabilities, including their pattern formation properties, are discussed. The importance of gravity for many common fluid instabilities is emphasized and used to understand the sometimes dramatically different behavior of fluids in microgravity environments. This is illustrated in greater detail, using recent results, for the case of the frozen wave instability, which leads to large columnar structures in the absence of gravity. The development of these highly nonlinear states is often complex, but can be manipulated through an appropriate choice of forcing amplitude, container length and height, initial inclination of the surface, and other parameters affecting the nonlinear and inhomogeneous growth process. The increased opportunity for controlling fluids and their instabilities via small forcing or parameter changes in microgravity is notable.

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Static and dynamic stability of pendant drops

Zhang

Zhou

2023

J. Fluid Mech.

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Despite the widespread occurrence of pendant drops in nature, there is still a lack of combined studies on their dynamic and static stability. This study focuses on the dynamic and static stability of elongated drops with either a free or pinned contact line on a plane. We first examine static stability for both axisymmetric and non-axisymmetric perturbations subject to volume or pressure constraints. The stability limits for volume and pressure disturbances (axisymmetric) correspond to the maximum volume and pressure of the drops, respectively. Drops with free contact lines are marginally stable to non-axisymmetric perturbations because of their horizontal translational invariance, whereas pinned drops are stable. The linear dynamic stability is then investigated numerically through a boundary element model, restricted to volume disturbances. Results show that when the stability limit is reached, the first zonal mode has a zero frequency, suggesting that the thresholds for static and dynamic stability are essentially equivalent. Furthermore, natural frequencies experience sharp changes as the stability limit is approached. Another zero frequency mode associated with the horizontal motion of the centre of mass is also revealed by the numerical results, reflecting the horizontal translational invariance of drops with free contact lines. Finally, the frequency spectrum modified by gravity is explored, resulting in the identification of five gravity-induced frequency shift patterns. The frequency shifts break the spectral degeneracy for hemispherical drops with free contact lines, leading to various spectral orderings according to polar and azimuthal wavenumbers.

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Surface waves along liquid cylinders. Part 1. Stabilising effect of gravity on the Plateau–Rayleigh instability

Cited by 7 publications

References 37 publications

Surface waves along liquid cylinders. Part 2. Varicose, sinuous, sloshing and nonlinear waves

Surface waves along liquid cylinders. Part 2. Varicose, sinuous, sloshing and nonlinear waves

A review of fluid instabilities and control strategies with applications in microgravity

Static and dynamic stability of pendant drops

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