Role of edge effects and fluid depth in azimuthal Faraday waves

Wilson, P.R.; Shao, Xingchen; Saylor, J. R.; Bostwick, Joshua

doi:10.1103/physrevfluids.7.014803

Cited by 5 publications

(9 citation statements)

References 63 publications

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“…These have been reviewed extensively by Batson et al [ 4 ] and compared with previous studies [ 17 – 19 ]. A recent article by Wilson et al very nicely and interestingly shows that the addition of a suitable surfactant such as Tritton in the aqueous solution has the effect of reducing side wall non-ideality [ 20 ]. As we exit this section, we comment on the effect of gravity on the response to Faraday forcing.…”

Section: Mechanical Faraday Instabilitymentioning

confidence: 99%

Pattern formation in Faraday instability—experimental validation of theoretical models

Dinesh

Livesay

Ignatius

et al. 2023

Phil. Trans. R. Soc. A.

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Two types of resonance-derived interfacial instability are reviewed with a focus on recent work detailing the effect of side walls on interfacial mode discretization. The first type of resonance is the mechanical Faraday instability, and the second is electrostatic Faraday instability. Both types of resonance are discussed for the case of single-frequency forcing. In the case of mechanical Faraday instability, inviscid theory can forecast the modal forms that one might expect when viscosity is taken into account. Experiments show very favourable validation with theory for both modal forms and onset conditions. Lowering of gravity is predicted to shift smaller wavelengths or choppier modes to lower frequencies. This is also validated by experiments. Electrostatic resonant instability is shown to lead to a pillaring mode that occurs at low wavenumbers, which is akin to Rayleigh Taylor instability. As in the case of mechanical resonance, experiments show favourable validation with theoretical predictions of patterns. A stark difference between the two forms of resonance is the observation of a gradual rise in the negative detuning instability in the case of mechanical Faraday and a very sharp one in the case of electrostatic resonance. This article is part of the theme issue ‘New trends in pattern formation and nonlinear dynamics of extended systems’.

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Section: Mechanical Faraday Instabilitymentioning

confidence: 99%

Pattern formation in Faraday instability—experimental validation of theoretical models

Dinesh

Livesay

Ignatius

et al. 2023

Phil. Trans. R. Soc. A.

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“…2021 a , b ; Wilson et al. 2022), the most common experimental condition is that of a moving contact line (Benjamin & Ursell 1954; Henderson & Miles 1990; Batson, Zoueshtiagh & Narayanan 2013; Li et al. 2015, 2016, 2019; Ward, Zoueshtiagh & Narayanan 2019; Wilson et al.…”

Section: Horizontally Infinite Hele-shaw Cellsmentioning

confidence: 99%

“…2015, 2016, 2019; Ward, Zoueshtiagh & Narayanan 2019; Wilson et al. 2022), which is not compatible with the no-slip condition satisfied by . One natural option would be to relax this no-slip condition by introducing a small slip region in the vicinity of the contact line, within which the flow quickly adapts from a no-slip to a slip condition (Miles 1990; Ting & Perlin 1995).…”

Section: Horizontally Infinite Hele-shaw Cellsmentioning

confidence: 99%

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A revised gap-averaged Floquet analysis of Faraday waves in Hele-Shaw cells

Bongarzone,

Jouron,

Viola

et al. 2023

J. Fluid Mech.

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Existing theoretical analyses of Faraday waves in Hele-Shaw cells rely on the Darcy approximation and assume a parabolic flow profile in the narrow direction. However, Darcy's model is known to be inaccurate when convective or unsteady inertial effects are important. In this work, we propose a gap-averaged Floquet theory accounting for inertial effects induced by the unsteady terms in the Navier–Stokes equations, a scenario that corresponds to a pulsatile flow where the fluid motion reduces to a two-dimensional oscillating Poiseuille flow, similarly to the Womersley flow in arteries. When gap-averaging the linearised Navier–Stokes equation, this results in a modified damping coefficient, which is a function of the ratio between the Stokes boundary layer thickness and the cell's gap, and whose complex value depends on the frequency of the wave response specific to each unstable parametric region. We first revisit the standard case of horizontally infinite rectangular Hele-Shaw cells by also accounting for a dynamic contact angle model. A comparison with existing experiments shows the predictive improvement brought by the present theory and points out how the standard gap-averaged model often underestimates the Faraday threshold. The analysis is then extended to the less conventional case of thin annuli. A series of dedicated experiments for this configuration highlights how Darcy's thin-gap approximation overlooks a frequency detuning that is essential to correctly predict the locations of the Faraday tongues in the frequency–amplitude parameter plane. These findings are well rationalised and captured by the present model.

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“…Additionally, natural frequencies for the pinned contact-line cases are invariably larger than those with freely sliding contact-line dynamics (Bostwick & Steen 2015; Wilson et al. 2022). This suggests that the frequency difference between the experimental case and theoretical prediction may be due to the non-ideal contact-line condition in our experiments, and the loss of the pinned end being exacerbated by the strong forcing.…”

Section: Theoretical Verificationmentioning

confidence: 99%

Pattern evolution and modal decomposition of Faraday waves in a brimful cylinder

Zhang,

Borthwick,

Lin

2023

J. Fluid Mech.

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This paper investigates the steady-state pattern evolution of symmetric Faraday waves excited in a brimful cylindrical container when driving parameters much exceed critical thresholds. In such liquid systems, parametric surface responses are typically considered as the resonant superposition of unstable standing waves. A modified free-surface synthetic Schlieren method is employed to obtain full three-dimensional spatial reconstructions of instantaneous surface patterns. Multi-azimuth structures and localized travelling waves during the small-elevation phases of the oscillation cycle give rise to modal decomposition in the form of $\nu$ -basis modes. Two-step surface-fitting results provide insight into the spatiotemporal characteristics of dominant wave components and corresponding harmonics in the experimental observations. Arithmetic combination of modal indices and uniform frequency distributions reveal the nonlinear mechanisms behind pattern formation and the primary pathways of energy transfer. Taking the hypothetical surface manifestation of multiple azimuths as the modal solutions, a linear stability analysis of the inviscid system is utilised to calculate fundamental resonance tongues (FRTs) with non-overlapping bottoms, which correspond to subharmonic or harmonic $\nu$ -basis modes induced by surface instability at the air–liquid interface. Close relationships between experimental observations and corresponding FRTs provide qualitative verification of dominant modes identified using surface-fitting results. This supports the validity and rationality of the applied $\nu$ -basis modes.

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Role of edge effects and fluid depth in azimuthal Faraday waves

Cited by 5 publications

References 63 publications

Pattern formation in Faraday instability—experimental validation of theoretical models

Pattern formation in Faraday instability—experimental validation of theoretical models

A revised gap-averaged Floquet analysis of Faraday waves in Hele-Shaw cells

Pattern evolution and modal decomposition of Faraday waves in a brimful cylinder

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