Pressure modes of the oscillating sessile drop

Ding, D.; Bostwick, Joshua

doi:10.1017/jfm.2022.494

Cited by 4 publications

(5 citation statements)

References 31 publications

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“…Unlike the free drop problem, there are generally no analytical expressions for the natural frequencies of sessile drops. For the small-amplitude oscillations, many theoretical models have been developed to predict the natural frequencies based on the normal-mode decomposition (Strani & Sabetta 1984, 1988; Gañán & Barrero 1990; Gañán 1991; Lyubimov, Lyubimova & Shklyaev 2004, 2006; Bostwick & Steen 2014; Sharma & Wilson 2021; Ding & Bostwick 2022 b ). These models are to solve a functional eigenvalue problem governing the linear dynamics of sessile drops (Myshkis et al.…”

Section: Introductionmentioning

confidence: 99%

“…Sharma & Wilson (2021) presented a fully analytical solution based on a toroidal analysis for the spherical-cap drop with a pinned CL. Recently, Ding & Bostwick (2022 b ) investigated the frequency spectrum of sessile drops under pressure constraints. The above theoretical results have compared favourably to experiments (Chang et al.…”

Section: Introductionmentioning

confidence: 99%

“…2018; Costalonga & Brunet 2020). Recently, several relevant instabilities have been reported in some theoretical literature (Bostwick & Steen 2018; Steen, Chang & Bostwick 2019; Ding & Bostwick 2022 a , b ). The walking drop instability is also illustrated by energy analysis by Bostwick & Steen (2014).…”

Section: Introductionmentioning

confidence: 99%

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Effects of gravity on natural oscillations of sessile drops

2023

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Natural oscillations of sessile drops with a free or pinned contact line in different gravity environments are studied based on a linear inviscid irrotational theory. The inviscid Navier–Stokes equations and boundary conditions are reduced to a functional eigenvalue problem by the normal-mode decomposition. We develop a boundary element method model to numerically solve the eigenvalue problem for predicting the natural frequencies. Emphasis is placed on the frequency shifts of modes due to gravity for a wide range of contact angles $\alpha$ and Bond numbers $Bo$ . Three types of $\alpha$ – $Bo$ diagrams reflecting how gravity shifts the frequency are identified. Specifically, the frequency of zonal modes shifts downwards (upwards) when $\alpha$ is smaller (larger) than a critical value, while the frequencies of most sectoral modes are shifted downwards regardless of $\alpha$ . As a result, gravity can transform the lowest mode from a zonal mode to a sectoral mode. The spectral degeneracy of hemispherical drops inherited from the Rayleigh–Lamb spectrum is also broken by gravity. However, we discover that gravity has no effect on the mode associated with the horizontal motion of the centre of mass, whose frequency is always zero regardless of $\alpha$ and $Bo$ . This implies that the ‘walking’ drop instability reported in previous literature does not exist.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effects of gravity on natural oscillations of sessile drops

2023

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“…Partially wetting drops on a plane are typical examples of stability analysis of capillary surfaces and have continued to receive special attention in recent years (Bostwick & Steen 2014, 2015, 2016; Chang et al. 2015; Steen, Chang & Bostwick 2019; Montanero & Ponce-Torres 2020; Ding & Bostwick 2022 a , b ; McCraney et al. 2022).…”

Section: Introductionmentioning

confidence: 99%

“…In these studies, only volume disturbances are allowed. Recently, Ding & Bostwick (2022 b ) studied the dynamic stability of spherical cap drops for pressure disturbances.…”

Section: Introductionmentioning

confidence: 99%

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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