A model to predict the oscillation frequency for drops pinned on a vertical planar surface

Sakakeeny, Jordan; Deshpande, C. G.; Deb, Sandipan; Alvarado, Jorge L.; Ling, Yue

doi:10.1017/jfm.2021.844

Cited by 8 publications

(8 citation statements)

References 19 publications

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“…2013, 2015) and numerical simulations (Basaran & DePaoli 1994; Olgac, Izbassarov & Muradoglu 2013; Sakakeeny & Ling 2020, 2021; Sakakeeny et al. 2021).…”

Section: Introductionmentioning

confidence: 99%

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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“…2013, 2015) and numerical simulations (Basaran & DePaoli 1994; Olgac, Izbassarov & Muradoglu 2013; Sakakeeny & Ling 2020, 2021; Sakakeeny et al. 2021).…”

Section: Introductionmentioning

confidence: 99%

Effects of gravity on natural oscillations of sessile drops

2023

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“…Drops and bubbles are closely related and we note that there has been a lot of recent research on sessile drop oscillations, including theoretical analysis (Bostwick & Steen 2014;Sharma & Wilson 2021) and experimental observations (Sharp, Farmer & Kelly 2011;Sharp 2012;Chang et al 2013Chang et al , 2015Sakakeeny et al 2021). The sessile drop frequency spectra computed by Bostwick & Steen (2014) exhibits a rich structure that includes features such as splitting of the Rayleigh drop degeneracy, spectral reordering and mode mixing, all of which have been verified experimentally.…”

Section: Introductionmentioning

confidence: 73%

“…2013, 2015; Sakakeeny et al. 2021). The sessile drop frequency spectra computed by Bostwick & Steen (2014) exhibits a rich structure that includes features such as splitting of the Rayleigh drop degeneracy, spectral reordering and mode mixing, all of which have been verified experimentally.…”

Section: Introductionmentioning

confidence: 99%

Oscillations of a partially wetting bubble

Ding

Bostwick

2022

J. Fluid Mech.

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We study the linear stability of a compressible sessile bubble in an ambient fluid that partially wets a planar solid support, where the gas is assumed to be an ideal gas that obeys the adiabatic law. The frequency spectrum is computed from an integrodifferential boundary value problem and depends upon the wetting conditions through the static contact angle $\alpha$ , the dimensionless equilibrium bubble pressure $\varPi$ , and the contact-line dynamics that we assume to be either (i) pinned or (ii) freely moving with fixed contact angle. Corresponding mode shapes are defined by the polar-azimuthal mode number pair $[k,\ell ]$ with $k+\ell =\mathbb {Z}^{+}_{even}$ . We report instabilities to the (i) $[0,0]$ breathing mode associated with volume change, and (ii) $[1,1]$ mode that is linked to horizontal centre-of-mass motion of the bubble. Stability diagrams and instability growth rates are computed, and the respective instability mechanisms are revealed through an energy analysis. The zonal $\ell =0$ modes are associated with volume change, and we show that there is a complex dependence between the classical volume and shape change modes for wetting conditions that differ from neutral wetting $\alpha =90^\circ$ . Finally, we show how the classical frequency degeneracy for the Rayleigh–Lamb modes of the free bubble splits for the azimuthal modes $\ell \neq 0,1$ .

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“…Recent interest in drop oscillations has focused on the role substrate contact has on the frequency spectrum for a variety of wetting conditions (Chebel, Risso & Masbernat 2011; Sharp, Farmer & Kelly 2011; Sharp 2012; Sakakeeny et al. 2021). Such drop wetting interactions are typified in the problem of sessile-drop oscillations.…”

Section: Introductionmentioning

confidence: 99%

“…The Rayleigh spectrum (1.1) has stood the test of time having been verified in both terrestrial (Trinh & Wang 1982) and microgravity (Wang, Anilkumar & Lee 1996) conditions. Recent interest in drop oscillations has focused on the role substrate contact has on the frequency spectrum for a variety of wetting conditions (Chebel, Risso & Masbernat 2011;Sharp, Farmer & Kelly 2011;Sharp 2012;Sakakeeny et al 2021). Such drop wetting interactions are typified in the problem of sessile-drop oscillations.…”

Section: Introductionmentioning

confidence: 99%

Pressure modes of the oscillating sessile drop

Ding

Bostwick

2022

J. Fluid Mech.

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Drop-on-demand printing applications involve a drop connected to a fluid reservoir between which volume can be exchanged, a situation that can be idealized as a sessile drop with prescribed volume flux across the drop/reservoir boundary. Here we compute the frequency spectrum for these pressure disturbances, as it depends upon the static contact-angle $\alpha$ (CA) and an empirical constant $\chi$ relating the reservoir pressure to volume exchanged, for either (i) pinned or (ii) free contact-lines. Mode shapes are characterized by the mode number pair $[k,\ell ]$ with property $k+\ell =\mathbb {Z}^{+}_{odd}$ that can be associated with the symmetry properties of the Rayleigh drop modes for the free sphere. We report instabilities to the axisymmetric $[1,0]$ and non-axisymmetric rocking $[2,1]$ modes that are related to centre-of-mass motions, and show how the spectral degeneracy of the Rayleigh drop modes breaks with the model parameters.

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A model to predict the oscillation frequency for drops pinned on a vertical planar surface

Cited by 8 publications

References 19 publications

Effects of gravity on natural oscillations of sessile drops

Effects of gravity on natural oscillations of sessile drops

Oscillations of a partially wetting bubble

Pressure modes of the oscillating sessile drop

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