On a toroidal method to solve the sessile-drop oscillation problem

Sharma, Saksham; Wilson, D.I.

doi:10.1017/jfm.2021.419

“…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: 72%

“…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. 2013, 2015; Sakakeeny et al.…”

Section: Introductionmentioning

confidence: 92%

Oscillations of a partially wetting bubble

Ding

¹

,

Bostwick

²

2022

View full text Add to dashboard Cite

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 $\ell \neq 0,1$ .

show abstract

“…In our view, to explain the observed morphological behaviour, we need to discuss the effects of interfacial phenomena, in particular that of surface tension. [87][88][89] We also look forward to experiments with pellet-grown vertical chemical gardens in similar setups but under other physicochemical conditions, such as with a different metal or in a different solution. Although the explosive rupturing of the membrane was observed in this study and of some relevance to our discussions, it has not been the focus of investigation in the present work.…”

Section: Discussionmentioning

confidence: 99%

Downward fingering accompanies upward tube growth in a chemical garden grown in a vertical confined geometry

Ding

¹

,

Gutiérrez-Ariza

²

,

Zheng

³

et al. 2022

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

show abstract

“…Limiting cases correspond to freely moving Λ = 0 and pinned Λ = ∞ CLs with intermediate cases Λ / = 0, ∞ corresponding to stick-slip behaviours (Shaikeea et al 2017). We note an analytical-based solution method has recently been proposed by Sharma & Wilson (2021) for pinned drops. The predictions of Bostwick & Steen (2014) have been verified for drops with pinned CLs (Λ = ∞) by Chang et al (2013Chang et al ( , 2015 over a range of α.…”

Section: Introductionmentioning

confidence: 99%

“…2017). We note an analytical-based solution method has recently been proposed by Sharma & Wilson (2021) for pinned drops. The predictions of Bostwick & Steen (2014) have been verified for drops with pinned CLs () by Chang et al.…”

Section: Introductionmentioning

confidence: 99%

Pressure modes of the oscillating sessile drop

Ding

¹

,

Bostwick

²

2022

View full text Add to dashboard Cite

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.

show abstract

On a toroidal method to solve the sessile-drop oscillation problem

Abstract: Abstract

Cited by 11 publications

References 32 publications

Oscillations of a partially wetting bubble

Oscillations of a partially wetting bubble

Downward fingering accompanies upward tube growth in a chemical garden grown in a vertical confined geometry

Pressure modes of the oscillating sessile drop

Contact Info

Product

Resources

About