Buoyancy instabilities in a liquid layer subjected to an oblique temperature gradient

Patne, Ramkarn; Oron, Alexander

doi:10.1017/jfm.2022.110

Cited by 2 publications

(25 citation statements)

References 49 publications

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“…The above-described numerical methodology has been utilised previously to solve similar problems by Patne & Shankar (2020), Patne, Agnon & Oron (2020 a ), Patne et al. (2020 b ), Patne, Agnon & Oron (2021 a , b ), Patne & Oron (2022) and Patne (2022).…”

Section: Numerical Methodologymentioning

confidence: 99%

Effect of inhaled air temperature on mucus dynamics in the proximal airways

Patne

2024

J. Fluid Mech.

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The aim of the present study is to understand the role of steam/cold-air inhalation on the mucus layer dynamics in the proximal airways. We model these flows as a viscoelastic liquid (lining the inner side of a tube) sheared by a turbulent airflow and subjected to a radial heat flow. The linear stability analysis of the resulting flow is carried out using numerical and thin-film approaches. The air–mucus interface tension, coupled with the azimuthal curvature, leads to the previously predicted axisymmetric capillary mode responsible for airway closure in distal airways. The viscoelasticity of the mucus leads to axisymmetric and new non-axisymmetric elastic modes, with the former possessing a higher growth rate. The axisymmetric elastic and capillary modes merge to give rise to a new ‘elasto-capillary mode’ possessing a growth rate nearly equal to the combined growth rate of the elastic and capillary modes. The analysis predicts a strong stabilising effect of the thermocapillarity induced by steam inhalation on the elasto-capillary mode. Thus steam decreases airway resistance, which could explain the observed therapeutic effect of steam inhalation. The opposite is the case when the inhaled air is colder than the body temperature, in agreement with the observations. The theoretical predictions are corroborated by the physical mechanism explaining the suppression/amplification of the elasto-capillary mode due to thermocapillarity.

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Section: Numerical Methodologymentioning

confidence: 99%

Effect of inhaled air temperature on mucus dynamics in the proximal airways

Patne

2024

J. Fluid Mech.

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“…Following the procedure of Mercier & Normand (1996) and Patne & Oron (2022), the fully developed, steady-state core flow is vx = − ηRa 48 (8y 3 − 15y 2 + 6y); vy = 0; vz = 0, (2.4a)…”

Section: Problem Formulationmentioning

confidence: 99%

“…In material processing and crystal growth (Lappa 2010), additive manufacturing (Kowal, Davis & Voorhees 2018), industrial processes (Kistler & Schweizer 1997;Patne & Oron 2022) and geophysical settings (Weber 1978;Ortiz-Pérez & Dávalos-Orozco 2011, 2014, the liquid layers are subjected to an oblique temperature gradient (OTG). Also, maintaining a purely vertical temperature gradient (VTG) or horizontal temperature gradient (HTG) in experiments while studying the thermally driven convection is difficult; thus, inadvertently, a liquid layer is subjected to an OTG (Shklyaev & Nepomnyashchy 2004;Nepomnyashchy & Simanovskii 2009).…”

Section: Introductionmentioning

confidence: 99%

“…The present study tries to answer this question by considering a simple model of a liquid layer in a rectangular cavity subjected to an OTG. These applications typically involve the bottom support or bottom wall as a perfectly conducting material; thus, we extend the analysis of Patne & Oron (2022) to a perfectly conducting bottom wall.…”

Section: Introductionmentioning

confidence: 99%

“…In the present analysis, we neglect the thermocapillary effect; thus, the results predicted here are applicable to thicker liquid layers. Following the estimates provided by Patne & Oron (2022), this restricts the applicability of our study to the liquid layers having a thickness greater than 1 cm. Hart (1972) first investigated the stability of the Hadley circulation.…”

Section: Introductionmentioning

confidence: 99%

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Linear dynamics of a thick liquid layer subjected to an oblique temperature gradient

Dixit,

Bukhari,

Patne

2024

J. Fluid Mech.

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The present study aims to demonstrate the application of the oblique temperature gradient (OTG) to manipulate the buoyancy instabilities and resulting mixing. To accomplish this, we consider a model consisting of a liquid layer supported by a perfectly conducting bottom wall from below and the upper surface is exposed to ambient inert gas in a shallow container. The stability analysis employs the pseudospectral method and perturbation energy budget approach. The imposed OTG consists of a negative vertical temperature gradient (VTG), which leads to unstable density stratification, and a negative horizontal temperature gradient (HTG) component responsible for the Hadley circulation, which can be utilised to control instabilities. Without the HTG, a Rayleigh–Bénard mode of instability exists due to the imposed VTG termed as a VTG mode. The imposed HTG induces a linear VTG term and a quintic polynomial VTG term in the bottom wall-normal coordinate $y$ . The induced linear VTG term reinforces the imposed VTG, while the induced quintic polynomial VTG term opposes the imposed VTG. For the vanishing Biot number ( $Bi$ ), the induced quintic VTG term stabilises the VTG mode for the Prandtl number, $Pr=7$ . However, for $Pr=0.01$ , the Reynolds stresses associated with the Hadley circulation destabilise the VTG mode. For non-zero $Bi$ , new streamwise and spanwise instability modes arise for $Pr=7$ due to the induced linear VTG term. Physical arguments show that the unstable density stratification near the gas–liquid interface caused by the synergistic effect of the imposed VTG and the induced linear VTG term lead to the existence of the predicted new modes. The present study thus shows that the strength of the HTG can be utilised to control the instability modes and critical parameters, thereby demonstrating the utility of the OTG in manipulating the buoyancy instabilities.

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Buoyancy instabilities in a liquid layer subjected to an oblique temperature gradient

Cited by 2 publications

References 49 publications

Effect of inhaled air temperature on mucus dynamics in the proximal airways

Effect of inhaled air temperature on mucus dynamics in the proximal airways

Linear dynamics of a thick liquid layer subjected to an oblique temperature gradient

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