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

Patne, Ramkarn; Agnon, Yehuda; Oron, Alexander

doi:10.1017/jfm.2020.747

Cited by 23 publications

(47 citation statements)

References 46 publications

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“…The stability of the linear and return flows was explored in detail by Smith & Davis (1983a,b). Furthermore, the thermocapillary instabilities arising due to an imposed OTG have been also investigated by Nepomnyashchy & Simanovskii (2004), Shklyaev & Nepomnyashchy (2004), Nepomnyashchy & Simanovskii (2009) and Patne, Agnon & Oron (2020b, 2021a. Shklyaev & Nepomnyashchy (2004) and Patne et al (2021a) revealed a strong stabilizing effect of the imposed HTG component on the instability triggered by the VTG component of the imposed OTG.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the thermocapillary instabilities arising due to an imposed OTG have been also investigated by Nepomnyashchy & Simanovskii (2004), Shklyaev & Nepomnyashchy (2004), Nepomnyashchy & Simanovskii (2009) and Patne, Agnon & Oron (2020b, 2021a. Shklyaev & Nepomnyashchy (2004) and Patne et al (2021a) revealed a strong stabilizing effect of the imposed HTG component on the instability triggered by the VTG component of the imposed OTG. Additionally, Patne et al (2021a) demonstrated the existence of an entirely new class of thermocapillary modes arising as a result of the interaction between the imposed HTG and VTG.…”

Section: Introductionmentioning

confidence: 99%

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

Patne

Oron

2022

J. Fluid Mech.

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We investigate the temporal and spatio-temporal buoyancy instabilities in a horizontal liquid layer supported by a poorly conducting substrate and subjected to an oblique temperature gradient (OTG) with horizontal and vertical components, denoted as HTG and VTG, respectively. General linear stability analysis (GLSA) reveals a strong stabilizing effect of the HTG on the instabilities introduced by the VTG for Prandtl numbers $Pr>1$ via inducing an extra vertical temperature gradient opposing the VTG through energy convection. For $Pr<1$ , a new mode of instability arises as a result of a velocity jump in the liquid layer caused by cellular circulation. A long-wave weakly nonlinear evolution equation governing the spatio-temporal dynamics of the temperature perturbations is derived. Spatio-temporal stability analysis reveals the existence of a convectively unstable long-wave regime due to the HTG. Weakly nonlinear stability analysis reveals the supercritical type of bifurcation changing from pitchfork in the presence of a pure VTG to Hopf in the presence of the OTG. Numerical investigation of the spatio-temporal dynamics of the temperature disturbances in the layer in the weakly nonlinear regime reveals the emergence of travelling wave regimes propagating against the direction of the HTG and whose phase speed depends on $Pr$ . In the case of a small but non-zero Biot number, the wavelength of these travelling waves is larger than that of the fastest-growing mode obtained from GLSA.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Patne

Oron

2022

J. Fluid Mech.

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“…Further details of the discretisation of the governing equations and boundary conditions, and the construction of the matrices A and B, are presented in the standard procedure described by Trefethen (2000) and Schmid & Henningson (2001). Application of the pseudospectral method for similar problems can be found in Patne, Agnon & Oron (2020, 2021. We use the polyeig MATLAB routine to solve the generalised eigenvalue problem given by (3.4).…”

Section: Methodsmentioning

confidence: 99%

Dynamics of a two-layer flow with an interfacial heat source/sink: viscosity stratification

et al. 2022

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The temporal stability of a two-layer plane Couette flow with an interfacial heat source/sink is studied, in the presence of a viscosity stratification, predicting unstable streamwise and spanwise perturbations. Based on the wavenumber at onset, the perturbations are further classified as long-wave and finite-wave, where the long-wave mode is investigated using asymptotic and numerical analyses. The finite-wave instability is expected to be relevant for highly viscous fluids. Generally, a heat source (sink) at the interface is found to have a stabilising (destabilising) effect on the flow. However, if the rate of heat release exceeds a certain threshold, a new instability emerges, referred to here as an ‘explosive’ instability, characterised by an unbounded growth rate of the perturbations. The interaction between the viscosity stratification, thermocapillarity and inertia leads to the emergence of another new mode of streamwise instability, termed the ‘interaction’ instability. The spanwise perturbations possess higher growth rates than the streamwise perturbations for the heat sink along the interface when inertia has a stabilising influence, and vice versa. The heat sink leads to the emergence of thermocapillary instability by generating a negative temperature gradient across the fluids. In contrast, a heat source increases the temperature of the interface, resulting in a positive temperature gradient across the fluids, leading to the suppression of the instabilities by the thermocapillary effect. If the heat source provides energy at a faster rate than the energy lost due to Marangoni convection and heat diffusion, then it leads to an accumulation of energy, which presumably leads to the explosive instability.

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“…Marangoni convection in an infinite thin liquid layer (Birikh 1966; Smith & Davis 1983; Hu et al. 2017; Kowal, Davis & Voorhees 2018; Patne, Agnon & Oron 2021), a rectangular cavity (Strani, Piva & Graziani 1983; Shieh & Yang 1987; Peltier & Biringen 1993; Chen & Xu 2021), a two layer system (Doi & Koster 1993; Liu, Roux & Velarde 1998), a point-heating cavity (Hamed & Floryan 2000; Wei, Liu & Lin 2012), a cylindrical cavity (Kang et al. 2016), a liquid bridge (Kang et al.…”

Section: Introductionmentioning

confidence: 99%

“…2018) with an oblique temperature gradient (Patne, Agnon & Oron 2020; Patne et al. 2021) or with phase change (Shmyrov et al. 2019; Salgado Sánchez et al.…”

Section: Introductionmentioning

confidence: 99%

Transient Marangoni convection induced by an isothermal sidewall of a rectangular liquid pool

Chen

Xu²

2021

J. Fluid Mech.

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Transient Marangoni convection induced by an isothermal sidewall of a rectangular pool under a zero-gravity condition is studied using scaling analysis. Scaling analysis shows that there exist a number of flow regimes in each evolution scenario, depending on the Marangoni number, the Prandtl number and the aspect ratio. In a typical evolution scenario, a horizontal surface flow and a vertical flow adjacent to the sidewall may appear. Additionally, a number of scaling laws of the velocity and thickness of transient Marangoni convection are obtained. Further, numerical simulation is performed for validation of the selected scaling laws. There exits good agreement between the numerical results and the scaling predictions.

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

Abstract: Abstract

Cited by 23 publications

References 46 publications

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

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

Dynamics of a two-layer flow with an interfacial heat source/sink: viscosity stratification

Transient Marangoni convection induced by an isothermal sidewall of a rectangular liquid pool

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