Long-wave Marangoni instability in a binary liquid layer on a thick solid substrate

Podolny, A.; Nepomnyashchy, Alexander; Oron, Alexander

doi:10.1103/physreve.76.026309

Cited by 18 publications

(7 citation statements)

References 19 publications

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“…To summarize, we use the minimal model of the surface-tension-driven convection in a layer of binary mixture, disregarding such effects as heat conduction in the substrate (Podolny et al 2007), adsorption-desorption kinetics (Mikishev and Nepomnyashchy 2010, Morozov et al 2013, deformation of the free surface (Podolny et al 2005, 2006, Bestehorn and Borcia 2010, Morozov et al 2013, diffuse interface (Frolovskaya et al 2008), dependence of the Soret coefficient on the concentration (Kalitzova-Kurteva et al 2009, evaporation (Mikishev and Nepomnyashchy 2013) and many others. However, the Soret effect is retained in order to create the gradient of solute concentration and, therefore, to give rise to the unusual mode, which is possible only in a binary liquid (Podolny et al 2005).…”

Section: Governing Equationsmentioning

confidence: 99%

Longwave Marangoni convection in a binary liquid layer heated from above: weakly nonlinear analysis

Shklyaev

Nepomnyashchy

2014

Fluid Dyn. Res.

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Nonlinear regime of longwave surface-tension-driven convection in a layer of binary mixture heated from above is considered. Under the assumption of the small Biot number, which corresponds to the almost heat insulated free surface, we derive the nonlocal amplitude equation. Analysis of pattern selection demonstrates that hexagons emerge subcritically and up-hexagons are stable within the entire domain of their existence. Squares become stable if the absolute value of the Marangoni number exceeds a certain value.

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Section: Governing Equationsmentioning

confidence: 99%

Longwave Marangoni convection in a binary liquid layer heated from above: weakly nonlinear analysis

Shklyaev

Nepomnyashchy

2014

Fluid Dyn. Res.

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“…In particular, due to the Soret effect, temperature differences induce a) Email: eglal.ellaban@ryerson.ca b) Email: jpascal@ryerson.ca c) Email: sdalessio@uwaterloo.ca molecular fluxes leading to non-uniformity in the concentration of the solute. The impact of the Soret effect on the stability of horizontal layers has been extensively studied [9][10][11][12][13][14] . The inclined flow case has received considerably less attention.…”

Section: Introductionmentioning

confidence: 99%

Instability of a binary liquid film flowing down a slippery heated plate

2017

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In this paper, we study the stability of a binary liquid film flowing down a heated slippery inclined surface. It is assumed that the heating induces concentration differences in the liquid mixture (Soret effect), which together with the differences in temperature affects the surface tension. A mathematical model is constructed by coupling the Navier-Stokes equations governing the flow with equations for the concentration and temperature. A Navier slip condition is applied at the liquid-solid interface. We carry out a linear stability analysis in order to obtain the critical conditions for the onset of instability. We use a Chebyshev spectral collocation method to obtain numerical solutions to the resulting Orr-Sommerfeld-type equations. We also obtain an asymptotic solution that yields an expression for the state of neutral stability of long perturbations as a function of the parameters controlling the problem. A weighted residual approximation is employed to derive a reduced model that is used to analyse the nonlinear effects. Good agreement between the linear stability analysis and nonlinear simulations provided by the weighted residual model is found.

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“…Afterwards, many investigations have been devoted to study the coupled thermal-solutal capillary and buoyancy flows [14][15][16][17]. Results have showed that the thermal-solutal capillary flow and buoyancy flow are coupled in different scales, generating different flow patterns and making diversity of instabilities types [18,19].…”

Section: Introductionmentioning

confidence: 99%

Flow Instabilities of Coupled Rotation and Thermal-Solutal Capillary Convection of Binary Mixture in Czochralski Configuration

Yuan

2019

Crystals

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In order to understand the flow instabilities of coupled rotation and thermal-solutal capillary convection of binary mixture in a Czochralski configuration subjected to simultaneous radial thermal and solutal gradients, a series of three-dimensional direct numerical simulation have been conducted. The capillary ratio of the silicon-germanium mixture is −0.2. The rotation Reynolds numbers of crystal and crucible, Res and Rec range from 0 to 3506 and 0 to 1403, respectively. Results show that the basic flow is axisymmetric and steady. It has rich flow structures in the meridian plane, depending on the competitions among the driving forces. With the increase of thermocapillary and rotation Reynolds numbers, the basic flow will transit to three dimensional oscillatory flow. For different combination of rotation rate and thermocapillary Reynolds number, the oscillatory flow can be displayed as spoke patterns which is steady in time but oscillate in space, spoke patterns propagate in azimuthal direction, rotational waves or coexistence of spokes and rotational waves. The crucible rotation has an inhibitory effect on the flow instability, inducing the monotonically increase of critical value for flow transitions, however, for crystal rotation, the critical thermocapillary Reynolds number increases at first and then decreases. When the rotation rate is large, two flow transitions are captured.

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Long-wave Marangoni instability in a binary liquid layer on a thick solid substrate

Cited by 18 publications

References 19 publications

Longwave Marangoni convection in a binary liquid layer heated from above: weakly nonlinear analysis

Longwave Marangoni convection in a binary liquid layer heated from above: weakly nonlinear analysis

Instability of a binary liquid film flowing down a slippery heated plate

Flow Instabilities of Coupled Rotation and Thermal-Solutal Capillary Convection of Binary Mixture in Czochralski Configuration

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