Longwave convection in a layer of binary mixture with modulated heat flux: weakly nonlinear analysis

Fayzrakhmanova, Irina S.; Shklyaev, Sergey; Nepomnyashchy, Alexander

doi:10.1088/0169-5983/46/4/041411

Cited by 5 publications

(3 citation statements)

References 27 publications

(51 reference statements)

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“…For Bi = 0 and  = W, one obtains the following system of the leading order equations [167,168]: ( ) ˜is the effective rescaled Marangoni number. Linear equations (181) and (182) were studied in [167], where the neutral stability curves * m K 0 ( ) were obtained.…”

Section: ( ) ( )mentioning

confidence: 99%

Longwave oscillatory patterns in liquids: outside the world of the complex Ginzburg–Landau equation

Nepomnyashchy¹,

Shklyaev²

2015

J. Phys. A: Math. Theor.

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A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class and a model equation, we show that branched stripe patterns emerge, which for a given parameter set are stable within a band of different wave numbers and different numbers of branching points (defects). Moreover, the branched patterns and unbranched ones (defect-free stripes) coexist over a finite parameter range. We propose two systems where this generic scenario can be found experimentally, surface wrinkling on elastic substrates and electroconvection in nematic liquid crystals, and relate them to the findings from the amplitude equation.

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confidence: 99%

Longwave oscillatory patterns in liquids: outside the world of the complex Ginzburg–Landau equation

Nepomnyashchy¹,

Shklyaev²

2015

J. Phys. A: Math. Theor.

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“…A host of long wavelength instability problems for binary liquid films including the interplay of Marangoni and Soret effects have been studied by Oron, Nepomnyashchy, and co-workers. [47][48][49][50][51][52][53][54][55] Two other notably important contributions which address these issues with the inclusion of gravity in the lubrication limit are the works by Bestehorn and Borcia 25 (linear stability analysis) and Borcia et al 56 (fully nonlinear simulations). Our present work differs from these in two different ways.…”

Section: Introductionmentioning

confidence: 99%

Thermodiffusion as a means to manipulate liquid film dynamics on chemically patterned surfaces

Kalpathy

Shreyes

2017

The Journal of Chemical Physics

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The model problem examined here is the stability of a thin liquid film consisting of two miscible components, resting on a chemically patterned solid substrate and heated from below. In addition to surface tension gradients, the temperature variations also induce gradients in the concentration of the film by virtue of thermodiffusion/Soret effects. We study the stability and dewetting behaviour due to the coupled interplay between thermal gradients, Soret effects, long-range van der Waals forces, and wettability gradient-driven flows. Linear stability analysis is first employed to predict growth rates and the critical Marangoni number for chemically homogeneous surfaces. Then, nonlinear simulations are performed to unravel the interfacial dynamics and possible locations of the film rupture on chemically patterned substrates. Results suggest that appropriate tuning of the Soret parameter and its direction, in conjunction with either heating or cooling, can help manipulate the location and time scales of the film rupture. The Soret effect can either potentially aid or oppose film instability depending on whether the thermal and solutal contributions to flow are cooperative or opposed to each other.

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“…The influence of heat flux modulation on the Marangoni instability in binary mixtures with Soret effect has been studied in the framework of the linear stability theory by Fayzrakhmanova, Shklyaev & Nepomnyashchy (2013b). The weakly nonlinear theory describing the excitation of a synchronous mode by a modulated heat flux was developed by Fayzrakhmanova, Shklyaev & Nepomnyashchy (2014).…”

Section: Introductionmentioning

confidence: 99%

Generation of nonlinear Marangoni waves in a two-layer film by heating modulation

Nepomnyashchy

Simanovskii

2015

J. Fluid Mech.

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Longwave Marangoni convection in two-layer films under the action of heating modulation is considered. The analysis is carried out in the lubrication approximation. The capillary forces are assumed to be sufficiently strong, and they are taken into account. Periodic or symmetric boundary conditions are applied on the boundaries of the computational region. Numerical simulations are performed by means of a finite-difference method. Two regions of parametric instabilities have been found. In the first region, one observes the competition or coexistence of standing waves parallel to the boundaries of the computational region. The multistability of the flow regimes is revealed. In the second region, the regimes found in the case of periodic boundary conditions are more diverse than in the case of symmetric boundary conditions.

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Longwave convection in a layer of binary mixture with modulated heat flux: weakly nonlinear analysis

Cited by 5 publications

References 27 publications

Longwave oscillatory patterns in liquids: outside the world of the complex Ginzburg–Landau equation

Longwave oscillatory patterns in liquids: outside the world of the complex Ginzburg–Landau equation

Thermodiffusion as a means to manipulate liquid film dynamics on chemically patterned surfaces

Generation of nonlinear Marangoni waves in a two-layer film by heating modulation

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