Nonlinear Marangoni waves in a two-layer film in the presence of gravity

Nepomnyashchy, Alexander; Simanovskii, Ilya B.

doi:10.1063/1.3690167

Cited by 29 publications

(13 citation statements)

References 20 publications

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“…For the liquid system described above, an oscillatory instability takes place by heating from above, i.e., for M ⊥ < 0. 19 In order to compare the predictions of the linear theory with the results of nonlinear simulations that are presented in Sec. IV, the following circumstance has to be taken into account.…”

Section: Linear Stability Theorymentioning

confidence: 99%

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Marangoni waves in a two-layer film under the action of an inclined temperature gradient

Nepomnyashchy

Simanovskii

2014

Physics of Fluids

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The development of the longwave deformational instability of a thermocapillary flow in a two-layer film under the action of an inclined temperature gradient is studied in the framework of the lubrication approximation. The stability boundaries with respect to different oscillatory modes are calculated by means of the linear stability theory. In a contradistinction to the case of a vertical temperature gradient, these boundaries strongly depend on the direction of the wave propagation. Numerical simulations of spatially periodic nonlinear regimes are fulfilled. It is shown that because of the anisotropy of the problem, the most typical kind of patterns is a traveling wave. For small inclination of the temperature gradient, temporally quasiperiodic waves are observed. A number of new three-dimensional traveling wave planforms is revealed.

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Section: Linear Stability Theorymentioning

confidence: 99%

“…The choice of the horizontal scale L * is arbitrary, because of the scaling properties of the problem. 19 We choose…”

Section: B Longwave Evolution Equationsmentioning

confidence: 99%

Marangoni waves in a two-layer film under the action of an inclined temperature gradient

Nepomnyashchy

Simanovskii

2014

Physics of Fluids

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“…The linear stability analysis revealed the existence of stationary and oscillatory unstable modes in this bilayer system. However, the complex coupling modes in the two-laye r flow system could not be studied by the long-wave theory [16][17][18]. Aside from that, to our knowledge, in previous works, oscillatory modes in multi-layer flow systems are all coupled with Rayleigh effects.…”

Section: Introductionmentioning

confidence: 98%

“…Recently, Nepomnyashch y and Simanovskii [18] reported nonlinear Marango ni waves in a heated two-layer film in the presence of gravity by a lubrication approximat ion. Both linear stability analysis and three dimensional nonlinear evolution study were carried out.…”

Section: Introductionmentioning

confidence: 99%

Linear instability analysis of thermocapillary convection in a bilayer system

Ding

Liu

2013

International Journal of Heat and Mass Transfer

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a b s t r a c tThe linear instability analysis of thermocapillary conve ction in a bila yer system consisting of silicon oil 10cS and fluorinert FC70 liquids was discussed in this paper. The bilayer system was bound below by a rigid plate and above by a free surface with a passive gas. The two immiscible liquids were separated by an interface. A constant horizontal temperature gradient was imposed along the interfaces. Two typical cases were studied: (i) streamwise homogeneou s disturbances (the streamwise disturbance wave number a = 0); (ii) spanwis e homogeneou s disturbances (the spanwis e disturbance wave number b = 0). When a = 0, it was found that convection in the two layers may occur in the form of stationary mode or oscillatory mode. The oscillatory mode takes the form of traveling wave, which propagates in either spanwis e direction. When b = 0, convection in the two layers occurs in the form of oscillatory mode, which takes the form of traveling wave propagating in the same direction as base flow. The three dimensional analysis suggested that disturbance in the spanwis e direction was the major cause of destabilization in the system. The influences of Biot number Bi and the depth ratio h on the unstable modes in the bilayer system were discussed.

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“…For example, the dynamics of a thin two-layer system was studied in [12]. It was shown that finite-amplitude alternating rolls are stable on a square lattice.…”

Section: Introductionmentioning

confidence: 99%

Oscillatory Longwave Marangoni Convection in a Binary Liquid. Part 2: Square Patterns

Shklyaev¹,

Nepomnyashchy²,

Oron³

2014

SIAM J. Appl. Math.

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As a natural extension for our recent work [SIAM J. Appl. Math., 73 (2013), pp. 2203-2223] we study pattern selection on a square lattice for longwave oscillatory Marangoni convection in a layer of binary liquid. In contrast to the previous studies dealing with weakly nonlinear dynamics of such systems only, in this recent work we developed a method based on the Fourier transform to describe the dynamics of finite-amplitude perturbations of both temperature and solute concentration. The method is then applied to study simple patterns on a rhombic lattice consisting of four or fewer interacting waves. The present paper is the first implementation of this theory to a problem with multiple interacting waves. In a wide range of parameters, alternating rolls (ARs) are the only stable pattern. For low values of the Schmidt number relevant for liquid semiconductors, a competition between ARs and traveling squares sets in and results in the emergence of a novel "asymmetric" pattern exhibiting properties of both traveling and standing regimes. Busse balloons for these patterns are found.

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Nonlinear Marangoni waves in a two-layer film in the presence of gravity

Cited by 29 publications

References 20 publications

Marangoni waves in a two-layer film under the action of an inclined temperature gradient

Marangoni waves in a two-layer film under the action of an inclined temperature gradient

Linear instability analysis of thermocapillary convection in a bilayer system

Oscillatory Longwave Marangoni Convection in a Binary Liquid. Part 2: Square Patterns

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