The effect of high-frequency vibration on the onset of Marangoni convection in a horizontal liquid layer

Zen'kovskaya, S. M.; Shleikel, A.L.

doi:10.1016/s0021-8928(02)00074-6

Cited by 7 publications

(15 citation statements)

References 2 publications

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“…For pure Marangoni stability in a onelayer system, the increase of Ra v also stabilizes the system. 16 It seems that in a two-layer system, the increase of Ra v has the same effect as that in a one-layer system for both the Rayleigh stability and the Marangoni stability.…”

Section: B Instabilities Under Vertical Vibrationsmentioning

confidence: 95%

Influence of high-frequency vibration on the Rayleigh–Marangoni instability in a two-layer system

Liu

2011

Physics of Fluids

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The influences of high-frequency vibrations on the Rayleigh–Marangoni instability in a two-layer system are investigated theoretically in the framework of the averaging method. We focus on the effects of vertical and horizontal vibrations on the stability of different convection modes. The results show that vertical vibrations significantly stabilize the system, while horizontal vibrations significantly destabilize it. In the presence of vertical vibrations, instability only occurs in a system heated from below. However, in the presence of horizontal vibrations, instability can also occur in a system cooled from below. When Marangoni effect is dominant at the interface, it is found that there are four types of coupling modes. The oscillatory convection is the result of the competition between different modes. In the presence of Marangoni effect at the interface, the structure of the interfacial flow is complicated. In some cases, small counter-rolls may develop to preserve the nonslip condition of fluids in either the upper layer or the lower layer.

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Section: B Instabilities Under Vertical Vibrationsmentioning

confidence: 95%

Influence of high-frequency vibration on the Rayleigh–Marangoni instability in a two-layer system

Liu

2011

Physics of Fluids

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“…In a moving coordinate system the dimensionless convection equations and the generalized OB approximation [33,35] are…”

Section: Problem Statementmentioning

confidence: 99%

“…The derivation of the averaged equations follows the scheme developed in [35,40]. Along with the slow time t, the fast time τ = ωt is introduced.…”

Section: High-frequency Asymptotics: Averagingmentioning

confidence: 99%

Averaging method and long-wave asymptotics in vibrational convection in layers with an interface

Zen'kovskaya

Novosiadliy

2010

J Eng Math

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A scheme for applying an averaging method to the problem of convection in a two-layer system with an interface under the influence of high-frequency vibration is proposed. The derivation of the averaging equations is given, and the stability of the equilibrium of the averaged problem is considered. Long-wavelength asymptotics of steady and oscillatory instability are constructed. The results of numerical calculations for acetonitrile-n-hexane and silicone oil-fluorinert systems are given. The directions in which the investigation of thermovibrational convection in problems with free surfaces and interfaces can be continued, are indicated.

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“…H 1 , H 2 denote the depths of the fluids, respectively. According to the results about the deformable interface (Zen'kovskaya and Shleikel, 2001;Birikh, 2003) before here the interface is considered to be flat. The interfacial tension at the interface is assumed to be a linear function of temperature: r ¼ r 0 À r T ðT À T 0 Þ, where T 0 is the reference temperature of the interface.…”

Section: Problem Description and Basic Equationsmentioning

confidence: 99%

“…It has been known that the convection in two-layer system has many new features, which have no counterpart in a single-layer system (Zen'kovskaya and Shleikel, 2001;Cisse et al, 2004). The effects of thermovibrations on the stabilities have been studied about the classical Rayleigh-Benard problem (Cisse et al, 2004) and for Marangoni convection (surface-tension-driven convection) in one-layer system (Zen'kovskaya and Shleikel, 2001).…”

Section: Introductionmentioning

confidence: 99%

Thermovibrational instability of Rayleigh–Marangoni–Benard convection in two-layer fluid systems

Liu

Zhou

Wang

et al. 2008

Advances in Space Research

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The thermovibrational instability of Rayleigh-Marangoni-Benard convection in a two-layer system under the high-frequency vibration has been investigated by linear instability analysis in the present paper. General equations for the description of the convective flow and within this framework, the generalized Boussinesq approximation are formulated. These equations are dealt with using the averaging method. The theoretical analysis results show that the high-frequency thermovibrations can change the Marangoni-Benard convection instabilities as well as the oscillatory gaps of the Rayleigh-Marangoni-Benard convection in two-layer liquid systems. It is found that vertical high-frequency vibrations can delay convective instability of this system, and damp the convective flow down.

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The effect of high-frequency vibration on the onset of Marangoni convection in a horizontal liquid layer

Cited by 7 publications

References 2 publications

Influence of high-frequency vibration on the Rayleigh–Marangoni instability in a two-layer system

Influence of high-frequency vibration on the Rayleigh–Marangoni instability in a two-layer system

Averaging method and long-wave asymptotics in vibrational convection in layers with an interface

Thermovibrational instability of Rayleigh–Marangoni–Benard convection in two-layer fluid systems

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