Onset of oscillatory interfacial instability and wave motions in Bénard layers

Velarde, Manuel G.; Nepomnyashchy, Alexander; Hennenberg, Marcel

doi:10.1016/s0065-2156(00)80006-x

Cited by 48 publications

(58 citation statements)

References 182 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As has been reemphasized recently by Regnier et al [29] and Velarde et al [4], it is important to ensure that the Boussinesq approximation is appropriate. In order for the Boussinesq approximation to be valid for two-fluid convection, the product ␣ i T * i must be small in each liquid, where T * i is the temperature difference across the individual liquid.…”

Section: The Effect Of Gravitymentioning

confidence: 99%

See 1 more Smart Citation

Two-Fluid Marangoni–Bénard Convection with a Deformable Interface

Tavener¹,

Cliffe²

2002

Journal of Computational Physics

View full text Add to dashboard Cite

Section: The Effect Of Gravitymentioning

confidence: 99%

“…Unlike the single fluid case, time-dependent flows may develop directly from the conducting solution. A comprehensive review of the considerable literature to date is provided by Velarde et al [4] and by Andereck et al [5].…”

Section: Introductionmentioning

confidence: 99%

Two-Fluid Marangoni–Bénard Convection with a Deformable Interface

Tavener¹,

Cliffe²

2002

Journal of Computational Physics

View full text Add to dashboard Cite

“…When the fluid layer is heated from below, convective instabilities can be driven by surface or buoyancy forces [1]. The role of surface-tension gradients in inducing convective instability through Marangoni stresses at the air-liquid interface in a thin layer initially at rest, heated from below, was characterized in the seminal works of Sternling and Scriven [2] and Smith [3] and the role of surface deformation and surface tension gradients in the onset of patterned convection and oscillatory instability is reviewed in [4].…”

Section: Introductionmentioning

confidence: 99%

Excitation of Surface Waves Due to Thermocapillary Effects on a Stably Stratified Fluid Layer

Zimmerman

Rees

2017

Applied Sciences

View full text Add to dashboard Cite

Abstract:In chemical engineering applications, the operation of condensers and evaporators can be made more efficient by exploiting the transport properties of interfacial waves excited on the interface between a hot vapor overlying a colder liquid. Linear theory for the onset of instabilities due to heating a thin layer from above is computed for the Marangoni-Bénard problem. Symbolic computation in the long wave asymptotic limit shows three stationary, non-growing modes. Intersection of two decaying branches occurs at a crossover long wavelength; two other modes co-exist at the crossover point-propagating modes on nascent, shorter wavelength branches. The dispersion relation is then mapped numerically by Newton continuation methods. A neutral stability method is used to map the space of critical stability for a physically meaningful range of capillary, Prandtl, and Galileo numbers. The existence of a cut-off wavenumber for the long wave instability was verified. It was found that the effect of applying a no-slip lower boundary condition was to render all long waves stationary. This has the implication that any propagating modes, if they exist, must occur at finite wavelengths. The computation of 8000 different parameter sets shows that the group velocity always lies within 1 2 to 2 3 of the longwave phase velocity.

show abstract

“…It occurs due to gradients of interfacial tension caused by gradients of temperature or concentration in the course of heat-or mass transfer. Marangoni convection is known to exhibit formation of spatio-temporal patterns with different symmetries: stationary patterns such as hexagons, rolls and squares [3,4,5,6,7,8,9,10] as well as oscillatory patterns such as nonlinear waves and solitons [11,12,13,14,15,16] (see also [1,2] for review). In [17,18,19] Marangoni convection induced by light was studied experimentally.…”

Section: Introductionmentioning

confidence: 99%

Marangoni Convection in a Photo-Chemically Reacting Liquid

Golovin

Volpert

2008

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

Abstract. Marangoni convection caused by a photochemical reaction of the type A hν B in a deep liquid layer is studied. Linear stability analysis is performed and the conditions for Marangoni convection to occur are obtained. It is shown that increasing the rate of the direct reaction, for example, by increasing the light intensity, destabilizes the steady state and causes convective motion of the fluid, whereas increasing the rate of the inverse reaction stabilizes the steady state. A weakly nonlinear analysis of the problem is performed that gives conditions for hexagonal convective patters to occur. It is shown that, in the case of small light absorption length, the hexagonal cells correspond to "down"-hexagons.

show abstract

Onset of oscillatory interfacial instability and wave motions in Bénard layers

Cited by 48 publications

References 182 publications

Two-Fluid Marangoni–Bénard Convection with a Deformable Interface

Two-Fluid Marangoni–Bénard Convection with a Deformable Interface

Excitation of Surface Waves Due to Thermocapillary Effects on a Stably Stratified Fluid Layer

Marangoni Convection in a Photo-Chemically Reacting Liquid

Contact Info

Product

Resources

About