Marangoni convection and heat transfer in thin liquid films on heated walls with topography: Experiments and numerical study

Alexeev, Alexander; Gambaryan‐Roisman, Tatiana; Stephan, Peter

doi:10.1063/1.1936933

Cited by 64 publications

(44 citation statements)

References 31 publications

(39 reference statements)

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“…If the effect of the heat convection can not be treated as a small correction, the full energy equation should be solved along with the evolution equation for the film thickness. If both inertia and the heat convection are important, or if the restriction A str K str << 1 is released, the full-scale numerical simulation of the governing equations should be performed (Alexeev et al 2004). Figure 3 illustrates the effect of the parameterM on the heat transfer enhancement due to the variation of the film thickness and of the gas layer thickness.…”

Section: Stationary Filmsmentioning

confidence: 99%

“…Several recent experimental and theoretical/numerical studies (Alexeev et al 2004;Gambaryan-Roisman et al 2005;Kabova et al 2005Kabova et al , 2006 have been devoted to the thermocapillarity-driven flow of thin liquid films on structured heated or cooled walls. It has been found that the thermocapillary convection in a liquid film, as well as the film stability to long-wave disturbances, crucially depend on the wall topography.…”

Section: Introductionmentioning

confidence: 99%

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Thermocapillary convection and interface deformation in a liquid film within a micro-slot with structured walls

Gambaryan‐Roisman

Stephan

2006

Microfluid Nanofluid

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Thermocapillary convection in a thin liquid film inside a micro-slot with structured walls kept at different temperatures is studied. The liquid film is wetting the substrate wall and is separated from the cover wall by a gas layer. If the slot walls are structured, the temperature at the liquid-gas interface is non-uniform. The temperature variation induces thermocapillary stresses which bring the liquid into motion and lead to the interface deformation. We investigate the film flow inside the micro-slot, the heat transfer, the liquid-gas interface deformations and the film stability in the framework of the long-wave theory. We show that the amplitude of the interface deformation increases with increasing of the wall structure period. We demonstrate that the structured walls lead to the heat transfer enhancement, which effect is for the studied range of parameters stronger if the cover wall is structured. We also show that the wall structure enhances the long-wave Marangoni instability. The destabilizing effect of the substrate structure is stronger than that of the cover wall structure.

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Section: Stationary Filmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermocapillary convection and interface deformation in a liquid film within a micro-slot with structured walls

Gambaryan‐Roisman

Stephan

2006

Microfluid Nanofluid

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“…Thermocapillary convection and film deformation on a heated substrate can be influenced by using substrates with topography [13][14][15][16][17]. If the substrate temperature is higher than that of the environment, the sites on the liquid-gas interface over the topography crests are hotter than the interface sites corresponding to the topography troughs.…”

Section: Introductionmentioning

confidence: 99%

Marangoni-induced deformation of evaporating liquid films on composite substrates

Gambaryan‐Roisman

2011

J Eng Math

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Marangoni convection plays an important role in hydrodynamics of evaporating liquid films and sessile drops. Evaporation of liquid films induces unsteady nonuniform temperature distribution across the liquid layer and in a substrate. If the substrate is composed of parts with different thermal properties, the interface temperature distribution becomes non-uniform, leading to appearance of Marangoni stresses, convective vortices, and film deformation. In this article, a model describing evaporation, Marangoni effect and interface dynamics of liquid films on composite substrates is developed. The film dynamics is described in the framework of long-wave theory. The unsteady heat conduction in the substrate is described using the Laplace transform method for semi-infinite substrates and using the separation of variables technique for substrates of finite thickness. The non-uniformity of substrate thermal properties has a pronounced effect on film dynamics.

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“…Similar to before, we expand µ ∼ i R(2, 1) + iδν and c = c (38) we findh =c/2. Now the only change for the analysis on h 0 is that (40) is replaced with…”

Section: B Bifurcations From the Trivial Statementioning

confidence: 99%

“…Other studies that have considered heat flow within the substrate are [38], which examines the combined effects of conjugate heat transfer and topography both experimentally and numerically by solving the full system of governing equations (in a low-Reynolds-number regime), and [39], which focuses on the importance of substrate heat conduction near the contact line of an evaporating droplet.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a thin film flowing down a heated wall with finite thermal diffusivity

2016

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Consider the dynamics of a thin film flowing down a heated substrate. The substrate heating generates a temperature distribution on the free surface which in turn induces surface-tension gradients and corresponding thermocapillary stresses that affect the free surface and therefore the fluid flow. We study here the effect of finite substrate thermal diffusivity on the film dynamics. Linear stability analysis of the full Navier-Stokes and heat transport equations indicates that if the substrate diffusivity is sufficiently small, the film becomes unstable at a finite wavelength and at a Reynolds number smaller than that predicted in the long-wavelength limit. This property is captured in a reducedorder system of equations derived using a weighted-residual integral-boundary-layer method. This reduced-order model is also used to compute the bifurcation diagrams of solution branches connecting the trivial flat film to traveling waves including solitary pulses. The effect of finite diffusivity is to separate a simultaneous Hopf/transcritical bifurcation into its individual component bifurcations. The appropriate Hopf bifurcation then connects only to the solution branch of negative-hump pulses, with wave speed less than the linear wave speed while the branch of positive-single-hump pulses merges with the branch of positive-two-hump pulses at a supercritical Reynolds number. In the regime where finite-wavelength instability occurs, there exists a Hopf-bifurcation pair connected by a branch of periodic solutions, whose period cannot be increased indefinitely. Numerical simulation of the reduced-order system shows the development of a train of coherent structures each of which resembles a stationary positive-hump pulse, and, in the regime of finite-wavelength instability, wavelength selection and saturation to periodic traveling waves.

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Marangoni convection and heat transfer in thin liquid films on heated walls with topography: Experiments and numerical study

Cited by 64 publications

References 31 publications

Thermocapillary convection and interface deformation in a liquid film within a micro-slot with structured walls

Thermocapillary convection and interface deformation in a liquid film within a micro-slot with structured walls

Marangoni-induced deformation of evaporating liquid films on composite substrates

Dynamics of a thin film flowing down a heated wall with finite thermal diffusivity

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