Stability of Thin Liquid Films Falling Down Isothermal and Nonisothermal Walls

Dávalos‐Orozco, L. A.

doi:10.1615/interfacphenomheattransfer.2013006655

Cited by 29 publications

(13 citation statements)

References 224 publications

(253 reference statements)

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“…The results of this paper are new not only because of the combination of viscoelasticity [37] and thermocapillarity [31] in flow on the surface of a cylinder, but also because the problem investigated is three dimensional. This can be seen in the review section on thin film flow down cylinders presented in Dávalos-orozco [17]. It is found that in the linear and non linear problems, mainly axial mode stability is investigated.…”

Section: Introductionmentioning

confidence: 93%

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Azimuthal instability modes in a viscoelastic liquid layer flowing down a heated cylinder

Moctezuma-Sánchez

Dávalos‐Orozco

2015

International Journal of Heat and Mass Transfer

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Section: Introductionmentioning

confidence: 93%

“…When a fluid layer flows down a wall, the thermocapillary effects are included by Joo et al [16,14] and Ramaswamy et al [15]. A complete review of this problem is found in Dávalos-orozco [17].…”

Section: Introductionmentioning

confidence: 99%

Azimuthal instability modes in a viscoelastic liquid layer flowing down a heated cylinder

Moctezuma-Sánchez

Dávalos‐Orozco

2015

International Journal of Heat and Mass Transfer

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“…There are some exceptions, as follows. [34,35] study linear stability properties and nonlinear evolution of a thin film flowing down an inclined heated wall and take into account the thermal conductivity and thickness of the wall. These studies are performed entirely within the context of a Benney-type equation, which has severe limitations as noted above.…”

Section: Introductionmentioning

confidence: 99%

“…The films considered are, therefore, always hydrodynamically stable; the issue of finite-time blow-up of Benney-type equations is thus avoided, but the equation cannot be used to analyze the effects of the conjugate heat transfer on the development of solitary pulses, which only exist for supercritical Reynolds numbers. Similarly to [34,35], the timescales of crossstream thermal diffusion in the liquid and the substrate are taken to be small enough so that the temperature profile in the film and the substrate is slaved to the local film thickness. In [37], this study is extended to include the regime in which the timescale of cross-stream thermal diffusion within the substrate can no longer be neglected, so that the temperature profile is not determined (to leading order) by the film thickness.…”

Section: Introductionmentioning

confidence: 99%

“…Our aim is to use this model to examine the quantitative and qualitative effect that finite substrate diffusivity has on the stability and dynamics of the film, including the properties of solitary pulses. We thus explore a regime not modeled by either [34,35], which do not consider the effect of finite substrate diffusivity and do not use the more widely applicable weighted-residual model, or [36,37], which only model low-Reynolds-number flows. In order to isolate the effect of finite substrate diffusivity, we assume large thermal diffusivity in the liquid film.…”

Section: Introductionmentioning

confidence: 99%

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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 stability of a thin liquid film falling down above or below an inclined thick wall with slip

Dávalos-Orozco

2023

Meccanica

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The linear and nonlinear instability of a thin liquid film flowing down above or below (Rayleigh-Taylor instability) an inclined thick wall with finite thermal conductivity are investigated in the presence of slip at the wall-liquid interface. A nonlinear evolution equation for the free surface deformation is obtained under the lubrication approximation. The curves of linear growth rate, maximum growth rate and critical Marangoni number are calculated. When the film flows below the wall it will be subjected to destabilizing and stabilizing Marangoni numbers. It is found that from the point of view of the linear growth rate the flow destabilizes with slip in a wavenumber range. However slip stabilizes for larger wavenumbers up to the critical (cutoff) wavenumber. From the point of view of the maximum growth rate flow slip may stabilize or destabilize increasing the slip parameter depending on the magnitude of the Marangoni and Galilei numbers. Explicit formulas were derived for the intersections (the wavenumber for the growth rate and the Marangoni number for the maximum growth rate) where slip changes its stabilizing and destabilizing properties. From the numerical solution of the nonlinear evolution equation of the free surface profiles, it is found that slip may suppress or stimulate the appearance of subharmonics depending on the magnitudes of the selected parameters. In the same way, it is found that slip may increase or decrease the nonlinear amplitude of the free surface deformation. The effect of the thickness and finite thermal conductivity of the wall is also investigated.

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Stability of Thin Liquid Films Falling Down Isothermal and Nonisothermal Walls

Cited by 29 publications

References 224 publications

Azimuthal instability modes in a viscoelastic liquid layer flowing down a heated cylinder

Azimuthal instability modes in a viscoelastic liquid layer flowing down a heated cylinder

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

Marangoni stability of a thin liquid film falling down above or below an inclined thick wall with slip

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