Marangoni-induced deformation of evaporating liquid films on composite substrates

Gambaryan‐Roisman, Tatiana

doi:10.1007/s10665-011-9498-9

Cited by 8 publications

(2 citation statements)

References 23 publications

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“…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. We refer to this as finite (rather than large) substrate diffusivity.…”

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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Section: Introductionmentioning

confidence: 99%