A falling film on a porous medium

Samanta, Arghya; Goyeau, Benoı̂t; Ruyer-Quil, Christian

doi:10.1017/jfm.2012.550

Cited by 44 publications

(50 citation statements)

References 32 publications

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“…The numerical experiment is carried out for an air-liquid system where flow parameters are selected as the viscosity ratio m = 1/m F = 100, density ratio r = 1/r F = 1000 and layer thickness ratio n = 1/9 (Frank 2006(Frank , 2008. The lower-layer liquid is chosen as a water-glycerine mixture with a density of 1070 kg m −3 , kinematic viscosity of 6.27 × 10 −6 m 2 s −1 and surface tension of 67 × 10 −3 N m −1 (Liu & Gollub 1994;Samanta et al 2013).…”

Section: Travelling Wavesmentioning

confidence: 99%

Effect of surfactant on two-layer channel flow

Samanta

2013

J. Fluid Mech.

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The effect of insoluble surfactant on the interfacial waves in connection with a two-layer channel flow is investigated for low to moderate values of the Reynolds number. Previous studies focusing on Stokes flow (are extended by including the inertial effect and the study of low-Reynolds-number flow (Blyth & Pozrikidis, J. Fluid Mech., vol. 521, 2004b, pp. 241-250) is enlarged up to moderate Reynolds number. Linear stability analysis based on the Orr-Sommerfeld boundary value problem identifies a surfactant mode together with an interface mode. The presence of surfactant on the interfacial mode is stabilizing at high viscosity ratio and destabilizing at low viscosity ratio. The threshold of instability is determined as a function of the Marangoni number. A long-wave model is developed to predict the families of nonlinear waves in the neighbourhood of the threshold of instability. Far from the threshold, wave dynamics is explored under the framework of a three-equation model in terms of lower layer flow rate q 2 (x, t), lower liquid-layer thickness h(x, t) and surfactant concentration Γ (x, t). Primary instability analysis of a three-equation model captures the result of the Orr-Sommerfeld boundary value problem very well for quite large values of wavenumber. In the nonlinear regime, travelling wave solutions demonstrate deceleration of maximum amplitude and acceleration of speed with the Marangoni number at high viscosity ratio m > 1 and show completely the opposite behaviour at low viscosity ratio m < 1. However, both maximum amplitude and speed attain a fixed value with increasing Reynolds number and this leads to saturation of instability.

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Section: Travelling Wavesmentioning

confidence: 99%

Effect of surfactant on two-layer channel flow

Samanta

2013

J. Fluid Mech.

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“…In the analysis, the influence of the porous medium was usually reduced as a slip condition [35,36]. The effect of a slip on the primary instability was investigated by Samanta et al [37,38]. It was found the slip played a destabilizing role close to the instability onset, while the flow was stabilizing at larger values of the Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

Fingering Instability of a Gravity-Driven Thin Film Flowing Down a Vertical Tube with Wall Slippage

Dong

et al. 2019

Applied Sciences

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Inspired by the antiwetting property of pitcher plants, specialists have designed different functional material with slippery surfaces, and a directional slippery surface has been fabricated. This paper considers a gravity-driven liquid film coating the interior surface of a vertical tube, and different slippery lengths in the azimuthal direction and the axial direction are taken into account. The evolution equation of coating flow is derived using the thin film model, and time responses for two dimensional flow are calculated. Linear stability analysis (LSA) is given based on the traveling wave solutions, demonstrating that the axial slippery effect suppresses the flow instability and causes a larger traveling wave speed. Simultaneously, the azimuthal slippery effect plays a destabilizing role for perturbations with small wavenumbers and it is stabilizing for large wavenumbers. Direct simulations of the fingering flow patterns agree well with the linear stability analysis. Our results offer insight into the influence of wall slippage on the flow stability of liquid in petroleum engineering.

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“…Substrate heating thus introduces new modes of instability relating to convection, and lowers the critical Reynolds number. The substrate behaviour can also be altered by allowing chemical coatings, elastic deformations, or interactions with flow through porous media (Thiele et al 2009;Ogden et al 2011;Samanta et al 2011Samanta et al , 2013, which is often modelled by an effective slip condition. External fields can also be used to stabilise or destabilise the interface.…”

Section: Introductionmentioning

confidence: 99%

“…It is found that an effective slippage takes place that enhances the instability in the sense that it reduces the critical Reynolds number. Slippage models were investigated further by Samanta et al (2011) and an alternative porous medium model is proposed and analysed by Samanta et al (2013).…”

Section: Introductionmentioning

confidence: 99%

Falling liquid films with blowing and suction

2015

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Flow of a thin viscous film down a flat inclined plane becomes unstable to long-wave interfacial fluctuations when the Reynolds number based on the mean film thickness becomes larger than a critical value (this value decreases as the angle of inclination to the horizontal increases, and in particular becomes zero when the plate is vertical). Control of these interfacial instabilities is relevant to a wide range of industrial applications including coating processes and heat or mass transfer systems. This study considers the effect of blowing and suction through the substrate in order to construct from first principles physically realistic models that can be used for detailed passive and active control studies of direct relevance to possible experiments. Two different long-wave, thin-film equations are derived to describe this system; these include the imposed blowing/suction as well as inertia, surface tension, gravity and viscosity. The case of spatially periodic blowing and suction is considered in detail and the bifurcation structure of forced steady states is explored numerically to predict that steady states cease to exist for sufficiently large suction speeds since the film locally thins to zero thickness, giving way to dry patches on the substrate. The linear stability of the resulting non-uniform steady states is investigated for perturbations of arbitrary wavelength, and any instabilities are followed into the fully nonlinear regime using time-dependent computations. The case of small amplitude blowing/suction is studied analytically both for steady states and their stability. Finally, the transition between travelling waves and non-uniform steady states is explored as the amplitude of blowing and suction is increased.

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A falling film on a porous medium

Cited by 44 publications

References 32 publications

Effect of surfactant on two-layer channel flow

Effect of surfactant on two-layer channel flow

Fingering Instability of a Gravity-Driven Thin Film Flowing Down a Vertical Tube with Wall Slippage

Falling liquid films with blowing and suction

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