The mechanism for surface wave instability in film flow down an inclined plane

Kelly, R. E.; Goussis, Dimitris A.; Lin, S. P.; Hsu, Frank K.

doi:10.1063/1.857379

Cited by 94 publications

(72 citation statements)

References 15 publications

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“…5 The disturbance originates at the free surface where vorticity is produced by the basic flow shear stress. 6,7 Owing to the effects of inertia, the perturbation vorticity tends to be advected downstream relative to the deflection of the free surface so as to cause instability. This shift is opposed by hydrostatic and surface tension forces.…”

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confidence: 99%

Nonlinear evolution of nonuniformly heated falling liquid films

et al. 2002

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The present theoretical study focuses on the dynamics of a thin liquid film falling down a vertical plate with a nonuniform, sinusoidal temperature distribution. The results are compared to those obtained in the case of the uniform temperature distribution. The governing evolution equation for the film thickness profile based on long-wave theory accounts for two instability mechanisms related to thermocapillarity. The first mechanism is due to an inhomogeneity of the temperature at the liquid-gas interface induced by perturbations of the film thickness, when heat transfer to the gas phase is present, while the second one is due to the nonuniform heating imposed at the plate and leads to steady-state deformations of the liquid-gas interface. For a moderate nonuniform heating the traveling waves obtained in the case of a uniform heating are modulated by an envelope. When the temperature modulation along the plate increases the shape of the liquid-gas interface becomes ''frozen'' and the oscillatory traveling wave regime is suppressed. The enhancement of the heat transfer due to permanent deformations and traveling waves is also assessed. The latter is found to have no significant effect on the heat transfer coefficient, while the former can increase it significantly. A good agreement between the theoretical model and the experimental data obtained for a step-wise temperature distribution at the plate is found and the reason for discrepancies is explained.

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confidence: 99%

Nonlinear evolution of nonuniformly heated falling liquid films

et al. 2002

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“…they did not include the apparently small effect of the gas phase into their analysis, which is, of course, suggested by the fact that the shear stress T at the gas-liquid interface is approximately zero. This approach has also been followed by Kelly et al (1989) and Smith (1990Smith ( , 1991, who give two different but in fact complementary explanations for the instability. Kelly et al show that the energy transfer TANg to these waves is indeed through the disturbance shear stresses at the interface, while Smith uses a long-wavelength expansion to discuss the forces and flow patterns involved in creating instability.…”

Section: Gravity-induced Instabilitymentioning

confidence: 99%

“…Our discussion on the physical meaning of the different terms in the energy equation [11] summarizes the clear one given by Kelly et al (1989). The terms KINj represent the spatially averaged rate of change of the disturbance kinetic energy.…”

Section: [18]mentioning

confidence: 99%

Classification of instabilities in parallel two-phase flow

Boomkamp

1996

International Journal of Multiphase Flow

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Abstract--There is extensive literature on the stability of parallel two-phase flow, both in the context of liquid-liquid as well as gas-liquid flow. Aimed at making this literature more transparent, this paper presents a classification scheme for the various instabilities arising in parallel two-phase flow..To achieve such a classification, the equation governing the rate of change of the kinetic energy of the disturbances is evaluated for relevant values of the physical parameters. This shows the existence of five different ways of energy transfer from the primary to the disturbed flow, which have their origin in density stratification, velocity profile curvature, viscosity stratification or shear effects. Each class is discussed on the basis of references covering the developments over the last 35 years. © 1997 Elsevier Science Ltd.

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“…Applying a periodic forcing at the inlet with a sufficiently large amplitude, for instance by periodically changing the flow rate of the liquid film, interfacial waves form as a result of the long-wave instability mechanism [17,18] and synchronize with the forcing frequency [19,20]. Depending on the frequency of the forcing, two wave families can be distinguished [19,21]: γ 1 -waves and γ 2 -waves.…”

Section: Introductionmentioning

confidence: 99%

“…The long-wave instability mechanism drives the initially exponential growth of the primary instability which via a secondary modulation instability leads to solitary waves [17,18], yet it has a stabilizing effect after the onset of flow recirculation in the main solitary wave hump as was shown recently by Denner et al [37]. As far as the saturated ("equilibrium") height of a solitary wave is concerned, it is governed by a balance of inertia and the streamwise component of gravity (destabilizing), with surface tension, viscous dissipation and the cross-stream component of gravity (stabilizing).…”

Section: Introductionmentioning

confidence: 99%

Self-similarity of solitary waves on inertia-dominated falling liquid films

et al. 2016

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We propose the first consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re = 20 − 120 and surface tension coefficients σ = 0.0512 − 0.072 N m −1 on substrates with inclination angles β = 19 • − 90 • . Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e. height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by non-linear effects and only driven by inertia, with surface tension and gravity having a negligible influence.

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The mechanism for surface wave instability in film flow down an inclined plane

Cited by 94 publications

References 15 publications

Nonlinear evolution of nonuniformly heated falling liquid films

Nonlinear evolution of nonuniformly heated falling liquid films

Classification of instabilities in parallel two-phase flow

Self-similarity of solitary waves on inertia-dominated falling liquid films

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