The Flow of Liquids in Thin Films

Fulford, George D.

doi:10.1016/s0065-2377(08)60008-3

Cited by 235 publications

(89 citation statements)

References 86 publications

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“…They find that, over this range of Reynolds number, the film thickness varies over time as waves form in the falling film, and that the mean film thickness is in good agreement with their model (equation (2.10)) across the whole range of Re f . Fulford (1964) notes that, for thin films, the transition to turbulence occurs over a wider range of flow rates (i.e. a wider range of Reynolds number) than for pipe flow because the boundary layer represents an appreciable fraction of the film thickness, even to relatively high Re f .…”

Section: (B) Falling Liquid Filmsmentioning

confidence: 99%

The thickness of the falling film of liquid around a Taylor bubble

et al. 2011

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We present the results of laboratory experiments that quantify the physical controls on the thickness of the falling film of liquid around a Taylor bubble, when liquid-gas interfacial tension can be neglected. We find that the dimensionless film thickness l (the ratio of the film thickness to the pipe radius) is a function only of the dimensionless parameter N f = r gD 3 /m, where r is the liquid density, g the gravitational acceleration, D the pipe diameter and m the dynamic viscosity of the liquid. For N f 10, the dimensionless film thickness is independent of N f with value l ≈ 0.33; in the interval 10 N f 10 4 , l decreases with increasing N f ; for N f 10 4 film thickness is, again, independent of N f with value l ≈ 0.08. We synthesize existing models for films falling down a plane surface and around a Taylor bubble, and develop a theoretical model for film thickness that encompasses the viscous, inertial and turbulent regimes. Based on our data, we also propose a single empirical correlation for l (N f ), which is valid in the range 10 −1 < N f < 10 5 . Finally, we consider the thickness of the falling film when interfacial tension cannot be neglected, and find that film thickness decreases as interfacial tension becomes more important.

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Section: (B) Falling Liquid Filmsmentioning

confidence: 99%

The thickness of the falling film of liquid around a Taylor bubble

et al. 2011

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“…The length of the rewetted region depends essentially on a balance between condensation in the cold section and evaporation in the hot zone. The Kapitsa criterion 13) for the stability of thin liquid films predicts wave formation at the film surface with disruption of the liquid film continuity when its thickness is about 10 mm. If this criterion had been applied, the rewetting zone would have been shorter than shown by plot (a), but cooling of dry-out zones would have been made by deposition of liquid droplets formed by the film disruption and transported by the vapour flow.…”

Section: Discussion Of Computed Resultsmentioning

confidence: 99%

Molecular Approach to Sodium Vapour Condensation, Rewetting and Vaporization in LMFBR Bundle under Hypothetical Accident Conditions

Bottoni¹

2004

Journal of Nuclear Science and Technology

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In the frame of safety analysis of Liquid Metal Fast Breeder Reactors (LMFBRs) under hypothetical Unprotected Loss-of-Flow (ULOF) conditions, two phase flow of sodium is simulated in a reactor core. Traditional approaches used in safety analysis codes to simulate sodium vapour condensation and vaporization rely upon application of macroscopic semi-empirical correlations for heat transfer and vapour condensation or evaporation rates. As an alternative to this macroscopic approach, we developed a microscopic methodology based upon the application of the basic laws of the kinetic theory for the determination of the evaporation and condensation rates of vapour in a reactor bundle. This microscopic approach is based upon a Monte Carlo simulation of the molecular trajectories, collision rates between vapour molecules and of the molecules with the surfaces of the claddings of the pins of a reactor bundle. The pins surfaces are treated in the Monte Carlo simulation as diffusely reflecting surfaces. Scattering of sodium particles is simulated with the ''hard sphere'' collision model. The ''step splitting'' technique is applied, which consists in separating the collisions dynamic calculation from collisionsless paths of the molecules. Vapour particles are assumed to condense on the surfaces of the pins when, after diffuse reflection, their velocity would be less than one third of the most probable velocity corresponding to the wall temperature. Rewetting of dried out regions of the cladding surfaces is simulated with a dynamic film model which computes the velocity distribution of the liquid across the film thickness and then the mean liquid film velocity. Evaporation of sodium molecules from the film yields a source of molecules which re-enter into the Monte Carlo calculation of the molecular dynamic approach. The coupling of the micro-and macroscopic models has been applied to the numerical simulation of an out-of pile sodium boiling experiment run at

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“…This could be observed from data reported by Tailby and Portalski (1961) on Newtonian thin film flow, but not from data of Davies and Vose (1965) on damping of waves on a deep liquid. It was calculated by Ternovskaya and Belopolski (Fulford, 1964) that the surfactant concentration which maximizes wave damping corresponded to quantities of surfactant just sufficient to form a saturated monolayer at the interface. Maximum wave damping could be related to the observed minimum in mass transfer rates from droplets falling in another continuous liquid phase as a function of surfactant concentration (Skelland and Caenepeel, 1972 It is evident from Fi es 1 to 4 that the change of surface tension with surfagnt concentration is virtually the same for water and for the pseudoplastic liquids studied, with minor differences due to small temperature variations during the experiments.…”

Section: Resultsmentioning

confidence: 99%

Stabilizing effects of surfactants on pseudoplastic falling films

Skelland

Popadić

1974

AIChE Journal

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The effects of nonionic surfactants on thin-film flow of pseudoplastic non-Newtonian liquids down a smooth vertical plate have been studied experimentally. For all, liquids examined there was a surfactant concentration at which the stavilizing action of surfactants was maximized. Comparison with experimedtal data showed that an existing equation, developed for the stabilizing actiop of surfactants on thin-film flow of Newtonian fluids, may be used to predict the effect of surfactants on the stability of pseudoplastic thin-film flow bp using the zero-shear rate apparent viscosity in place of the Newtonian viscosity.

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The Flow of Liquids in Thin Films

Cited by 235 publications

References 86 publications

The thickness of the falling film of liquid around a Taylor bubble

The thickness of the falling film of liquid around a Taylor bubble

Molecular Approach to Sodium Vapour Condensation, Rewetting and Vaporization in LMFBR Bundle under Hypothetical Accident Conditions

Stabilizing effects of surfactants on pseudoplastic falling films

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