Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers

Joo, Sang Woo; Davis, Stephen H.; Bankoff, S. G.

doi:10.1017/s0022112091000733

Cited by 249 publications

(204 citation statements)

References 16 publications

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“…Chang (1994) already evocated this condition speaking about constant-average thickness or constant-flux formulation. Many authors, as for instance (Joo et al 1991;Salamon et al 1994;Oron & Gottlieb 2002;Scheid et al 2002), implicitly prescribed the closed flow condition. This is due to the fact that in time-dependent simulations, using periodic boundary conditions, the amount of liquid leaving the domain downstream is reinjected upstream.…”

Section: Frame and Objectives Of This Workmentioning

confidence: 99%

“…Equation (2.2) was obtained by Joo et al (1991). However, here we neglect evaporation that was included there.…”

Section: The Benney Equationmentioning

confidence: 99%

“…In contrast with several previous works (Joo et al 1991Scheid et al 2002), the value of the aspect ratio is not assumed a priori. However, doing so results merely in a rescaling of λ, as for instance in Joo et al (1991) where the wavenumber is defined by (2000) elaborated a model that predicts accurately and economically the linear and nonlinear properties of film flows up to relatively high Reynolds numbers.…”

Section: Travelling-wave Solutionsmentioning

confidence: 99%

“…However, doing so results merely in a rescaling of λ, as for instance in Joo et al (1991) where the wavenumber is defined by (2000) elaborated a model that predicts accurately and economically the linear and nonlinear properties of film flows up to relatively high Reynolds numbers. This model was derived in the frame of the integral boundary layer (IBL) approximation by combining a gradient expansion to weighted residual techniques with polynomials as test functions.…”

Section: Travelling-wave Solutionsmentioning

confidence: 99%

“…decreasing S and/or Ka, reduces the range of validity of the BE in the linearly unstable domain. Joo et al (1991) have performed time-dependent simulations of the BE for isothermal falling films using the closed flow condition. Their figures 5-9 present the respective wave evolutions for increasing domain size, i.e.…”

Section: Influence Of Inclinationmentioning

confidence: 99%

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Validity domain of the Benney equation including the Marangoni effect for closed and open flows

Scheid¹,

Ruyer-Quil²,

Thiele³

et al. 2005

J. Fluid Mech.

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The Benney equation including thermocapillary effects is considered to study a liquid film flowing down a homogeneously heated inclined wall. The link between finite-time blow-up of the Benney equation and absence of one-hump travelling-wave solution of the associated dynamical system is accurately demonstrated in the whole range of linearly unstable wavenumbers. Then the blow-up boundary is tracked in the whole space of parameters accounting for flow rate, surface tension, inclination and thermocapillarity. Especially, the latter two effects can strongly reduce the validity range of the Benney equation. It is also shown that the subcritical bifurcation found for falling films with the Benney equation is related to the blow-up of solutions and is unphysical in any case, even with the thermocapillary effect, in contrast with horizontally heated films. The accuracy of bounded solutions of the Benney equation is also analysed by comparison with a reference weighted integral boundary layer model. A distinction is made between closed and open flow conditions, when calculating travelling-wave solutions; the former corresponding to the conservation of mass and the latter to the conservation of flow rate. The open flow condition matches experimental conditions more closely and is explored for the first time through the associated dynamical system. It yields bounded solutions for larger Reynolds numbers than the closed flow condition. Finally, solutions that are conditionally bounded are found to be unstable to disturbances of larger periodicity. In this case, coalescence is the pathway yielding finite-time blow-up.

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Section: Frame and Objectives Of This Workmentioning

confidence: 99%

“…Equation (2.2) was obtained by Joo et al (1991). However, here we neglect evaporation that was included there.…”

Section: The Benney Equationmentioning

confidence: 99%

Section: Travelling-wave Solutionsmentioning

confidence: 99%

Section: Travelling-wave Solutionsmentioning

confidence: 99%

Section: Influence Of Inclinationmentioning

confidence: 99%

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Validity domain of the Benney equation including the Marangoni effect for closed and open flows

Scheid¹,

Ruyer-Quil²,

Thiele³

et al. 2005

J. Fluid Mech.

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Counter‐current gas‐liquid wavy film flow between the vertical plates analyzed using the Navier‐Stokes equations

Trifonov

2009

AIChE Journal

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in Wiley InterScience (www.interscience.wiley.com).The article is devoted to a theoretical analysis of counter-current gas-liquid wavy film flow between vertical plates. We consider two-dimensional nonlinear waves on the interface over a wide variation of parameters. The main interest is to analyse the wave structure at the parameter values corresponding to the onset of flooding observed in experiments. We use the Navier-Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use two models: (1) the Navier-Stokes system and (2) the simplified Benjamin-Miles approach where the liquid phase is a small disturbance for the laminar or turbulent gas flow. With the superficial gas velocity increasing and starting from some value of the velocity, the waves demonstrate a rapid decreasing of both the minimal film thickness and the phase wave velocity. We obtain a region of the gas velocity where we have two solutions at one set of the problem parameters and where the flooding takes place. Both the phase wave velocity and the minimal film thickness are positive numbers at such values of the velocity. We calculate the flooding point dependences on the liquid Reynolds number for two different liquids. The wave regime corresponding to the flooding point demonstrates negative u-velocities in the neighbourhood of the interface near the film thickness maximum. At smaller values of the superficial gas velocity, the negative uvelocities take place in the neighbourhood of the film thickness minimumHere, Re ¼ 20 and k neut /L ¼ 0.25; (a) and (e) correspond to U GS ¼ 2.5 m/s; (b) and (f), U GS ¼ 7.0 m/s; (c) and (g) U GS ¼ 8.5 m/s; (d) and (h) U GS ¼ 9.07 m/s. Lines 1-3 correspond to water at k neut /L ¼ 0.25, 0.2, 0.15, respectively. Lines 4-6 correspond to 2.5% butanol at k neut /L ¼ 0.25, 0.2, 0.15, respectively.

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Three‐dimensional wave dynamics on a falling film and associated mass transfer

2003

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Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers

Cited by 249 publications

References 16 publications

Validity domain of the Benney equation including the Marangoni effect for closed and open flows

Validity domain of the Benney equation including the Marangoni effect for closed and open flows

Counter‐current gas‐liquid wavy film flow between the vertical plates analyzed using the Navier‐Stokes equations

Three‐dimensional wave dynamics on a falling film and associated mass transfer

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