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

Park, C. D.; Nosoko, Takehiro

doi:10.1002/aic.690491105

Cited by 142 publications

(115 citation statements)

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“…For Re = 6, the wave patterns on the interface are similar to those observed in isothermal conditions (see e.g. [2,4,10]) even though channels aligned with the flow can be observed in some places and seem to be the precursor to rivulet formation. In fact, rivulet structures never show up, for at least a long period of time -10000 time units, corresponding to several meters in a real experiment-dur- ing which a 'stationary' wave regime takes place with a nearly constant energy of deformations in both directions: E x ≈ E z ≈ cst.…”

Section: B Large-size Domainmentioning

confidence: 46%

“…[2]). Experiments by Liu, Schneider & Gollub [3] and more recently by Park & Nosoko [4] have provided a clear picture of the phenomenology and intricate dynamics of interacting 3D waves in isothermal film flows, that includes synchronously deformed fronts, subharmonic patterns and horseshoe-like waves. From the theoretical point of view and with the exception of direct 3D numerical simulations, the modeling of falling films generally relies on the 'boundary-layer approximation' in which the pressure is eliminated by integrating across the film the cross-stream component of the momentum equation where the inertia effects are neglected.…”

Section: Introductionmentioning

confidence: 43%

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Interaction of three-dimensional hydrodynamic and thermocapillary instabilities in film flows

et al. 2008

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We study three-dimensional wave patterns on the surface of a film flowing down a uniformly heated wall. Our starting point is a model of four evolution equations for the film thickness h, the interfacial temperature θ and the streamwise and spanwise flow rates, q and p, respectively, obtained by combining a gradient expansion with a weighted residual projection. This model is shown to be robust and accurate in describing the competition between hydrodynamic waves and thermocapillary Marangoni effects for a wide range of parameters. For small Reynolds numbers, i.e. in the 'drag-gravity regime', we observe regularly spaced rivulets aligned with the flow and preventing the development of hydrodynamic waves. The wavelength of the developed rivulet structures is found to closely match the one of the most amplified mode predicted by linear theory. For larger Reynolds numbers, i.e. in the 'drag-inertia regime', the situation is similar to the isothermal case and no rivulets are observed. Between these two regimes we observe a complex behavior for the hydrodynamic and thermocapillary modes with the presence of rivulets channeling quasi-two-dimensional waves of larger amplitude and phase speed than those observed in isothermal conditions, leading possibly to solitary-like waves. Two subregions are identified depending on the topology of the rivulet structures that can be either 'ridgelike' or 'groovelike'. A regime map is further proposed that highlights the influence of the Reynolds and the Marangoni numbers on the rivulet structures. Interestingly, this map is found to be related to the variations of amplitude and speed of the twodimensional solitary-wave solutions of the model. Finally, the heat transfer enhancement due to the increase of interfacial area in the presence of rivulet structures is shown to be significant.

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Section: B Large-size Domainmentioning

confidence: 46%

Section: Introductionmentioning

confidence: 43%

Interaction of three-dimensional hydrodynamic and thermocapillary instabilities in film flows

et al. 2008

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“…Transition from 2D to 3D flows is shown to be strongly dependent on initial conditions. The herringbone patterns, the synchronously deformed fronts and the threedimensional solitary waves observed in experiments (Liu et al 1995;Park & Nosoko 2003;Alekseenko et al 1994) are recovered using our regularised model, which is found to be an excellent compromise between the complete model, which has seven equations, and the simplified model, which does not include the second-order inertia corrections. Those corrections are found to play a role in the selection of the type of secondary instability as well as of the spanwise wavelength of the emerging pattern.…”

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confidence: 42%

Wave patterns in film flows: modelling and three-dimensional waves

2006

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In a previous work, two-dimensional film flows were modelled using a weighted-residual approach that led to a four-equation model consistent at order 2 . A two-equation model resulted from a subsequent simplification but at the cost of lowering the degree of the approximation to order only (Ruyer-Quil & Manneville 2000). A Padé approximant technique is applied here to derive a refined two-equation model consistent at order 2 . This model, formulated in terms of coupled evolution equations for the film thickness h and the flow rate q, accounts for inertia effects due to the deviations of the velocity profile from the parabolic shape, and closely sticks to the asymptotic long-wave expansion in the appropriate limit. Comparisons of two-dimensional wave properties with experiments and direct numerical simulations show good agreement for the range of parameters where a two-dimensional wavy motion is reported in experiments.The stability of two-dimensional travelling waves against three-dimensional perturbations is investigated based on the extension of the models to include spanwise dependence. The secondary instability is found to be not much selective, which explains the widespread presence of the synchronous instability observed in the experiments by Liu et al. (1995) whereas Floquet analysis predicts a subharmonic scenario in most cases. Three-dimensional wave patterns are next computed assuming periodic boundary conditions. Transition from 2D to 3D flows is shown to be strongly dependent on initial conditions. The herringbone patterns, the synchronously deformed fronts and the threedimensional solitary waves observed in experiments (Liu et al. 1995;Park & Nosoko 2003;Alekseenko et al. 1994) are recovered using our regularised model, which is found to be an excellent compromise between the complete model, which has seven equations, and the simplified model, which does not include the second-order inertia corrections. Those corrections are found to play a role in the selection of the type of secondary instability as well as of the spanwise wavelength of the emerging pattern.

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“…Hence, a falling liquid film can serve as a canonical reference system for the study of weak/dissipative turbulence. Three-dimensional hydrodynamic waves have been investigated experimentally by various authors [3][4][5] who have provided a clear picture of the phenomenology and intricate dynamics of interacting 3D waves in isothermal film flows. When the falling film is uniformly heated from the wall, as encountered in thin-film evaporators and cooling of electronics, its dynamics is influenced, in addition to inertia and surface tension, by the variation of surface tension with temperature, namely the long-wave thermocapillary (Marangoni) effect [6][7][8], which possibly leads to rivulet-(a) E-mail: bscheid@ulb.ac.be like structures aligned with the flow as predicted by linear stability analysis [9].…”

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confidence: 44%

Spontaneous channeling of solitary pulses in heated-film flows

et al. 2008

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Abstract. -We investigate the dynamics of a liquid film flowing down a uniformly heated wall. We use a four-field weighted-average model for the film thickness, the surface temperature and the two-dimensional flow rate vector. Time-dependent simulations are rationalized in a phase diagram. For small Reynolds numbers we observe regularly spaced rivulets aligned with the flow that prevent the development of hydrodynamic waves while for large Reynolds numbers, the evolution is similar to that observed in the isothermal case, i.e. wave-dominated. The transition between the two regimes is characterized by an intricate pattern formation dynamics, including regimes of quasi-2D solitary pulses riding the crests of rivulets.

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

Cited by 142 publications

References 50 publications

Interaction of three-dimensional hydrodynamic and thermocapillary instabilities in film flows

Interaction of three-dimensional hydrodynamic and thermocapillary instabilities in film flows

Wave patterns in film flows: modelling and three-dimensional waves

Spontaneous channeling of solitary pulses in heated-film flows

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