Surface wave and thermocapillary instabilities in a liquid film flow

Goussis, Dimitris A.; Kelly, R. E.

doi:10.1017/s0022112091001313

Cited by 101 publications

(105 citation statements)

References 21 publications

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“…2. The solid line shows the linear stability result found from the pure thermocapillary problem [9] or equivalently from our model by suppressing the streamwise dependence:…”

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confidence: 81%

“…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]. Joo et al [10] modeled the nonlinear stage of such rivulet structures by incorporating the Marangoni effect into the Benney equation (MBE).…”

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confidence: 99%

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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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“…2. The solid line shows the linear stability result found from the pure thermocapillary problem [9] or equivalently from our model by suppressing the streamwise dependence:…”

mentioning

confidence: 81%

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confidence: 99%

Spontaneous channeling of solitary pulses in heated-film flows

et al. 2008

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“…We restrain the present study to the two-dimensional case for at least the three follow-ing reasons: (i) we want to benefit from the dynamical-system theory (see §2.1.2) that cannot be applied with a third coordinate; (ii) the linear growth rate of transverse waves was found by Goussis & Kelly (1991) to be always larger than that of longitudinal rolls as far as the long-wave modes are concerned. Note that this result extends the one obtained for the pure hydrodynamic mode by Yih (1955) who extended the Squire's approach to free surface flows (Huerre & Rossi 1998); (iii) as a consequence of the previous point and as shown experimentally, it always exists a transition zone of purely two-dimensional flow when the film is periodically forced at the inlet (Liu et al 1995).…”

Section: Frame and Objectives Of This Workmentioning

confidence: 99%

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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“…The linear stability analysis by Ludviksson & Lightfoot [11] considered the free surface as adiabatic thus demonstrating the crucial role of the imposed streamwise temperature gradient in the instability mechanism. On the contrary, Goussis & Kelly [18] analyzed the case of an inclined plate maintained at constant temperature, and showed that only a non-adiabatic free surface in this case can lead to the long-wave thermocapillary instability and concomitant streamwise roll cells, i.e. rivulets, A sketch of rivulet structures is given in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…The mechanism in this case is the same that the one described by Smith [19] to explain the dewetting of a thin film on a heated horizontal substrate: a spontaneous modulation of the freesurface elevation generates a temperature gradient at the interface and once flow starts, it is again maintained by the externally imposed temperature gradient (directed across the film). Goussis & Kelly [18] have therefore shown that a gravity-driven flow due to the plate inclination breaks the isotropy of the long-wave thermocapillary instability and aligns the structure with the flow. The wavelength of the instability, however, remains unchanged, at least in the linear regime.…”

Section: Introductionmentioning

confidence: 99%

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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Surface wave and thermocapillary instabilities in a liquid film flow

Cited by 101 publications

References 21 publications

Spontaneous channeling of solitary pulses in heated-film flows

Spontaneous channeling of solitary pulses in heated-film flows

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

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

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