Free-surface thin-film flows over uniformly heated topography

Saprykin, Sergey; Trevelyan, P. M. J.; Koopmans, R. J.; Kalliadasis, Serafim

doi:10.1103/physreve.75.026306

Cited by 60 publications

(68 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consequently, we will refer to rupture when the film reaches this minimal thickness, independently of the subsequent dynamics that depends on the nature of these intermolecular forces (see e.g. [29,30]), even though they could be easily incorporated in the model by a disjoining pressure term. Note, therefore, that the terms 'dewetting/rewetting' are used hereinafter to indicate the trend of the film thickness evolution in thin regions, i.e.…”

Section: Numerical Resultsmentioning

confidence: 99%

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

et al. 2008

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

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

et al. 2008

Self Cite

View full text Add to dashboard Cite

show abstract

“…4 This one-sided evaporation model has recently been extended to include a detailed analysis of the vapor diffusion, 5 and other recent studies focus on the influence of wall topography. 6,7 The stability of a liquid film flowing over a uniformly heated, inclined plane has also been studied extensively. For example, Joo et al 8 developed a model to study the competition of the surface-wave instability due to inertia with thermocapillary and/or evaporative instabilities, which extended the work of Burelback et al 4 to inclined surfaces with gravity-driven flow and hydrostatic pressure.…”

Section: Introductionmentioning

confidence: 99%

Linear stability of a volatile liquid film flowing over a locally heated surface

Tiwari

Davis

2009

Physics of Fluids

View full text Add to dashboard Cite

The dynamics and linear stability of a volatile liquid film flowing over a locally heated surface are investigated. The temperature gradient at the leading edge of the heater induces a gradient in surface tension that leads to the formation of a pronounced capillary ridge. Lubrication theory is used to develop a model for the film evolution that contains three key dimensionless groups: a Marangoni parameter ͑M͒, an evaporation number ͑E͒, and a measure of the vapor pressure driving force for evaporation ͑K͒, which behaves as an inverse Biot number. The two-dimensional, steady solutions for the local film thickness are computed as functions of these parameters. A linear stability analysis of these steady profiles with respect to perturbations in the spanwise direction reveals that the operator of the linearized system can have both a discrete and a continuous spectrum. The continuous spectrum exists for all values of the spanwise wave number and is always stable. The discrete spectrum, which corresponds to eigenfunctions localized around the ridge, appears for values of M larger than a critical value for a finite band of wave numbers separated from zero. Above a second, larger critical value of M, a portion of the discrete spectrum becomes unstable, corresponding to rivulet formation at the forward portion of the capillary ridge. For sufficiently large heat transfer at the free surface, due either to phase change or to convection, a second band of unstable discrete modes appears, which is associated with an oscillatory, thermocapillary instability above the heater. The critical Marangoni parameter above which instability develops, M crit ͑K , E͒, has a nonmonotonic dependence on the steepness of the temperature increase at the heater, in contrast to the monotonic decrease for a nonvolatile film at vanishing Biot number. An energy analysis reveals that the dominant instability mechanism resulting from perturbations to the film thickness is either streamwise capillary flow or gravity for weakly volatile fluids and thermocapillary flow due to spanwise temperature gradients for more volatile fluids. The stability results are rather sensitive to the steepness of the temperature increase and heater width due to the nonlinear coupling of gravity, capillary pressure gradients, thermocapillary flow, and evaporation through the base states.

show abstract

“…Further details on the reduction of the NavierStokes and energy equations can be found in previous work. 24,47 For consistency with some previous studies of instabilities in thin liquid films flowing over locally heated, planar surfaces, [24][25][26] the temperature profile along the substrate is modeled as…”

Section: ͑2͒mentioning

confidence: 99%

“…Such ridges that form in response to step-down, mound, and trench features are stable to transverse perturbations. 40,41 The nonlinear evolution equations for the local thickness of liquid films flowing over surfaces with nonuniform heating, 20 topographical features, 38 and both types of heterogeneity 4,47 have been derived previously using a longwave lubrication analysis, so only a brief derivation is given here. A linear variation in surface tension with temperature is assumed, ␥͑T ͒ = ␥ 0 − ␥ T ͑T − T ϱ ͒, where ␥ T = ‫␥ץ‬ / ‫ץ‬T Ͼ 0 and ␥ 0 is the surface tension at the ambient temperature T ϱ .…”

Section: Problem Formulationmentioning

confidence: 99%

“…Gambaryan-Roisman and Stephan 45 and Helbig et al 46 investigated the influence of longitudinal minigrooves aligned with the flow on the stability and heat transfer in liquid films falling as rivulets along a structured wall maintained at a constant temperature. The dynamics of a liquid film on a heated horizontal wall with topography has also been considered recently for chemically uniform 3 and heterogeneous 47 surfaces.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

Tiwari¹,

Davis²

2010

Physics of Fluids

View full text Add to dashboard Cite

A long-wave lubrication analysis is used to study the influence of topographical features on the linear stability of noninertial coating flows over a locally heated surface. Thin liquid films flowing over surfaces with localized heating develop a pronounced ridge at the upstream edge of the heater. This ridge becomes unstable to transverse perturbations above a critical Marangoni number and evolves into an array of rivulets even in the limit of noninertial flow. Similar fluid ridges form near topographical variations on isothermal surfaces, but these ridges are stable to perturbations. The influence of basic topographical features on the stability of the locally heated film is analyzed. In contrast to its destabilizing influence on liquid films resting on heated, horizontal walls, even such nonoptimized topography is found to be effective at stabilizing the flowing film with respect to rivulet formation and subsequent rupture. Optimal topographical features that suppress variations in the free-surface shape are also determined. The critical Marangoni number at the instability threshold increases substantially with appropriate topography even for nonzero Biot numbers. An energy analysis is used to provide insight into the mechanism by which the topography stabilizes the flow. Because the stabilizing effect of the topographical features is only weakly sensitive to the governing parameters and particular temperature profile, the use of such features could be a simple alternative in applications to more complicated methods of stabilization.

show abstract

Free-surface thin-film flows over uniformly heated topography

Cited by 60 publications

References 53 publications

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

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

Linear stability of a volatile liquid film flowing over a locally heated surface

Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

Contact Info

Product

Resources

About