Stabilizing the Advancing Front of Thermally Driven Climbing Films

Kataoka, Dawn E.; Troian, Sandra M.

doi:10.1006/jcis.1998.5499

Cited by 54 publications

(51 citation statements)

References 16 publications

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“…This mechanism is quite different, however, from the fingering behavior observed at the leading edge of other free surface spreading problems, like the flow down an inclined plane 30,31 or the thermocapillary driven spreading of a thin liquid film. 32,33 In these other spreading processes, the instability occurs right at the leading edge and causes the spreading front to separate into long narrow rivulets which never undergo spreading, shielding, or tip-splitting. Furthermore, when the amplitude of the advancing ridge approaches values on the order of the thickness of the pre-existing liquid film, the fingering disappears altogether, in sharp contrast to a spreading surfactant film.…”

Section: A Linearized Transient Responsementioning

confidence: 99%

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Matar

Troian

1999

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We describe the response of an insoluble surfactant monolayer spreading on the surface of a thin liquid film to small disturbances in the film thickness and surfactant concentration. The surface shear stress, which derives from variations in surfactant concentration at the air-liquid interface, rapidly drives liquid and surfactant from the source toward the distal region of higher surface tension. A previous linear stability analysis of a quasi-steady state solution describing the spreading of a finite strip of surfactant on a thin Newtonian film has predicted only stable modes. ͓Dynamics in Small Confining Systems III, Materials Research Society Symposium Proceedings, edited by J. M. Drake, J. Klafter, and E. R. Kopelman ͑Materials Research Society, Boston, 1996͒, Vol. 464, p. 237; Phys. Fluids A 9, 3645 ͑1997͒; O. K. Matar Ph.D. thesis, Princeton University, Princeton, NJ, 1998͔. A perturbation analysis of the transient behavior, however, has revealed the possibility of significant amplification of disturbances in the film thickness within an order one shear time after the onset of flow ͓Phys. Fluids A 10, 1234 ͑1998͒; ''Transient response of a surfactant monolayer spreading on a thin liquid film: Mechanism for amplification of disturbances,'' submitted to Phys. Fluids͔. In this paper we describe the linearized transient behavior and interpret which physical parameters most strongly affect the disturbance amplification ratio. We show how the disturbances localize behind the moving front and how the inclusion of van der Waals forces further enhances their growth and lifetime. We also present numerical solutions to the fully nonlinear 2D governing equations. As time evolves, the nonlinear system sustains disturbances of longer and longer wavelength, consistent with the quasi-steady state and transient linearized descriptions. In addition, for the parameter set investigated, disturbances consisting of several harmonics of a fundamental wavenumber do not couple significantly. The system eventually singles out the smallest wavenumber disturbance in the chosen set. The summary of results to date seems to suggest that the fingering process may be a transient response which nonetheless has a dramatic influence on the spreading process since the digitated structures redirect the flux of liquid and surfactant to produce nonuniform surface coverage. © 1999 American Institute of Physics. ͓S1054-1500͑99͒02001-7͔ Surfactant molecules play a vital role in many biological and industrial processes because of their native ability to lower surface tension in proportion to their concentration. Their presence greatly improves the wetting and spreading capability of commonplace substances like inks, paints, and herbicides. Lung surfactants produced in the alveoli are critical in maintaining lung compliance. A deficiency in lung surfactant production, for example, is known to cause pulmonary edema and other respiratory difficulties. When surfactant molecules contact a liquid surface of higher surface tension, a shear stress develops...

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Section: A Linearized Transient Responsementioning

confidence: 99%

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Matar

Troian

1999

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…This updated interpretation was shown 20 to give consistent results for prior studies. 31,32 While the relevance of this new interpretation to the present problem is less clear because the neutrally stable mode for q =0 is continuous and the unstable modes are discrete, using this enhanced interpretation does not qualitatively alter the results shown in Fig. 10 because the Ė n for the discrete modes is much larger in magnitude than for the mode corresponding to q =0.…”

Section: B Energy Analysismentioning

confidence: 78%

“…10. The original interpretation of the energy analysis for spreading films [30][31][32] was subsequently improved 20,33 by considering not the absolute energy production rates of various terms but instead the deviation of the energy gains relative to their values for the transversely invariant, neutrally stable mode, Ė n ͑q͒ − Ė n ͑q =0͒. This updated interpretation was shown 20 to give consistent results for prior studies.…”

Section: B Energy Analysismentioning

confidence: 93%

“…Instability can occur even for a Biot number ͑Bi͒ of zero, in contrast to the thermocapillary instability of a thin film flowing over a uniformly heated plate. 29 The energy analysis of the governing linearized operator, which was introduced for spreading liquid films, [30][31][32] was subsequently interpreted 20,33 not based on the absolute energy production rates of various terms but instead on the deviation of the energy gains relative to their values for the transversely invariant, neutrally stable mode. It was revealed from this revised interpretation that the dominant instability mechanisms for zero Biot number are streamwise flow from the capillary pressure gradient ͑induced by the fluid ridge͒ and from gravity ͑mobility differences between slightly perturbed regions of the film͒.…”

Section: Introductionmentioning

confidence: 99%

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

Tiwari¹,

Davis²

2010

Physics of Fluids

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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.

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“…In particular, the behavior of thin Newtonian liquid films driven to spread by thermocapillary forcing has been studied during the past few years. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] A thin wetting film in contact with a solid surface bearing a thermal gradient experiences a surface shear stress that forces the liquid to spread from warmer to cooler regions. Complete surface coverage may be compromised by the nucleation of holes or dry spots in the spreading film or by a rivulet instability at the leading edge that can leave strips of the surface dry and exposed.…”

Section: Introductionmentioning

confidence: 99%

Transient dynamics and structure of optimal excitations in thermocapillary spreading: Precursor film model

2006

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Linearized modal stability theory has shown that the thermocapillary spreading of a liquid film on a homogeneous, completely wetting surface can produce a rivulet instability at the advancing front due to formation of a capillary ridge. Mechanisms that drain fluid from the ridge can stabilize the flow against rivulet formation. Numerical predictions from this analysis for the film speed, shape, and most unstable wavelength agree remarkably well with experimental measurements even though the linearized disturbance operator is non-normal, which allows transient growth of perturbations. Our previous studies using a more generalized nonmodal stability analysis for contact lines models describing partially wetting liquids ͑i.e., either boundary slip or van der Waals interactions͒ have shown that the transient amplification is not sufficient to affect the predictions of eigenvalue analysis. In this work we complete examination of the various contact line models by studying the influence of an infinite and flat precursor film, which is the most commonly employed contact line model for completely wetting films. The maximum amplification of arbitrary disturbances and the optimal initial excitations that elicit the maximum growth over a specified time, which quantify the sensitivity of the film to perturbations of different structure, are presented. While the modal results for the three different contact line models are essentially indistinguishable, the transient dynamics and maximum possible amplification differ, which suggests different transient dynamics for completely and partially wetting films. These differences are explained by the structure of the computed optimal excitations, which provides further basis for understanding the agreement between experiment and predictions of conventional modal analysis.

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Stabilizing the Advancing Front of Thermally Driven Climbing Films

Cited by 54 publications

References 16 publications

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

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

Transient dynamics and structure of optimal excitations in thermocapillary spreading: Precursor film model

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