Stability and evolution of a dry spot

Lopez, Patrice; Miksis, Michael J.; Bankoff, S. G.

doi:10.1063/1.1369607

Cited by 26 publications

(33 citation statements)

References 27 publications

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“…[37] and [38] for example, for the Newtonian case) additional phenomena come into play, providing other directions in which the analysis could be generalised.…”

Section: Discussionmentioning

confidence: 98%

Surface-tension-driven dewetting of Newtonian and power-law fluids

Flitton

King

2004

J Eng Math

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The dewetting over a planar substrate of a thin layer of highly viscous fluid under the action of surface tension is considered, with a doubly-nonlinear fourth-order degenerate parabolic equation governing the flow of a power-law fluid. Asymptotic methods are applied to analyse the motion in the shear-thinning, shear-thickening and Newtonian cases, the last of these corresponding mathematically to a critical value of the relevant exponent. In particular, the role played by the local behaviour in the neighbourhood of the contact line is analysed and the dependence of the one-dimensional large-time dewetting behaviour on the fluid's constitutive properties characterised. Stability issues are also touched upon.

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“…[37] and [38] for example, for the Newtonian case) additional phenomena come into play, providing other directions in which the analysis could be generalised.…”

Section: Discussionmentioning

confidence: 98%

Surface-tension-driven dewetting of Newtonian and power-law fluids

Flitton

King

2004

J Eng Math

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“…The shape and stability of a hole in a static liquid film on a planar substrate was studied by Taylor & Michael [26], and subsequently revisited by Sharma & Ruckenstein [23], Moriarty & Schwartz [16], Wilson & Terrill [33], Wilson & Duffy [31] and López, Miksis & Bankoff [12]. The formation of rivulets and dry patches at an advancing contact line has been studied intensively both theoretically and experimentally (see, for example, the work of Huppert [11] and Troian et al [28] and the recent review article by Oron, Davis & Bankoff [18]) but, despite considerable advances, remains only partly understood.…”

Section: Introductionmentioning

confidence: 99%

On a slender dry patch in a liquid film draining under gravity down an inclined plane

2001

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This version is available at https://strathprints.strath.ac.uk/2037/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the (Received 9 October 1998; revised 21 February 2000) In this paper two similarity solutions describing a steady, slender, symmetric dry patch in an infinitely wide liquid film draining under gravity down an inclined plane are obtained. The first solution, which predicts that the dry patch has a parabolic shape and that the transverse profile of the free surface always has a monotonically increasing shape, is appropriate for weak surface-tension effects and far from the apex of the dry patch. The second solution, which predicts that the dry patch has a quartic shape and that the transverse profile of the free surface has a capillary ridge near the contact line and decays in an oscillatory manner far from it, is appropriate for strong surface-tension effects (in particular, when the plane is nearly vertical) and near (but not too close) to the apex of the dry patch. With the average volume flux per unit width (or equivalently with the uniform height of the layer far from the dry patch) prescribed, both solutions contain a free parameter. For each value of this parameter there is a unique solution in the first case and either no solution or a one-parameter family of solutions in the second case. The solutions capture some of the qualitative features observed in experiments.

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“…Despite the association of a capillary ridge with the fingering instability in coating flows over flat surfaces, this result does not hold for flow over topographical features. 25,26 and the stability of stationary capillary ridges induced by topographical features, and also links the instability to the internal flow pattern of the film.…”

Section: Introductionmentioning

confidence: 99%

Generalized linear stability of noninertial coating flows over topographical features

Davis

Troian

2005

Physics of Fluids

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The transient evolution of perturbations to steady lubrication flow over a topographically patterned surface is investigated via a nonmodal linear stability analysis of the non-normal disturbance operator. In contrast to the capillary ridges that form near moving contact lines, the stationary capillary ridges near trenches or elevations have only stable eigenvalues. Minimal transient amplification of perturbations occurs, regardless of the magnitude or steepness of the topographical features. The absence of transient amplification and the stability of the ridge are explained on physical grounds. By comparison to unstable ridge formation on smooth, flat, and homogeneous surfaces, the lack of closed, recirculating streamlines beneath the capillary ridge is linked to the linear stability.

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Stability and evolution of a dry spot

Cited by 26 publications

References 27 publications

Surface-tension-driven dewetting of Newtonian and power-law fluids

Surface-tension-driven dewetting of Newtonian and power-law fluids

On a slender dry patch in a liquid film draining under gravity down an inclined plane

Generalized linear stability of noninertial coating flows over topographical features

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