Corner singularity of a contact line moving on a solid substrate

Howard A. Stone; Laurent Limat; Stephen K. Wilson; J. M. Flesselles; Thomas Podgorski

doi:10.1016/S1631-0705(02)01288-4

Corner singularity of a contact line moving on a solid substrate

Howard A. Stone, Laurent Limat, Stephen K. Wilson, J. M. Flesselles, Thomas Podgorski

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

In conditions of partial wetting and at sufficiently high capillary number Ca, a dynamic contact line that recedes on a solid surface assumes a 'saw-tooth' shape. We show that the flow inside this liquid 'corner' is a similarity solution of the lubrication equations governing steady thin-film flows in which the free surface is cone shaped. The interface slope Ω defined in its symmetry plane is linked to the corner angle 2φ by the approximate relationship Ω ³ ≈ (3/2)Ca tan ² φ. We also suggest a possible explanation of droplet emission from the corner which occurs when φ reaches π/6.

Original language	English (US)
Pages (from-to)	103-110
Number of pages	8
Journal	Comptes Rendus Physique
Volume	3
Issue number	1
DOIs	https://doi.org/10.1016/S1631-0705(02)01288-4
State	Published - 2002

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Keywords

Contact lines
Dewetting
Film flows
Lubrication theory
Singularities
Wetting

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10.1016/S1631-0705(02)01288-4

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@article{9adf593126b8444782413aae64c34968,

title = "Corner singularity of a contact line moving on a solid substrate",

abstract = " In conditions of partial wetting and at sufficiently high capillary number Ca, a dynamic contact line that recedes on a solid surface assumes a 'saw-tooth' shape. We show that the flow inside this liquid 'corner' is a similarity solution of the lubrication equations governing steady thin-film flows in which the free surface is cone shaped. The interface slope Ω defined in its symmetry plane is linked to the corner angle 2φ by the approximate relationship Ω 3 ≈ (3/2)Ca tan 2 φ. We also suggest a possible explanation of droplet emission from the corner which occurs when φ reaches π/6.",

keywords = "Contact lines, Dewetting, Film flows, Lubrication theory, Singularities, Wetting",

author = "Stone, {Howard A.} and Laurent Limat and Wilson, {Stephen K.} and Flesselles, {J. M.} and Thomas Podgorski",

note = "Funding Information: This note is a summary of discussions between the authors that took place during the stay of Prof. H.A. Stone and Dr. S.K. Wilson at ESPCI in June 2000, as Visiting Professors. We thank ESPCI and the City of Paris for their financial support. More recent observations of the drops from the side [10] support our model, especially with respect to the conical structure of the interface and to the non-zero value of the apparent contact angle implied by Fig. 3a.",

year = "2002",

doi = "10.1016/S1631-0705(02)01288-4",

language = "English (US)",

volume = "3",

pages = "103--110",

journal = "Comptes Rendus Physique",

issn = "1631-0705",

publisher = "Elsevier Masson",

number = "1",

}

TY - JOUR

T1 - Corner singularity of a contact line moving on a solid substrate

AU - Stone, Howard A.

AU - Limat, Laurent

AU - Wilson, Stephen K.

AU - Flesselles, J. M.

AU - Podgorski, Thomas

N1 - Funding Information: This note is a summary of discussions between the authors that took place during the stay of Prof. H.A. Stone and Dr. S.K. Wilson at ESPCI in June 2000, as Visiting Professors. We thank ESPCI and the City of Paris for their financial support. More recent observations of the drops from the side [10] support our model, especially with respect to the conical structure of the interface and to the non-zero value of the apparent contact angle implied by Fig. 3a.

PY - 2002

Y1 - 2002

N2 - In conditions of partial wetting and at sufficiently high capillary number Ca, a dynamic contact line that recedes on a solid surface assumes a 'saw-tooth' shape. We show that the flow inside this liquid 'corner' is a similarity solution of the lubrication equations governing steady thin-film flows in which the free surface is cone shaped. The interface slope Ω defined in its symmetry plane is linked to the corner angle 2φ by the approximate relationship Ω 3 ≈ (3/2)Ca tan 2 φ. We also suggest a possible explanation of droplet emission from the corner which occurs when φ reaches π/6.

AB - In conditions of partial wetting and at sufficiently high capillary number Ca, a dynamic contact line that recedes on a solid surface assumes a 'saw-tooth' shape. We show that the flow inside this liquid 'corner' is a similarity solution of the lubrication equations governing steady thin-film flows in which the free surface is cone shaped. The interface slope Ω defined in its symmetry plane is linked to the corner angle 2φ by the approximate relationship Ω 3 ≈ (3/2)Ca tan 2 φ. We also suggest a possible explanation of droplet emission from the corner which occurs when φ reaches π/6.

KW - Contact lines

KW - Dewetting

KW - Film flows

KW - Lubrication theory

KW - Singularities

KW - Wetting

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U2 - 10.1016/S1631-0705(02)01288-4

DO - 10.1016/S1631-0705(02)01288-4

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SN - 1631-0705

VL - 3

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EP - 110

JO - Comptes Rendus Physique

JF - Comptes Rendus Physique

IS - 1

ER -

Corner singularity of a contact line moving on a solid substrate

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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