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Moving Common Lines, Thin Films, and Dynamic Contact Angles

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Modelling Macroscopic Phenomena at Liquid Boundaries

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 318))

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Abstract

When a common line or three-phase line of contact moves over a rigid solid, an unbounded force must be generated at the common line, if the usual no-slip boundary condition of fluid mechanics is valid.

Since an unbounded force is unrealistic, our description of the physics in this statement must be incorrect. There are various possibilities. Real solids are not rigid. Perhaps the no-slip boundary condition fails within the immediate neighborhood of the common line. In some situations there is undoubtedly mass transfer in the neighborhood of the apparent common line, and there is displacement over an existing film of fluid without a common line ever having been formed. In other situations, a sequence of stationary common lines may be formed in the thin film of fluid within the immediate neighborhood of the apparent common line, giving the appearance of a moving common line to an observer on the macroscale.

Section 1 is a review of what is known about moving common lines on relatively rigid solids. In Sec. 2, I illustrate with at least one computation that continuum mechanics can be applied successfully to very thin films, such as those within the immediate neighborhood of the common line. In Sec. 3 I discuss contact angles, with a demonstration computation for the dynamic contact angle as a function of the apparent speed of displacement of the common line.

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Authors and Affiliations

  1. Texas A&M University, College Station, TX, USA

    J. C. Slattery

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  1. IPPT-PAN, Warsaw, Poland

    W. Kosinski

  2. University of Strathclyde, UK

    A. I. Murdoch

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Slattery, J.C. (1991). Moving Common Lines, Thin Films, and Dynamic Contact Angles. In: Kosinski, W., Murdoch, A.I. (eds) Modelling Macroscopic Phenomena at Liquid Boundaries. International Centre for Mechanical Sciences, vol 318. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2612-7_6

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  • DOI: https://doi.org/10.1007/978-3-7091-2612-7_6

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  • Print ISBN: 978-3-211-82327-9

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