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Modelling Line Tension in Wetting

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Book cover Modeling of Soft Matter

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 141))

Abstract

Line tension can be viewed as the analogue, for three-phase contact, of surface tension. However, obtaining a coherent picture from the different avenues followed to model line tension is much harder than the analogous operation for surface tension. This essentially reflects the extreme sensitivity of line tension to the details of the model employed. Line tension has an impact on the equilibrium and stability of fluid droplets laid on a rigid substrate, in the presence of a vapor phase. In particular, the sign of line tension is a critical issue, that gave rise to conflicting interpretations. Here, we review the approaches to line tension from microscopic to macroscopic scales, stressing the mathematical problems involved. We also illustrate a stability criterion for wetting functionals to clarify the rôle of the sign of line tension. As an application, we discuss how stability of liquid bridges near the wetting or the dewetting transition mirrors the scaling laws for surface and line tension.

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Authors and Affiliations

  1. Dipartimento di Matematica, Istituto Nazionale di Fisica della Materia, Università di Pavia, Via Ferrata 1, 27100, Pavia, Italy

    Riccardo Rosso

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  1. Riccardo Rosso
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Editors and Affiliations

  1. School of Mathematics, University of Minnesota, USA

    Maria-Carme T. Calderer

  2. Cavendish Laboratory, Cambridge University, Cambridge

    Eugene M. Terentjev

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Rosso, R. (2005). Modelling Line Tension in Wetting. In: Calderer, MC.T., Terentjev, E.M. (eds) Modeling of Soft Matter. The IMA Volumes in Mathematics and its Applications, vol 141. Springer, New York, NY. https://doi.org/10.1007/0-387-32153-5_6

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