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Capillary Drops: Contact angle hysteresis and sticking drops

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Abstract

This paper is concerned with the homogenization of a capillary equation for liquid drops lying on an inhomogeneous solid plane. We show in particular that the homogenization of the Young–Laplace law leads to a contact angle condition of the form \(\cos \gamma \in [\beta_{1},\beta_{2}]\), which justifies the so-called contact angle hysteresis phenomenon.

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References

  1. Caffarelli L.A., Córdoba A. (1993) An elementary regularity theory of minimal surfaces. Differ. Integral Equ. 6(1): 1–13

    MATH  Google Scholar 

  2. Caffarelli, L.A., Lee, K.-A., Mellet, A.: Homogenization and flame propagation in periodic excitable media: The asymptotic speed of propagation. Commum. Pure Appl. Math. (2006) (in press)

  3. Caffarelli, L.A., Mellet, A.: Capillary drops on an inhomogeneous surface. Preprint (2005)

  4. Dussan, V., Chow, R.: On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. J. Fluid Mech. 137, 1–29

  5. Finn R., Shinbrot M. (1988) The capillary contact angle. II. The inclined plane. Math. Methods Appl. Sci. 10(2): 165–196

    Article  MATH  MathSciNet  Google Scholar 

  6. Finn R. (1986) Equilibrium Capillary Surfaces. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  7. Giusti E. (1984) Minimal Surfaces and Functions of Bounded Variation. Birkhauser, Basel

    MATH  Google Scholar 

  8. Gonzalez E., Massari U., Tamanini I. (1983) On the regularity of boundaries of sets minimizing perimeter with volume constraint. Indiana Univ. Math. J. 32, 25–37

    Article  MATH  MathSciNet  Google Scholar 

  9. Hocking L.M. (1995) On contact angles in evaporating liquids. Phys. Fluids 7(12): 2950–2955

    Article  MATH  MathSciNet  Google Scholar 

  10. Hocking L.M. (1995) The wetting of a plane surface by a fluid. Phys. Fluids 7(6): 1214–1220

    Article  MATH  MathSciNet  Google Scholar 

  11. Huh, C., Mason, S.G.: Effects of surface roughness on wetting (theoretical). J. Colloid Interface Sci. 60, 11–38

  12. Joanny, J.-F., de Gennes, P.-G.: A model for contact angle hysteresis. J. Chem. Phys. 81 (1984)

  13. Leger L., Joanny J.-F. (1992) Liquid spreading. Rep. Prog. Phys. 55, 431–486

    Article  Google Scholar 

  14. Wente H.C. (1980) The symmetry of sessile and pendent drop. Pac. J. Math. 88, 387–397

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    L. A. Caffarelli & A. Mellet

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  1. L. A. Caffarelli
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  2. A. Mellet
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Correspondence to L. A. Caffarelli.

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Caffarelli, L.A., Mellet, A. Capillary Drops: Contact angle hysteresis and sticking drops. Calc. Var. 29, 141–160 (2007). https://doi.org/10.1007/s00526-006-0036-y

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  • DOI: https://doi.org/10.1007/s00526-006-0036-y

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