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Mutual Attractions of Partially Immersed Parallel Plates

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We complete a study initiated in an earlier paper, on the horizontal attracting and repelling forces acting on two parallel semi-infinite plates, partly immersed in an infinite liquid bath and subject to capillary attractions in a uniform gravity field. We find a considerable range of behavior patterns, depending on the contact angles on the plate sides and on the plate separation, in ways that we did not anticipate.

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  1. Mariotte, E.: Œuvres: posthumous publication; Pierre Vander, Leyden (1717). See also: Ré édition. J. Peyroux, Bordeaux (2001)

  2. McCuan J.: A variational formula for floating bodies. Pac. J. Math. 231(1), 167–191 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Laplace, P.S.: Traité de mécanique céleste, Œuvres complète, vol. 4, Gauthier-Villars, Paris, 1805, Supplément 1, livre X, pp. 771–777. See also the annotated English translation by N. Bowditch 1839. Chelsea, New York (1966)

  4. Laplace, P.S.: Traité de mécanique céleste, Œuvres complète, vol. 4, Gauthier-Villars, Paris, 1806, Supplément 2, Livre X, pp. 909–945. See also the annotated English translation by N. Bowditch 1839. Chelsea, New York (1966)

  5. Finn R.: On Young’s Paradox, and the attractions of immersed parallel plates. Phys Fluids 22, 017103 (2010)

    Article  ADS  Google Scholar 

  6. von Segner, J.A.: Superficies fluidorum concavas ostendit. Comment. Soc. Reg. Göttingen 1(301), 1751

  7. Young T.: An essay on the cohesion of fluids. Philos. Trans. R. Soc. Lond. 95, 65–87 (1805)

    Article  Google Scholar 

  8. Lunati I.: Young’s law and the effects of interfacial energy on the pressure at the solid-fluid interface. Phys. Fluids 19, 118105 (2007)

    Article  ADS  Google Scholar 

  9. Shikhmurzaev Y.D.: On Young’s (1805) equation and Finn’s (2006) ‘counterexample’. Phys. Lett. A 372, 704–707 (2008)

    Article  ADS  MATH  Google Scholar 

  10. Finn R.: Comments related to my paper “The contact angle in capillarity”. Phys. Fluids 20, 107104 (2008)

    Article  ADS  Google Scholar 

  11. Finn, R., McCuan, J., Wente, H.C.: Thomas Young’s surface tension diagram: its history, legacy, and irreconcilabilities. J. Math. Fluid Mech. doi:10.1007/s00021-011-0079-5

  12. Finn R., Hwang J.-F.: On the comparison principle for capillary surfaces. J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 36(1), 131–134 (1989)

    MathSciNet  MATH  Google Scholar 

  13. Minkowski, H., Kapillarität. Enz. Mat. Wiss. Bd. 5-1, pp. 559–608. B.G. Teubner, Leipzig (1906)

  14. Finn, R.: Equilibrium Capillary Surfaces, Grundlehren Series 284. Springer, Berlin (1986)

  15. Finn, R.: Capillary surfaces. In: Françoise, J.-P., Naber, G.L., Tsou, S.T. (eds.) Encyclopedia of Mathematical Physics, pp. 431–445. Elsevier, Amsterdam (2006)

  16. Siegel D.: Height estimates for capillary surfaces. Pac. J. Math. 88, 471–516 (1980)

    Article  MATH  Google Scholar 

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Correspondence to Robert Finn.

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The former author dedicates his contribution in this work to the memory of Margaret Keidel, whose talents should have been better recognized.

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Finn, R., Lu, D. Mutual Attractions of Partially Immersed Parallel Plates. J. Math. Fluid Mech. 15, 273–301 (2013).

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