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The Force Singularity for Partially Immersed Parallel Plates

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Abstract

In earlier work, we provided a general description of the forces of attraction and repulsion, encountered by two parallel vertical plates of infinite extent and of possibly differing materials, when partially immersed in an infinite liquid bath and subject to surface tension forces. In the present study, we examine some unusual details of the exotic behavior that can occur at the singular configuration separating infinite rise from infinite descent of the fluid between the plates, as the plates approach each other. In connection with this singular behavior, we present also some new estimates on meniscus height details.

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References

  1. Laplace, P.S.: Traité de mécanique céleste, oeuvres complète, vol. 4, Gauthier-Villars, Paris, 1805, Supplément 1, livre X, pp. 771–777. Supplément 2, livre X, pp. 909–945

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

    Article  ADS  MATH  Google Scholar 

  3. Finn R., Lu D.: Mutual attractions of partially immersed parallel plates. J. Math. Fluid Mech. 15(2), 273–301 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Bhatnagar, R., Finn, R.: Attractions and repulsions of parallel plates partially immersed in a liquid bath: III. Bound. Value Probl. 2013, 277 (2013)

  5. Aspley A., He C., McCuan J.: Force profiles for parallel plates partially immersed in a liquid bath. J. Math. Fluid Mech. 17(1), 87–102 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Bhatnagar, R., Finn, R.: Addenda to the preceding paper. J. Math. Fluid Mech. Following in this issue

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

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  9. Bhatnagar, R., Finn, R.: On the capillarity equation in two dimensions. J. Math. Fluid Mech. Preceding in this issue

  10. Miersemann, E.: Under Lecture Notes “Liquid Interfaces” (Version December 2013), p. 122. http://www.math.uni-leipzig.de/miersemann/

  11. Bhatnagar, R., Finn, R.: Comments relating to a paper by Vella and Mahadevan. (submitted)

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Authors and Affiliations

  1. Department of Biochemistry and Biophysics, California Institute for Quantitative Biosciences, University of California at San Franciso, San Francisco, CA, 94158, USA

    Rajat Bhatnagar

  2. Mathematics Department, Stanford University, Stanford, CA, 94025, USA

    Robert Finn

Authors
  1. Rajat Bhatnagar
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  2. Robert Finn
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Correspondence to Robert Finn.

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Bhatnagar, R., Finn, R. The Force Singularity for Partially Immersed Parallel Plates. J. Math. Fluid Mech. 18, 739–755 (2016). https://doi.org/10.1007/s00021-016-0260-y

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  • DOI: https://doi.org/10.1007/s00021-016-0260-y

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