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Stability of axisymmetric liquid bridges

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Abstract

Based on the Weierstrass representation of second variation, we develop a non-spectral theory of stability for isoperimetric problem with minimized and constrained two-dimensional functionals of general type and free endpoints allowed to move along two given planar curves. We establish the stability criterion and apply this theory to the axisymmetric liquid bridge between two axisymmetric solid bodies without gravity to determine the stability of menisci with free contact lines. For catenoid and cylinder menisci and different solid shapes, we determine the stability domain. The other menisci (unduloid, nodoid and sphere) are considered in a simple setup between two plates. We find the existence conditions of stable unduloid menisci with and without inflection points.

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Authors and Affiliations

  1. Department of Civil Engineering, Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Leonid G. Fel

  2. Stowers Institute for Medical Research, 1000 E 50th St, Kansas City, MO, 64110, USA

    Boris Y. Rubinstein

Authors
  1. Leonid G. Fel
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  2. Boris Y. Rubinstein
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Correspondence to Leonid G. Fel.

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Fel, L.G., Rubinstein, B.Y. Stability of axisymmetric liquid bridges. Z. Angew. Math. Phys. 66, 3447–3471 (2015). https://doi.org/10.1007/s00033-015-0555-5

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  • DOI: https://doi.org/10.1007/s00033-015-0555-5

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