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The Stability of Cylindrical Pendant Drops


About this Title

John McCuan

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 250, Number 1189
ISBNs: 978-1-4704-0938-8 (print); 978-1-4704-4202-6 (online)
DOI: https://doi.org/10.1090/memo/1189
Published electronically: September 7, 2017

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Table of Contents


Chapters

  • Introduction
  • Chapter 1. Normalization, stability condition, and elementary properties
  • Chapter 2. One Parameter Families; Definition of $s_2$
  • Chapter 3. Stability
  • Chapter 4. Infinitely long drops
  • Chapter 5. Zero gravity and soap bubbles
  • Chapter 6. Open problems
  • Appendix 1: Explicit formulas
  • Appendix 2: Sturm-Liouville Theory
  • Appendix 3: Elliptic integrals
  • Acknowledgement

Abstract


We consider the stability of certain liquid drops in a gravity field satisfying a mixed boundary condition. We also consider as special cases portions of cylinders that model either the zero gravity case or soap films with the same kind of boundary behavior.

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