A long history of peristaltic perturbations
DOI: 10.1063/1.2709539
Yves Pomeau and Emmanuel Villermaux, in their article “Two Hundred Years of Capillarity Research” (Physics Today, March 2006, page 39 ), give a comprehensive overview. It is noteworthy, however, that the stability condition mentioned in the section on breakup and fragmentation was known decades before Joseph Antoine Ferdinand Plateau’s 1873 publication cited it. The condition that peristaltic perturbations are naturally unstable if their longitudinal wavelength is larger than the cylinder’s circumference was known to Plateau as early as 1850. 1 His analytical result was quoted by August Beer in 1855. 2 In correspondence with William Thomson (later Lord Kelvin), James Clerk Maxwell referred to this limiting condition in 1857. 3 Maxwell’s phrase “it is easy to show” suggests he had derived the result, though it is plausible he also read the earlier discussion by Plateau. Some of these references have been noted much more recently, in conjunction with an investigation of the nonlinear capillary response of liquid cylinders. 4
References
1. J. Plateau, Ann. Phys. Chem. 80, 566 (1850).
2. A. Beer, Ann. Phys. Chem. 96, 1 (1855);
96, 210 (1855).3. J. C. Maxwell to W. Thomson, letter dated 24 August 1857, reproduced in S. G. Brush, C. W. F. Everitt, E. Garber, eds.,Maxwell on Saturn’s Rings, MIT Press, Cambridge, MA (1983), p. 44.
See also P. M. Harman, ed., The Scientific Letters and Papers of James Clerk Maxwell: Volume 1, 1846–1862, Cambridge U. Press, New York (1990), p. 533.4. W. Wei, D. B. Thiessen, P. L. Marston, Phys. Rev. E. 72, 067304 (2005).
More about the Authors
Philip L. Marston. (marston@wsu.edu) Washington State University, Pullman, US .
