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Small Oscillations of a Soap Bubble
Author(s) -
Grinfeld P.
Publication year - 2012
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2011.00523.x
Subject(s) - inviscid flow , bubble , soap bubble , soap film , surface tension , dispersion (optics) , mechanics , physics , linearization , limit (mathematics) , compressibility , classical mechanics , mathematics , mathematical analysis , optics , thermodynamics , nonlinear system , quantum mechanics
We analyze the spectrum of small oscillations of a soap bubble surrounded by incompressible inviscid air. The analysis is based on the linearization of the exact system for the dynamics of free fluid films. The underlying model takes into account variations in the film's shape and thickness. The resulting dispersion relationship shows the fundamental interplay among these variations. In the limit of vanishing soap bubble mass, the presented dispersion relationship agrees with Rayleigh's classical formula for an oscillating liquid droplet under the influence of surface tension.