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Comparison of Rayleigh's, Herring's, and Gilmore's Models of Gas Bubbles

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Abstract:

Significant bubble wall positions computed in Rayleigh's, Herring's, modified Herring's, and Gilmore's models of freely oscillating gas bubbles are mutually compared. The computations were performed for a non-linear amplitude of bubble oscillationsA, ranging from 1 to 10. A is defined as the ratio of the maximum (R M) to the equilibrium (R e) radius of a bubble. Gilmore's model is used as a reference model and it is found that Rayleigh's model gives satisfactory results for amplitudes A ≦ 2, and both the original and the modified Herring models for amplitudes A ≦ 4.5.

Zusammenfassung

Es werden die Lagen einer Blasenwand, berechnet nach dem Rayleighschen, dem Herringschen, einem modifizierten Herringschen und dem Gilmoreschen Modell freischwingender Gasblasen miteinander verglichen. Die Berechnungen werden durchgeführt für einen Wertebereich der nichtlinearen Schwingungsamplitude A zwischen 1 und 10. Dabei ist A als das Verhältnis des Maximalradius zum Gleichgewichtsradius einer Blase definiert. Das Gilmoresche Modell wird als Referenzmodell benutzt; es zeigt sich, daß das Rayleighsche Modell zufriedenstellende Ergebnisse für Amplituden A = 2, das ursprüngliche und das modifizierte Herringsche Modell dagegen für Amplituden A ≦ 4,5 liefert.

Sommaire

On compare entre elles les positions significatives de la paroi d'une bulle de gaz en oscillation libre, ces positions ayant été calculées successivement à partir du modèle de Rayleigh, du modèle d'Herring, du modèle d'Herring modifié et du modèle de Gilmore. Les calculs ont été effectués pour diverses valeurs du paramètre A («amplitude» non-linéaire des oscillations d'une bulle) comprises entre 1 et 10. On définit A comme le rapport entre la valeur maximale R M et la valeur à l'équilibre R e du rayon de la bulle. Le modèle de Gilmore a été pris comme élément de référence. La comparaison montre que le modèle de Rayleigh donne satisfaction aux amplitudes A inférieures ou égales à 2 et que les deux modèles d'Herring restent satisfaisants jusqu'à A ≦ 4,5.

Document Type: Research Article

Publication date: January 1, 1986

More about this publication?
  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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