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Radial Oscillations of Gas-Vapor Bubbles in Liquids Part I: Mathematical Formulation

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A general mathematical formulation for small-amplitude, forced radial oscillations of an isolated bubble in a liquid-gas solution is given. The bubble content consists of a mixture of the vapor of the liquid and of the gas present in the solution. A special feature of the formulation is the use (if very general thermodynamic relations for mixtures. A careful discussion of the relevance of the theory for experimental investigations is also given. The spacial non-uniformities of the various fields (density, pressure, velocity, temperature and concentration) both inside and outside the bubble are taken into proper account.

Zusammenfassung

Es wird eine allgemeine, mathematische Beschreibung erzwungener Radialschwingungen kleiner Amplitude einer isolierten Blase in einer Flüssigkeits-Gas-Lösung angegeben. Der Blaseninhalt besteht aus einer Mischung von Dampf aus der Flüssigkeit und von in der Lösung vorliandenem Gas. Ein spezielles Merkmal der Beschreibung ist die Verwendung sehr allgemeiner, thermodynamischer Beziehungen für Mischungen. Die Relevanz der Theorie für experimentelle Untersuchungen wird einer sorgfältigen Diskussion unterzogen. Die räumliehen Ungleichförmigkeiten der verschiedenen Felder (Dichte, Druck, Schnelle, Temperatur und Konzentration) sowohl innerhalb als auch außerhalb der Blase werden in geeigneter Form berücksichtigt.

Sommaire

On propose une formulation mathématique générale décrivant les oscillations radiales forcées de faible amplitude d'une bulle isolée dans un liquide contenant des gaz en solution. Le contenu de la bulle est un mélange de la vapeur du liquide et des gaz qui y sont dissous. Un point fort de la présente théorie est l'emploi de relations thermodynamiques très générates concernant les mélanges. On discute soigneusement de l'adéquation vis-à-vis des études expérimentales sur le sujet. Il a été tenu compte, d'une manière convenable, du comportement non uniforme des champs de densité, pression, vitesse, température et concentration à l'intérieur et à l'extérieur de la bulle.
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Document Type: Research Article

Publication date: March 1, 1981

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  • 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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