Inviscid dynamics of a wet foam drop with monodisperse bubble size distribution

J. Gregory McDaniel, Iskander Akhatov, R. Glynn Holt

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Motivated by recent experiments involving the acoustic levitation of foam drops, we develop a model for nonlinear oscillations of a spherical drop composed of monodisperse aqueous foam with void fraction below 0.1. The model conceptually divides a foam drop into many cells, each cell consisting of a spherical volume of liquid with a bubble at its center. By treating the liquid as incompressible and inviscid, a nonlinear equation is obtained for bubble motion due to a pressure applied at the outer radius of the liquid sphere. Upon linearizing this equation and connecting the cells at their outer radii, a wave equation is obtained with a dispersion relation for the sound waves in a bubbly liquid. For the spherical drop, this equation is solved by a normal mode expansion that yields the natural frequencies as functions of standard foam parameters. Numerical examples illustrate how the analysis may be used to extract foam parameters, such as void fraction and bubble radius, from the experimentally measured natural frequencies of a foam drop.

Original languageEnglish
Pages (from-to)1886-1894
Number of pages9
JournalPhysics of Fluids
Volume14
Issue number6
DOIs
Publication statusPublished - Jun 2002
Externally publishedYes

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