Review of theory for scattering and extinction cross-sections, damping factors and resonance frequencies of spherical gas bubbles

Ainslie, M.A. and Leighton, T.G. (2011) Review of theory for scattering and extinction cross-sections, damping factors and resonance frequencies of spherical gas bubbles. Journal of the Acoustical Society of America, 130 (5), 3184-3208. (doi:10.1121/1.3628321).

Abstract

Perhaps the most familiar concepts when discussing acoustic scattering by bubbles are the resonance
frequency for bubble pulsation, the bubbles’ damping, and their scattering and extinction
cross-sections, all of which are used routinely in oceanography, sonochemistry, and biomedicine.
The apparent simplicity of these concepts is illusory: there exist multiple, sometimes contradictory
definitions for their components. This paper reviews expressions and definitions in the literature for
acoustical cross-sections, resonance frequencies, and damping factors of a spherically pulsating gas
bubble in an infinite liquid medium, deriving two expressions for “resonance frequency” that are
compared and reconciled with two others from the reviewed literature. In order to prevent errors,
care is needed by researchers when combining results from different publications that might have
used internally correct but mutually inconsistent definitions. Expressions are presented for acoustical
cross-sections associated with forced pulsations damped by liquid shear and (oft-neglected)
bulk or dilatational viscosities, gas thermal diffusivity, and acoustic re-radiation. The concept of a
dimensionless “damping coefficient” is unsuitable for radiation damping because different crosssections
would require different functional forms for this parameter. Instead, terms based on the ratio
of bubble radius to acoustic wavelength are included explicitly in the cross-sections where
needed.

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Contributors

Author: T.G. Leighton

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