Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses—Theory

Abstract

Deformations of drops and bubbles opposed by surface tension and driven by radiation stresses at the interface are calculated using spherical harmonic expansions for the radial and tangential stresses. Superimposed acoustic waves produce stresses which oscillate at the difference frequency ω of the waves in addition to static stresses. When the effects of viscosity on the acoustic waves are omitted, the tangential radiation stress vanishes; a procedure is proposed for calculating the radial stresses from the theory for ’’Acoustic Radiation Pressure on a Compressible Sphere’’ [K. Yosioka and Y. Kawasima, Acustica 5, 167–173 (1955)]. The calculation of the response assumes incompressible second-order flow and omits the body forces which are normally asociated with acoustic streaming. Resonance phase shifts and enhancements of the response should occur when ω is close to the natural oscillation frequency of a mode. Quadrupole resonance phase shifts and enhancements have been observed by the author [J. Acoust. Soc. Am. 67, 27–37 (1980)]. Diverse applications of the theory include the possibilities of: inference of the interfacial tension from the response; emulsification by exciting large amplitude oscillations; and deformation or splitting of bubbles by radiation stresses. The decay time of free oscillation is also calculated; a new term is found which is small but significant for drops surrounded by a liquid and supplements the theory for ’’The Oscillations of a Fluid Droplet Immersed in Another Fluid’’ [C. A. Miller and L. E. Scriven, J. Fluid Mech. 32, 417–435 (1968)].