Acoustic microstreaming around an isolated encapsulated microbubble.

An analytical theory has been developed to calculate microstreaming velocity inside and outside an encapsulated microbubble (EMB) in a viscous liquid produced by its oscillations driven by an ultrasound field, taking account of two predominant modes of the EMB's motion: a monopole (pulsation) and a dipole (translational harmonic vibrations). Analytical expressions of radial as well as tangential stresses are derived near the shell of the EMB. Numerical calculations in parameter regimes applicable to sonoporation are presented. For the calculation the following parameters unless specified otherwise are used: f=1 MHz, r(0)=2 microm, kappa=1.4, rho(L)=1000 kg/m(3), rho(s)=1100 kg/m(3), P(0)=100 kPa, micro(s)=0.05 Pa s, micro(L)=0.001 Pa s, sigma(1)=0.04 N/m, sigma(2)=0.005 N/m, and G(s)=15 MPa. The calculated results show that the streaming velocity and stresses near an EMB are functions of the mechanical properties of shell and gas. Overall, the streaming velocity and stresses for an EMB are found to be greater than those for a similar size free bubble under the same ultrasound excitation. This finding is consistent with the existing theory of acoustic streaming of an oscillating bubble near a boundary given by Nyborg (1958) [J. Acoust. Soc. Am. 30, 329-339].