A general theoretical approach to the development of zero-thickness encapsulation models for contrast microbubbles is proposed. The approach describes a procedure that allows one to recast available rheological laws from the bulk form to a surface form which is used in a modified RayleighPlesset equation governing the radial dynamics of a contrast microbubble. By the use of the proposed procedure, the testing of different rheological laws for encapsulation can be carried out. Challenges of existing shell models for lipid-encapsulated microbubbles, such as the dependence of shell parameters on the initial bubble radius and the "compression-only" behavior, are discussed. Analysis of the rheological behavior of lipid encapsulation is made by using experimental radius-time curves for lipid-coated microbubbles with radii in the range 1.2 -2.5 μm. The curves were acquired for a research phospholipid-coated contrast agent insonified with a 20-cycle, 3.0 MHz, 100 kPa acoustic pulse. The fitting of the experimental data by a model which treats the shell as a viscoelastic solid gives the values of the shell surface viscosity increasing from 0.30×10 -8 kg/s to 2.63×10 -8 kg/s for the range of bubble radii indicated above. The shell surface elastic modulus increases from 0.054 N/ m to 0.37 N/m. It is proposed that this increase may be a result of the lipid coating possessing the properties of both a shear-thinning and a strain-softening material. We hypothesize that these complicated rheological properties do not allow the existing shell models to satisfactorily describe the dynamics of lipid encapsulation. In the existing shell models, the viscous and the elastic shell terms have the linear form which assumes that the viscous and the elastic stresses acting inside the lipid shell are proportional to the shell shear rate and the shell strain, respectively, with constant coefficients of proportionality. The analysis performed in the present paper suggests that a more general, nonlinear theory may be more appropriate. It is shown that the use of the nonlinear theory for shell viscosity allows one to model the "compression-only" behavior. As an example, the results of the simulation for a 2.03-μm-radius bubble insonified with a 6-cycle, 1.8 MHz, 100 kPa acoustic pulse are given. These parameters correspond to the acoustic conditions under which the "compression-only" behavior was observed by de Jong et al. [Ultrasound Med. Biol. 33 (2007) 653-656]. It is also shown that the use of the Cross law for the modeling of the shear-thinning behavior of shell viscosity reduces the variance of experimentally estimated values of the shell viscosity and its dependence on the initial bubble radius.

Using the Lagrangian formalism, equations of radial and translational motions of two coupled spherical gas bubbles have been derived up to terms of third order in the inverse distance between the bubbles. The equations of radial pulsations were then modified, for the purpose of allowing for effects of liquid compressibility, using Keller-Miksis' approach, and the equations of translation were added by viscous forces in the form of the Levich drag. This model was then used in a numerical investigation of the translational motion of two small, driven well below resonance, bubbles in strong acoustic fields with pressure amplitudes exceeding 1 bar. It has been found that, if the forcing is strong enough, the bubbles form a bound pair with a steady spacing rather than collide and coalesce, as classical Bjerknes theory predicts. Moreover, the viscous forces cause skewness in the system, which results in self-propulsion of the bubble pair. The latter travels as a unit along the center line in a direction that is determined by the ratio of the initial bubble radii. The results obtained are of immediate interest for understanding and modeling collective bubble phenomena in strong fields, such as acoustic cavitation streamers.

The acoustic radiation pressure exerted by a plane — progressive or standing — sound wave on a compressible sphere suspended freely in a viscous fluid is calculated. In deriving the general expression for the radiation pressure, it is supposed that the radius of the sphere is arbitrary. Two limiting cases of interest are then considered. In the first of these, it is assumed that the sound wavelength is much larger than the radius of the sphere which is, in turn, much larger than the viscous wavelength, it being supposed that this condition is satisfied both outside and inside the sphere. In the second case, the situation is investigated when the radius of the sphere is small compared with the viscous wavelength which is, in turn, much smaller than the sound wavelength, it being supposed that this condition is satisfied, as before, both outside and inside the sphere. It is shown that in both cases the expressions for the radiation pressure are drastically different from the well-known expressions for the radiation pressure in a perfect fluid: the calculation of the radiation pressure from the formulae obtained for a perfect fluid in the cases when the effect of viscosity is not negligible gives both quantitatively and qualitatively wrong results.

The acoustic radiation force exerted by an axisymmetric sound field on a spherical particle is calculated assuming that the surrounding fluid is viscous and heat conducting. The incident sound field pressure amplitude is supposed to be small enough such that nonlinear effects like generation of subharmonics do not occur. No restrictions are imposed on the particle size, which means that the particle can be of an arbitrary radius with respect to the sound, viscous, and thermal wavelengths in the surrounding fluid. The obtained formula for the radiation force is general in that it is applicable to first, any axisymmetric sound field, such as a plane, traveling or standing wave and a spherical wave, and, second, any of the following types of dispersed particles: a gas bubble, a liquid drop, a rigid or elastic sphere, a spherical shell, etc. The force is expressed in terms of the linear scattering coefficients to be determined by the particle type. Thus, to obtain the force on a specific particle the problem of linear scattering for that particle must be solved. Problems of this sort are known not to be mathematically difficult, but can be laborious enough if a particle at issue has a complicated internal structure. The radiation forces on particles of most interest are examined in papers that follow [J. Acoust. Soc. Am. 101, 722–740 (1997)].

Lipid-coated perfluorocarbon nanodroplets are submicrometer-diameter liquid-filled droplets with proposed applications in molecularly targeted therapeutics and ultrasound (US) imaging. Ultrasonic molecular imaging is unique in that the optimal application of these agents depends not only on the surface chemistry, but also on the applied US field, which can increase receptor-ligand binding and membrane fusion. Theory and experiments are combined to demonstrate the displacement of perfluorocarbon nanoparticles in the direction of US propagation, where a traveling US wave with a peak pressure on the order of megapascals and frequency in the megahertz range produces a particle translational velocity that is proportional to acoustic intensity and increases with increasing center frequency. Within a vessel with a diameter on the order of hundreds of micrometers or larger, particle velocity on the order of hundreds of micrometers per second is produced and the dominant mechanism for droplet displacement is shown to be bulk fluid streaming. A model for radiation force displacement of particles is developed and demonstrates that effective particle displacement should be feasible in the microvasculature. In a flowing system, acoustic manipulation of targeted droplets increases droplet retention. Additionally, we demonstrate the feasibility of US-enhanced particle internalization and therapeutic delivery.