Investigation of transition frequencies of two acoustically coupled bubbles using a direct numerical simulation technique

The theoretical results regarding the ``transition frequencies'' of two acoustically interacting bubbles have been verified numerically. The theory provided by Ida [Phys. Lett. A 297 (2002) 210] predicted the existence of three transition frequencies per bubble, each of which has the phase difference of $\pi /2$ between a bubble's pulsation and the external sound field, while previous theories predicted only two natural frequencies which cause such phase shifts. Namely, two of the three transition frequencies correspond to the natural frequencies, while the remaining does not. In a subsequent paper [M. Ida, Phys. Rev. E 67 (2003) 056617], it was shown theoretically that transition frequencies other than the natural frequencies may cause the sign reversal of the secondary Bjerknes force acting between pulsating bubbles. In the present study, we employ a direct numerical simulation technique that uses the compressible Navier-Stokes equations with a surface-tension term as the governing equations to investigate the transition frequencies of two coupled bubbles by observing their pulsation amplitudes and directions of translational motion, both of which change as the driving frequency changes. The numerical results reproduce the recent theoretical predictions, validating the existence of the transition frequencies not corresponding to the natural frequency.Comment: 18 pages, 8 figures, in pres

Vaporization dynamics of volatile perfluorocarbon droplets: A theoretical model and in vitro validation

Perfluorocarbon (PFC) microdroplets, called phase-change contrast agents (PCCAs), are a promising tool in ultrasound imaging and therapy. Interest in PCCAs is motivated by the fact that they can be triggered to transition from the liquid state to the gas state by an externally applied acoustic pulse. This property opens up new approaches to applications in ultrasound medicine. Insight into the physics of vaporization of PFC droplets is vital for effective use of PCCAs and for anticipating bioeffects. PCCAs composed of volatile PFCs (with low boiling point) exhibit complex dynamic behavior: after vaporization by a short acoustic pulse, a PFC droplet turns into a vapor bubble which undergoes overexpansion and damped radial oscillation until settling to a final diameter. This behavior has not been well described theoretically so far. The purpose of our study is to develop an improved theoretical model that describes the vaporization dynamics of volatile PFC droplets and to validate this model by comparison with in vitro experimental data

Standing waves for acoustic levitation

Standing waves are the most popular method to achieve acoustic trapping. Particles with greater acoustic impedance than the propagation medium will be trapped at the pressure nodes of a standing wave. Acoustic trapping can be used to hold particles of various materials and sizes, without the need of a close-loop controlling system. Acoustic levitation is a helpful and versatile tool for biomaterials and chemistry, with applications in spectroscopy and lab-on-a-droplet procedures. In this chapter, multiple methods are presented to simulate the acoustic field generated by one or multiple emitters. From the acoustic field, models such as the Gor'kov potential or the Flux Integral are applied to calculate the force exerted on the levitated particles. The position and angle of the acoustic emitters play a fundamental role, thus we analyse commonly used configurations such as emitter and reflector, two opposed emitters, or arrangements using phased arrays

Vaporization dynamics of volatile perfluorocarbon droplets: A theoretical model and in vitro

PURPOSE: Perfluorocarbon (PFC) microdroplets, called phase-change contrast agents (PCCAs), are a promising tool in ultrasound imaging and therapy. Interest in PCCAs is motivated by the fact that they can be triggered to transition from the liquid state to the gas state by an externally applied acoustic pulse. This property opens up new approaches to applications in ultrasound medicine. Insight into the physics of vaporization of PFC droplets is vital for effective use of PCCAs and for anticipating bioeffects. PCCAs composed of volatile PFCs (with low boiling point) exhibit complex dynamic behavior: after vaporization by a short acoustic pulse, a PFC droplet turns into a vapor bubble which undergoes overexpansion and damped radial oscillation until settling to a final diameter. This behavior has not been well described theoretically so far. The purpose of our study is to develop an improved theoretical model that describes the vaporization dynamics of volatile PFC droplets and to validate this model by comparison with in vitro experimental data. METHODS: The derivation of the model is based on applying the mathematical methods of fluid dynamics and thermodynamics to the process of the acoustic vaporization of PFC droplets. The used approach corrects shortcomings of the existing models. The validation of the model is carried out by comparing simulated results with in vitro experimental data acquired by ultrahigh speed video microscopy for octafluoropropane (OFP) and decafluorobutane (DFB) microdroplets of different sizes. RESULTS: The developed theory allows one to simulate the growth of a vapor bubble inside a PFC droplet until the liquid PFC is completely converted into vapor, and the subsequent overexpansion and damped oscillations of the vapor bubble, including the influence of an externally applied acoustic pulse. To evaluate quantitatively the difference between simulated and experimental results, the L2-norm errors were calculated for all cases where the simulated and experimental results are compared. These errors were found to be in the ranges of 0.043–0.067 and 0.037–0.088 for OFP and DFB droplets, respectively. These values allow one to consider agreement between the simulated and experimental results as good. This agreement is attained by varying only 2 of 16 model parameters which describe the material properties of gaseous and liquid PFCs and the liquid surrounding the PFC droplet. The fitting parameters are the viscosity and the surface tension of the surrounding liquid. All other model parameters are kept invariable. CONCLUSIONS: The good agreement between the theoretical and experimental results suggests that the developed model is able to correctly describe the key physical processes underlying the vaporization dynamics of volatile PFC droplets. The necessity of varying the parameters of the surrounding liquid for fitting the experimental curves can be explained by the fact that the parts of the initial phospholipid shell of PFC droplets remain on the surface of vapor bubbles at the oscillatory stage and their presence affects the bubble dynamics