Buckling resistance of solid shell bubbles under ultrasound

Abstract

Thin solid shell contrast agents bubbles are expected to undergo different volume oscillating behaviors when the acoustic power is increased: small oscillations when the shell remains spherical, and large oscillations when the shell buckles. Contrary to bubbles covered with thin lipidic monolayers that buckle as soon as compressed, solid shell bubbles resist compression, making the buckling transition abrupt. Numerical simulations that explicitly incorporate a shell bending modulus give the critical buckling pressure and post-buckling shape, and show the appearance of a finite number of wrinkles. These findings are incorporated in a model based on the concept of effective surface tension. This model compares favorably to experiments when adjusting two main parameters: the buckling tension and the rupture shell tension. The buckling tension provides a direct estimation of the acoustic pressure threshold at which buckling occurs.

Ultra-high-speed fluorescence imaging

“…The rupture is achieved when the shell material is elongated more than a critical elongation e max , and occurs at a pressure P buckling = 3E(d/R)e max . The experimental data were compared with the theory of Marmottant et al as shown in figure 7.4 [127]. They also stated that above a certain shell thickness/ diameter ratio, no buckling will be observed and the bubbles will only rupture while releasing their gas content, which is in perfect agreement with our observations.…”

“…For the capsules with the larger shell thickness/diameter ratio this behavior was no longer observed and the capsules only responded by instant rupturing when the ultrasound pressure was above the release threshold. This behavior corresponds nicely with the recent theory of Marmottant et al [127] where they predicted the rupture and buckling threshold for varying bubble radii. When the shell thickness to bubble diameter ratio is varied, the pressure for buckling onset is predicted to vary as P buckling = E(d/R) 2 , with E the elastic Youngs modulus, d the shell thickness and R the bubble radius.…”

“…By mixing capsules with two shell thickness to diameter ratios, selective triggering can be performed by applying different acoustic pressures. The measured thresholds correspond well to a recent theoretical model for hard-shelled agents by Marmottant et al [127] The application of ultra-high-speed fluorescence imaging for the visualization of microbubble phenomena has great potential. The matters addressed here represent only a small number of all possible experiments that can benefit from such an imaging technique.…”

“…Plot of the ratio of capsule shell to capsule diameter against the acoustic pressure, together with the theoretical prediction for the onset of buckling and rupturing. The following parameters were used: a Youngs modulus of E = 225 MPa, and a critical elongation for rupture of e max = 1.8% [127]. Symbols in the graph represent the measured data points.…”

“…Recently Marmottant et al have developed a new theory describing the behavior of hard-shelled microbubbles when undergoing buckling or rupturing using ultrasonic pressure [127]. Such microbubbles can more easily sustain inplane compression in contrast to the soft-shelled microbubbles, thus allowing for stabilization against dissolution of the gas inside.…”