Compression-only behavior: Effect of prestress and shell rheology on bifurcation diagrams and parametric stability of coated microbubbles in an unbounded flow

Abstract

Lipid-shelled microbubbles exhibit a strain-softening behavior and thus are characterized by preferential excursion from equilibrium during expansion at insonation. However, experimental studies have reported a counterintuitive behavior, identified as the compression-only behavior, where they pulsate mainly in the compression phase. We construct bifurcation diagrams of lipid and polymer-shelled microbubbles indicating the existence of a parameter range for which buckled shapes that are characterized by significantly smaller volume and lower total energy level, in comparison with the spherosymmetric state, are expected to spontaneously arise. The timescale for such a transition depends on the amplitude and frequency of the initial disturbance but more importantly on shell rheology in terms of the bending vs area dilatation modulus and shear vs dilatational viscosity. We show by performing stability analysis and constructing phase diagrams of coated microbubbles that an initially prestressed shell facilitates the onset of buckling at relatively small sound amplitudes. Moreover, low values of the shell bending modulus and shear viscosity in comparison with the area dilatation modulus and dilatational viscosity, respectively, facilitate the onset of shape modes that characterize bifurcating branches leading to deformed shapes with significant volume compression at relatively low sound amplitudes. By performing dynamic simulations for lipid-shelled microbubbles, we capture the onset of compression-only effect during which the shell tends to oscillate around compressed buckled shapes when subject to an acoustic disturbance. When phase diagrams of polymeric shells are examined the amplitude threshold for dynamic buckling to occur typically arrives before the onset of parametric shape mode excitation. Therefore the shell cohesion is compromised before it achieves a steady pulsation around a compressed shape, and this is verified by our simulations. © 2022 American Physical Society.