Nonspherical gas bubble dynamics in viscoelastic soft materials

Abstract

Nonspherical gas bubble dynamics in viscoelastic materials influence the stress transmission and energy dissipation of their surroundings and are difficult to predict. Their accurate prediction is essential in applications ranging from biomedical procedures to high-strain-rate rheological measurements. However, existing models do not sufficiently capture the nonspherical rotational dynamics. We formulate and superpose a rotational contribution to the perturbed deformation with a potential contribution. Linearised forward and inverse coordinate maps are formulated based on the deformation field which are used to compute velocities, accelerations, and stresses. The addition of the rotational degree of freedom satisfies the momentum balance equations and stress continuity at the bubble surface. The material surrounding the bubble is modelled with a Kelvin-Voigt constitutive model with Newtonian viscosity and quadratic strain-stiffening neo-Hookean elasticity. The model agrees with previous viscous fluids models when elastic effects are neglected and radial oscillations are small. When viscous effects are small relative to elastic, shear waves radiate from the bubble surface into the material. The resulting strain energy is delocalised and increases damping of the perturbation amplitude in time relative to potential-based models. We show agreement between the stability of the shape modes with previous ultrasound forced experiments and temporal evolution of different shape modes with previous laser-induced cavitation experimental data.