Generalized Rayleigh-Plesset equation for bubbles in viscoelastic liquids

The spherical dynamics of microbubbles in liquids is well understood. Yet, the problem becomes markedly more complex if the bubble is embedded in viscoelastic materials. This is the case in many biomedical applications including ultrasound imaging, drug delivery, and ablation therapies. Several studies have proposed models based on extended forms of the Rayleigh-Plesset equation that account for viscoelastic stresses. However, the validity of these models remain restricted to a particular choice of constitutive model and/or to small deformations. Here, we derive a generalized equation for bubbles in viscoelastic materials by borrowing concepts from finite-strain theory and stress relaxation functions. The proposed theory is applicable to viscoelastic media with arbitrary complex modulus and remains valid for large bubble deformations. We demonstrate the effectiveness of our approach by comparing it to previously published models of viscoelastic solids and liquids with specific constitutive equations.