A variational model of bubble cavitation in soft gels and its experimental validation

Abstract

The transient dynamic behavior of soft gels under a sudden impact is often associated with the cavitation of bubbles. This phenomenon has gained rising attention, essentially due to the vast emergence of different biomedical applications and the gels’ use to replicate soft body parts.In this contribution, a variational approach to cavitation is presented, and it is employed to derive a thermodynamically consistent model for the dynamics of bubble cavitation. Following the classic ideas of continuum thermodynamics, the different energy contributions compete to optimize the system’s total energy. For the dissipative process of cavitation, the governing equation is provided by the principle of maximum dissipation.The resulting differential equation of bubble motion corresponds to previously introduced models and emphasizes now the specific application of viscoelastic soft gels. The versatility of the variational approach allows us to enhance the model with other influences on bubble growth. Exemplarily, a non-local energy contribution is added through which interactions with neighboring bubbles can be considered. A gradient energy allows interactions over a critical length and considers their influence on the individual bubble size.The derived model of bubble cavitation is studied numerically and compared to experimental results of a drop-tower test with agarose gel.