Mathematical model for collective bubble dynamics in strong ultrasound fields

Using the Lagrangian formalism, coupled equations are derived that describe radial and translational motions of an arbitrary bubble in a three-dimensional cluster subject to an ultrasound field. The obtained equations incorporate the nonlinear coupling of the volume and the translational modes of bubbles as well as interactions between all bubbles in the cluster up to terms of third order in the inverse separation distances. Solving these equations for each bubble in a multibubble structure, consisting of N bubbles with arbitrary spatial arrangement, the collective dynamics of this structure can be simulated. The potentialities of the proposed model in simulating the bubble dynamics in strong ultrasound fields are illustrated by numerical examples.