Mixing of spherical bubbles with time-dependent radius in incompressible flows

The motion of contracting and expanding bubbles in an incompressible chaotic flow is analyzed in terms of the finite-time Lyapunov exponents. The viscous forces acting on the bubble surface depend not only on the relative acceleration but also on the time dependence of the bubble volume, which is modeled by the Rayleigh-Plesset equation. The effect of bubble coalescence on the coherent structures that develop in the flow is studied using a simplified bubble merger model. Contraction and expansion of the bubbles is favored in the vicinity of the coherent structures. Time evolution of coalescence bubbles follows a Lévy distribution with an exponent that depends on the initial distance between bubbles. Mixing patterns were found to depend heavily on merging and on the time-dependent volume of the bubbles.