Coupled dynamics of translation and collapse of acoustically driven microbubbles

Pressure gradients drive the motion of microbubbles relative to liquids in which they are suspended. Examples include the hydrostatic pressure due to a gravitational field, and the pressure gradients in a sound field, useful for acoustic levitation. In this paper, the equations describing the coupled dynamics of radial oscillation and translation of a microbubble are given. The formulation is based on a recently derived expression for the hydrodynamic force on a bubble of changing size in an incompressible liquid [J. Magnaudet and D. Legendre, Phys. Fluids 10, 550-556 (1998)]. The complex interaction between radial and translation dynamics is best understood by examination of the added momentum associated with the liquid motion caused by the moving bubble. Translation is maximized when the bubble collapses violently. The new theory for coupled collapse and translation dynamics is compared to past experiments and to previous theories for decoupled translation dynamics. Special attention is paid to bubbles of relevance in biomedical applications.