Selected for the October issue of Virtual Journal of Nanoscale Science and Technology

We studied experimentally the unsteady translation of coated microbubbles propelled by acoustic radiation force. Two microbubbles of the type used as contrast agent in ultrasound medical imaging, pulsating in ultrasound, attract each other as a result of secondary Bjerknes force. We use optical tweezers to isolate a bubble pair from neighboring boundaries, so that it can be regarded as if in an unbounded fluid, and the hydrodynamic forces acting on the system can be identified unambiguously. The radial and translational dynamics, excited by a 2.25 MHz ultrasound wave, is recorded with an ultra-high speed camera at 15 million frames per second. The time-resolved measurements reveal a quasi-steady component of the translational velocity, at an average translational Reynolds number of 0.5, and an oscillatory component at the same frequency as the radial pulsations, as predicted by existing models. Since the coating enforces a no-slip boundary condition, an increased viscous dissipation is expected due to the oscillatory component, similar to the case of an oscillating rigid sphere that was first described by Stokes. A history force term is therefore included in the force balance, in the form originally proposed by Basset and extended to the case of time-dependent radius by Takemura and Magnaudet. The instantaneous values of the hydrodynamic forces extracted from the experimental data confirm that the history force accounts for the largest part of the viscous force. The trajectories of the bubbles predicted by numerically solving the equations of motion are in very good agreement with experiment.

V. Garbin, B. Dollet, M. Overvelde, D. Cojoc, E. Di Fabrizio, L. van Wijngaarden, A. Prosperetti, N. de Jong, D. Lohse, M. Versluis, Physics of Fluids 21 (2009)