Stable arrays of resonant bubbles in a 1-MHz standing-wave acoustic field

Abstract

As observed microscopically, bubbles in a standing-wave acoustic field move to the pressure nulls and oscillate, in elliptical orbits, about a common axis. The orbits of individual bubbles are equally spaced about 100 μm apart along the axis, forming a linear array. These arrays form in tap water for peak pressure amplitudes of 10–20 bar, but persist at levels as low as 1.5 bar. The 7-μm diameter of the bubbles is approximately the theoretical size for resonant air bubbles in water driven at the 986 kHz frequency of the field. The radius of the orbits is approximately inversely proportional to the pressure gradient at the pressure null, with proportionality constant 0.25 bar. In a simplified model of the orbit phenomenon the expected proportionality constant is given by (2)1/2ps, where ps is the threshold pressure amplitude for rectified diffusion and has the value 0.18 bar. Calculations of ps, based on current theories for rectified diffusion, are in substantial agreement with the this value. The period of the orbital motion is about 1 msec for an orbit radius B of 35 μm, and increases to about 6.5 msec for B=100 μm. Two adjacent bubbles are synchronized in their orbits approximately 90° out of phase, as required for stability of the arrays under Bjerknes forces.