BJERKNES FORCE THRESHOLD FOR STABLE SINGLE BUBBLE SONOLUMINESCENCE

An investigation of the primary Bjerknes force acting on a bubble in a strong acoustic field is presented. The approach takes into account the nonlinear resonancelike response of small bubbles to strong acoustic pressure amplitudes. It is shown that for high pressure amplitudes even very small bubbles are repelled from the pressure antinode. This result is in contrast to predictions using Bjerknes forces based on harmonic bubble oscillations. The relevance of this high pressure instability for single bubble sonoluminescence experiments is discussed. @S1063-651X~97! 07203-6# The light emission associated with strong bubble collapse in an external sound field is called sonoluminescence ~SL! Since the work of Marinesco and Trillat @1#, it has been investigated by many authors ~see the review by Walton and Reynolds @2#! This type of sonoluminescence is now called multibubble sonoluminescence~MBSL! and generically occurs in acoustic cavitation @3‐5# and sonochemistry @6‐8#. The interest in SL was restimulated by the elaborate experiments of Gaitan et al. @9#, who investigated SL of a single bubble in water trapped by a strong acoustic standing-wave field. This phenomenon is calledsingle bubble sonoluminescence ~SBSL! and was subsequently studied in a number of papers @10#. A prerequisite for SBSL are oscillating bubbles that remain stable in the presence of strong sound fields. Stability theories have been presented ~taking into account rectified diffusion! that provide explanations for the existence of small, stably oscillating bubbles that have been observed in experiments on SBSL @11#. However, the source of the instability of SBSL occurring at even larger pressure amplitudes has not been totally clarified yet. The most popular idea presented until now considers the onset of surface oscillations to be the main mechanism leading to an instability of the bubble at the pressure antinode @12,13#. However, no theory exists connecting surface oscillation instability with trapping instability. Trapping is caused by the primary Bjerknes force and is a combined effect of the sound field and ~nonlinear! bubble oscillations. In this paper we investigate the influence of the primary Bjerknes force on the positional stability of a single nonlinearly oscillating bubble in the vicinity of the pressure antinode of the levitating and driving sound field. A body of volume V in a liquid under a pressure gradient „p experiences a force F52V„p. If these quantities vary periodically in time or are fluctuating fast, the net force on the body is the time average of F. The net radiation force acting on a spherical bubble in a standing-wave sound field is called the primary Bjerknes force FB @3,14# and equals FB52 4 p^R 3 ~t! „p~t! &, ~1! where ^iii& denotes the time averaging over a period of the acoustic field. For a quantitative investigation of the primary Bjerknes force acting on a bubble in a strong acoustic field we consider the problem in spherically symmetric geometry in a compressible liquid with forced radial excitation, i.e., a spherical bubble trap. The pressure distribution of the first radial mode, as a solution of the linear wave equation in spherical geometry, may be written in the following way: