J. Fluid zyxwvutsrqpo Mech. zyxwvutsrq (1993), zyxwvutsr 1101. 254, pp. 501-527 Copyright zyxwvutsrq Q 1993 Cambridge University Press zyxwvu 50 1 Bjerknes forces between two bubbles. Part 2. Response to an oscillatory pressure field By NIKOLAOS A. PELEKASIS AND JOHN A. TSAMOPOULOS Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA (Received 11 November 1991 and in revised form 16 March 1993) The motion of two gas bubbles in response to an oscillatory disturbance in the ambient pressure is studied. It is shown that the relative motion of bubbles of unequal size depends on the frequency of the disturbance. If this frequency is between the two natural frequencies for volume oscillations of the individual bubbles, the two bubbles are seen to move away from each other; otherwise attractive forces prevail. Bubbles of equal size can only attract each other, irrespective of the oscillation frequency. When the Bond number, Bo (based on the average acceleration) lies above a critical region, spherical-cap shapes appear with deformation confined on the side of the bubbles facing away from the direction of acceleration. For Bo below the critical region shape oscillations spanning the entire bubble surface take place, as a result of subharmonic resonance. The presence of the oscillatory acoustic field adds one more frequency to the system and increases the possibilities for resonance. However, only subharmonic resonance is observed because it occurs on a faster timescale, O(l/s), where E is the disturbance amplitude. Furthermore, among the different possible periodic variations of the volume of each bubble, the one with the smaller period determines which Legendre mode will be excited through subharmonic resonance. Spherical-cap shapes also occur on a timescale O( 1 zyxwvu /e). When the bubbles are driven below resonance and for quite large amplitudes of the acoustic pressure, E % 0.8, a subharmonic signal at half the natural frequency of volume oscillations is obtained. This signal is primarily associated with the zeroth mode and corresponds to volume expansion followed by rapid collapse of the bubbles, a behaviour well documented in acoustic cavitation experiments. zyxwvu 1. Introduction It is very well documented in the field of acoustic cavitation that pressure changes determine the dynamic, and eventually destructive, behaviour of bubbles in high-speed flows. In order to study the effect of pressure, it is common practice in experimental studies of cavitation to set the host fluid along with the trapped bubbles in pulsation using a sound field. In the pioneering work of Kornfeld & Suvorov (1944), a vibrating cylinder was used for the generation of air bubbles in water which were then observed as they oscillated and in some cases translated in the fluid at a high speed. The accelerating motion of the bubbles was attributed by the above investigators to the well-known 'Bjerknes effect'. According to Bjerknes (1906, 1909) two bubbles oscillating in a sound field will attract or repel each other depending on whether they oscillate in or out of phase, respectively. In the same study it was observed that increasing the amplitude of vibrations intensifies the accelerating motion of the bubbles