Numerical simulations of the primary Bjerknes force experienced by bubbles in a standing ultrasonic field: Nonlinear vs. linear

•We perform simulations of the primary Bjerknes force in a nonlinear standing wave.•We examine the translation of the bubbles in the cavity at high amplitudes.•We analyze the importance of both nonlinearities (bubble dynamics, acoustic wave).•These nonlinearities strongly affect the force field and the bubble motion.•We also model the nonlinear ultrasonic field after the bubbles form agglomerates.

The primary Bjerknes force experienced by a population of multiple bubbles in a liquid set in a nonlinear ultrasonic standing field and their translation are calculated and analyzed by numerical simulations. The force field is evaluated by considering the nonlinear bubble oscillations as well as the nonlinear character of the ultrasonic pressure field (both variables are unknown in the coupled nonlinear differential system). The results at small amplitudes agree with the classical theory on bubble translation, depending on the driving frequency in relation to the bubble resonance. It is shown that, when amplitudes are raised, the force field exhibits important modifications that strongly affect the motion of the bubbles and the way they form agglomerates. An analysis is performed on the importance of the terms in the differential system that provoke (a) the nonlinearity of the bubble oscillations and (b) the nonlinearity of the acoustic wave. This study reveals that both features should be considered to better approximate the primary Bjerknes force field. Simulations of the nonlinear ultrasonic field after the bubbles form agglomerates under the influence of this force are also performed.