Primary Bjerknes force in a three-dimensional nonlinear resonator: Numerical simulations

The effect of the primary Bjerknes force caused by a three-dimensional nonlinear standing ultrasonic wave on a population of nonlinear oscillating bubbles is studied in this paper by analyzing the results obtained from simulations performed with a numerical model at low and moderate pressure amplitudes. Small air bubbles are evenly distributed in a water filled cavity excited at resonance for which axial symmetry is assumed. Both the bubble oscillation variable and the pressure variable are unknown in the nonlinear set of coupled differential equations that describes the interaction of ultrasound and bubbles. Simulation results show that the three-dimensional primary Bjerknes force field is strongly amplitude dependent. We also analyze whether taking the term in the differential system that defines the nonlinear behavior of the pressure field into account is determinant or not on the computation of the force field. The corresponding results corroborate the one-dimensional conclusions on the fundamental importance of considering this nonlinear acoustic term to obtain an accurate approximation of the force in a cavity.