Predicting Bubble Migration due to Bjerknes Force in a Complex 3D Geometry: Numerical and Experimental Results

Abstract

While the Bjerknes force is not the only force experienced by a bubble subjected to an acoustic field; studies of bubble translation in non-flowing fluid have identified Bjerknes force as being the most influential. Therefore, Bjerknes force can be used to trap bubbles in predefined locations of maximum and minimum absolute pressure. Specifically challenging is to determine these locations in complex geometries because direct measurement of the acoustic pressure for the whole system is generally not possible. The objective of this research is to numerically predict Bjerknes force effect on bubble migration and accumulation in a complex 3D geometry that includes piezoelectric materials, elastic materials and a fluid media. A numerical solution of the acoustic pressure field was obtained for this geometry, valid in the range of small pressure oscillations. Additionally, using the linearized Rayleigh-Plesset equation, which gives the volumetric oscillations of a bubble subjected to an acoustic field, the Bjerknes force was numerically computed. By knowing the Bjerknes force, a bubble migration pattern upon entering the system was predicted. A CMOS high speed camera was used to experimentally monitor bubble multimode excitation and bubble response to a stationary pressure field validating our numerical results. Results are presented for experiments conducted for a 1mm bubble diameter with acoustic fields ranging from 7 to 10 kHz which correspond to values of the structure and/or the bubble’s resonant frequency.