Path Instability of Strongly Collapsing Bubbles Driving by Bi-Frequency Excitation at Finite Reynolds Numbers

Abstract

In this work we present a study of the path instability that may be developed by strongly collapsing bubbles in highly viscous liquids. In particular we modify the driving pressure field by the addition of a high frequency component in order to suppress the pseudo-orbits. The condition of spatially fixed bubbles is necessary for an accurate experimental characterization of it. We investigate different modes for the high frequency component. In the present work we show that the spatial stabilization of the bubble could be obtained with different kind of harmonics. We also performed a sensibility analysis of the solutions under different phases between the low and high frequency components of the pressure field. Furthermore, we present a verification test to secure that the history force action cause the path instability and we also made a validation of the model with experimental measurements of the bubble radius driving with bi-harmonic and bi-frequency excitation showing a quite good agreement between them.