Acoustic standing wave driven bubble dynamics in Oldroyd-B fluids using a semi analytical approach.

Bubble oscillation plays a pivotal role in a multitude of medical and industrial applications. In this study, we employ a semi-analytical method to investigate the oscillation of a bubble in a viscoelastic fluid. The bubble is assumed to oscillate isothermally, and the well-known Rayleigh-Plesset equation for bubble dynamics is employed alongside the Oldroyd-B constitutive equation for the viscoelastic fluid. By applying the Leibniz integral rule, the governing integro-differential equation is converted into a system of four ordinary differential equations, which are then solved numerically. The results demonstrate that modifying each dimensionless parameter exerts a distinct influence on bubble oscillation, depending on the elasticity number and other parameters such as the amplitude of acoustic pressure. In the range of non-dimensional values under consideration, an increase in the Reynolds number, acoustic pressure, and acoustic frequency has been observed to exert a significant influence on the amplitude of bubble oscillation, relative to the influence of other parameters. As the Reynolds number approaches approximately 1.1, the bubble oscillations become chaotic. In contrast, at lower Reynolds numbers, the oscillations remain periodic. Moreover, our findings indicate that a Deborah number of 2.4 represents the most elastic fluid in which bubble oscillations were observed. When the elasticity number is approximately 10 or higher and the Reynolds number remains constant, further increases in elastic effects do not significantly impact the oscillations.