The effect of high viscosity on the collapse-like chaotic and regular periodic oscillations of a harmonically excited gas bubble

Abstract

In the last decade many industrial applications have emerged based on the rapidly developing ultrasonic technology such as ultrasonic pasteurization, alteration of the viscosity of food systems, and mixing immiscible liquids. The fundamental physical basis of these applications is the prevailing extreme conditions (high temperature, pressure and even shock waves) during the collapse of acoustically excited bubbles. By applying the sophisticated numerical techniques of modern bifurcation theory, the present study intends to reveal the regions in the excitation pressure amplitude-ambient temperature parameter plane where collapse-like motion of an acoustically driven gas bubble in highly viscous glycerine exists. We report evidence that below a threshold temperature the bubble model, the Keller-Miksis equation, becomes an overdamped oscillator suppressing collapse-like behaviour. In addition, we have found periodic windows interspersed with chaotic regions indicating the presence of transient chaos, which is important from application point of view if predictability is required.

Keywords: Bifurcation structure; Bubble dynamics; Chaos; Continuation technique; High viscosity; Keller–Miksis equation.