Bubble oscillation and inertial cavitation in viscoelastic fluids

Abstract

Non-linear acoustic oscillations of gas bubbles immersed in viscoelastic fluids are theoretically studied. The problem is formulated by considering a constitutive equation of differential type with an interpolated time derivative. With the aid of this rheological model, fluid elasticity, shear thinning viscosity and extensional viscosity effects may be taken into account. Bubble radius evolution in time is analyzed and it is found that the amplitude of the bubble oscillations grows drastically as the Deborah number (the ratio between the relaxation time of the fluid and the characteristic time of the flow) increases, so that, even for moderate values of the external pressure amplitude, the behavior may become chaotic. The quantitative influence of the rheological fluid properties on the pressure thresholds for inertial cavitation is investigated. Pressure thresholds values in terms of the Deborah number for systems of interest in ultrasonic biomedical applications, are provided. It is found that these critical pressure amplitudes are clearly reduced as the Deborah number is increased.