Periodic and chaotic acoustic oscillations of a bubble gas immersed in an Upper Convective Maxwell fluid

Abstract

In the present work, the non-linear dynamics of a spherical gas bubble oscillating in a viscoelastic liquid is investigated numerically. The radial oscillations of the bubble are governed by a modified Rayleigh–Plesset equation due to the viscoelastic behavior of the liquid. For simplicity, the Upper Convective Maxwell model is chosen as the fluid constitutive equation. In addition, thermal dissipation effects within the gas bubble are taken into account and comparing with previous approaches, we consider the nearly isothermal model for the compression gas. The purely adiabatic case is also included. The resulting nondimensional governing equations depend on different dimensionless parameters; however, the rheological character is directly dictated by the Deborah number, De. The numerical results for the radial oscillations predict periodic solutions for values of De between 1 and 4 and showing a clear chaotic behavior for De ∼ 4.4, independently of the intensity of the thermal damping. In addition, the physical influence of other relevant parameters, like the characteristic Reynolds number, is also clarified.