Bifurcation Structure of Bubble Oscillators in Polymer Solutions

The effect of polymer concentration on the bifurcation structure of a bubble oscillator is theoretically examined in terms of bifurcation diagrams and phase diagrams. The equation describing the driven spherical oscillations of a gas bubble in carboxymethylcellulose aqueous solutions is obtained by using a Williamson model fluid. The mathematical formulation includes the shear-thinning characteristic of liquid viscosity, density and surface tension. The numerical results revealed the suppression of chaotic oscillations of gas bubbles by polymer additives.