Bubble dynamics in a compressible shear-thinning liquid

The radial dynamics of a spherical gas bubble in a compressible shear-thinning liquid is studied by means of a singular perturbation method to first order in the bubble-wall Mach number. The Williamson rheological model is adopted to describe the shear-thinning characteristic of liquid viscosity. The equation of motion for the bubble radius, the equation of the natural frequency of the bubble and the pressure equation are derived. Numerical calculations are presented using the experimental data for two polymer aqueous solutions, viz. HEC and CMC solutions, and water. It is found that the shear-thinning characteristic of liquid viscosity strongly influences only the behaviour of bubbles with initial radii smaller than 10(-1) mm and the rheological parameter with the strongest influence on bubble collapse is the infinite-shear viscosity. The effect of polymer additives, including their surfactant properties, on spherical bubble collapse is also discussed. (C) 1998 The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.