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 rheologi cal model is adopted to describe the shear-thinning characteristic of liquid viscosity. The equation of motion for the bubble radius, the eq uation of the natural frequency of the bubble and the pressure equatio n are derived. Numerical calculations are presented using the experime ntal data for two polymer aqueous solutions, viz. HEC and CMC solution s, and water. It is found that the shear-thinning characteristic of li quid viscosity strongly influences only the behaviour of bubbles with initial radii smaller than 10(-1) mm and the rheological parameter wit h the strongest influence on bubble collapse is the infinite-shear vis cosity. The effect of polymer additives, including their surfactant pr operties, on spherical bubble collapse is also discussed. (C) 1998 The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.