Modeling of bubble formation in viscous fluids considering the influence of gas jets

Abstract

A theoretical method was developed for modeling the non-spherical axisymmetric bubble formation by incorporating two sets of evolution equations on arbitrary surface elements: a Rayleigh-Plesset type equation for the radial expansion and a force balance equation for vertical motion. The proposed method considered the morphological deformation of gas jets based on the free turbulent jet theory of the circular section. The calculated results were compared satisfactorily with the experimental shapes in oil and polyacrylamide aqueous solutions, especially for the shapes featured with sharp tips accounting for jet instabilities. The mean relative errors of the bubble volume, the surface area, the height, and the weight were respectively 5.78%, 4.22%, 3.01%, and 4.67%. The time evolution of force amplitudes on surface elements was examined. At early stage, the radial expansion dominated while the vertical elongation was inhibited. As the bubble volume increased, the positive vertical resultant force made the element elongated to form sharp tip or neck. In particular, the viscosity increased the damping rate, thus suppressing the element fluctuations, while the shear thinning effect weakened the suppression. The contributions of the gas chamber to both the jet instability and the increment of penetration length were analyzed, as these contributions affected the bubble detachment.