Bubbles in viscous liquids: Time dependent behaviour and wake characteristics

Abstract

The dynamics of a bubble, initially stationary and spherical, rising in a viscous Newtonian liquid have been studied numerically using 3-D Volume-of-Fluid (VOF) method implemented in the Gerris flow solver. The study encompasses 8.7≤Eo (=ΔρgD2/σΔρgD2/σ)≤641 and Re≤151. Additionally, results published in the literature encompassing bubbles with lower values of Eo numbers were also considered, such that the overall dependencies of bubble shape, wake characteristics, and drag coefficient over a large range of Eo and Re values can be identified. While it was found that the deformation of the bubbles as predicted through the numerical study can generally replicate experimental observations presented, several limitations were identified, such as in the representation of skirt formation behind a skirted bubble and the formation of satellite bubbles behind a bubble rising at high Reynolds numbers. The dependency of the bubble aspect ratio on the Weber and Morton numbers was confirmed for cases of spherical and ellipsoidal bubbles; whilst for spherical cap and skirted bubbles the aspect ratio was found to depend largely on the Reynolds and Capillary numbers, respectively. Finally, the expansion and formation of closed/open laminar wakes behind the rising bubble were analysed and was found to correlate well with the bubble Re and Eo numbers.