A new approach to unravel the lift force phenomenon of a single bubble rising in stagnant and sheared liquids

Abstract

The lateral distribution of bubbles rising in plumes is determined by the lift force induced on the bubbles. The lift force is exerted due to the presence of vorticity in the immediate vicinity of the bubble. Here, we have proposed a new approach to describe how the interface deformation governed by the surface tension force contributes to the vorticity generation near the bubble, subsequently leading to the lift force’s emergence. Using the vorticity transport equation, we compute the vorticity generation rate due to the bubble deformation, and compare it to the bubble lateral acceleration, which is a representation of the lateral forces acting on the bubble. Using the interface-resolved volume of fluid (VOF) method, we have simulated single bubbles rising in both stagnant liquid, and under the influence of a background shear flow. Bubbles with different sizes were simulated inside various liquid media, corresponding to a wide range of Eotvos numbers ($0.55<\text{Eo}<5.96$) and Morton numbers (−10.5 $<Log\text{Mo}<$ −3.8). Results disclose a consistent match between vorticity generation rate due to the bubble deformation and the lateral force induced on the bubble on both freely-rising condition and rising with presence of a background shear. This theory implies a physical interconnection between these phenomena which not only describes the zigzag movements of bubbles when rising freely, but also explains the direction change of bubble lateral migration in shear flows. The findings hold a direct implication in defining a universal lift force model for describing bubble lateral movements.