Path of a pair of deformable bubbles rising initially in line and close to a vertical wall

TL;DR

This study numerically investigates how a vertical wall influences the stability and separation paths of a pair of deformable bubbles rising in line, revealing two distinct mechanisms governing their lateral and wall-normal separation behaviors.

Contribution

It introduces a detailed analysis of bubble pair dynamics near a wall, highlighting the effects of buoyancy, viscous, and capillary forces on stability and separation mechanisms.

Findings

Wall proximity affects bubble pair separation paths.

Two mechanisms identified: shear flow attraction and vortex shedding influence bubble escape.

Separation behavior depends on Galilei and Bond number ratios.

Abstract

It is known that in an unbounded fluid, the inline configuration of a freely rising bubble pair is often unstable with respect to lateral disturbances. This work numerically examines the stability of this configuration in the presence of a nearby vertical wall. The focus is on moderately inertial regimes, where two bubbles rising initially in line typically separate laterally from each other under unbounded conditions. In the presence of the wall, our results indicate that while the path of the bubble pair predominantly separates laterally, the plane of separation largely depends on the wall bubble interaction. This interaction involves a competition between two distinct effects, with the dominance determined by the ratios of buoyancy to viscous and buoyancy to capillary forces, which define the Galilei (Ga) and Bond (Bo) numbers, respectively. When Bo is below a critical Ga-dependent threshold, irrotational effects dominate, initially stabilizing both bubbles near the wall until horizontal separation among them occurs in the wall parallel plane. Conversely, at higher Bo, vortical effects dominate such that both bubbles migrate away from the wall. During the departure, asymmetric interactions cause the wall normal velocities of the two bubbles to differ, leading to horizontal separation in the wall-normal plane. These two separation motions, both newly identified in the present study, are found to result from two distinct mechanisms: one associated with the shear flow generated in the gap separating the wall and the leading bubble, which attracts the trailing bubble toward the wall, and the other linked to vortex shedding from the leading bubble, which promotes the trailing bubble's faster escape from the wall.