Three-dimensional dynamics of a pair of deformable bubbles rising initially in line. Part 1: Moderately inertial regimes

TL;DR

This study uses high-resolution simulations to analyze the complex three-dimensional dynamics of two deformable bubbles rising in line in a liquid, revealing non-axisymmetric behaviors and the influence of deformation on their interactions.

Contribution

It provides new insights into the non-axisymmetric evolution and deformation effects of bubble pairs in moderately inertial regimes, extending understanding beyond previous axisymmetric assumptions.

Findings

Bubbles never reach axisymmetric equilibrium configurations.

Different evolution scenarios depend on $Ga$ and $Bo$ numbers, including drafting-kissing-tumbling and lateral drift.

Bubble deformation significantly influences wake vortices and lateral forces.

Abstract

The buoyancy-driven motion of two identical gas bubbles released in line in a liquid at rest is examined with the help of highly resolved simulations, focusing on moderately inertial regimes in which the path of an isolated bubble is vertical. Assuming first an axisymmetric evolution, equilibrium configurations of the bubble pair are determined as a function of the buoyancy-to-viscous and buoyancy-to-capillary force ratios which define the Galilei ($Ga$) and Bond ($Bo$) numbers of the system, respectively. The three-dimensional solutions reveal that this axisymmetric equilibrium is actually never reached. Instead, provided $Bo$ stands below a critical $Ga$-dependent threshold determining the onset of coalescence, two markedly different evolutions are observed. At the lower end of the explored $(Ga,\,Bo)$-range, the tandem follows a Drafting-Kissing-Tumbling scenario which eventually yields a planar side-by-side motion. For larger $Ga$, the trailing bubble drifts laterally and gets out of the wake of the leading bubble, barely altering the path of the latter. In this second scenario, the late configuration is characterized by a significant inclination of the tandem ranging from $30^\circ$ to $40^\circ$ with respect to the vertical. Bubble deformation has a major influence on the evolution of the system. It controls the magnitude of vortical effects in the wake of the leading bubble, hence the strength of the attractive force acting on the trailing bubble. It also governs the strength and even the sign of the lateral force acting on this bubble, a mechanism of particular importance when the tandem is released with a small angular deviation.