Buoyancy-driven bubbles in a constricted vertical capillary

Abstract

We numerically study the dynamics of buoyancy-driven bubbles in a constricted vertical capillary in which a throat with an arc shape is present. To investigate at what conditions and how the bubble would be entrapped at the capillary throat, a diffuse-interface immersed-boundary method is used in numerical simulations. Axisymmetric simulations are performed for various bubble and throat sizes, represented by the diameter ratio of the throat to the bubble, η (0.55 ≤ η ≤ 1.35), the Bond number (0.1 ≤ B o ≤ 15), and the Reynolds number (78.5 ≤ R e ≤ 3367). We find that small bubbles have insignificant deformation and, thus, cannot pass through a throat with η < 1, while relatively large bubbles encounter noticeable interface oscillations at their lower part when approaching the throat. In particular, the interface oscillations are composed of a standing wave arising from buoyancy and a capillary wave propagating radially. A phase diagram is presented regarding the eventual bubble morphology: pass-through and entrapment. For the critical diameter ratio ηc at the onset of bubble entrapment, we proposed two scaling laws based on the analysis of the deformability and oscillation of the bubble, i.e., η c ≈ 1.1 for Bo < 1 and η c ∼ B o - 1 / 4 for Bo > 1. These theoretical predictions are in good agreement with our numerical results.