Connected-component labeling: A tool for the numerical investigation of buoyancy-driven bubbly flows

We investigate the motion of buoyant bubbles rising in a quiescent liquid using a Volume-of-Fluid Connected-Component Labeling (VOFCCL) technique. Although the Eulerian VOF framework excels at interface-capturing and provides valuable insight into the behavior of the dispersed phase, it inherently loses local detail due to the spatial-averaging required for volume-fraction-dependent quantities. To address the loss of this topological metadata, we consider a Lagrangian tagging approach that recovers key information about individual bubbles without modifying the underlying multiphase solver. Building on the connected-component labeling algorithm of Herrmann (2010), we implement and extend a VOFCCL method to identify and track bubbles in VOF simulations. The extended algorithm makes use of the color function C to adapt the original Level-set-based method to VOF, and incorporates an additional retagging procedure that streamlines the post-processing of bubble information. Verification of the VOFCCL algorithm is first carried out, followed by validation of the two-phase flow solver through single-bubble rise simulations at different Morton numbers ( M o ). Finally, we demonstrate the viability of the method as a tool to analyze bubbly flows and extract bubble-resolved statistical quantities such as bubble count evolution and spatial distribution, which are otherwise inaccessible quantities in traditional VOF analyses.