Depth-Aware Machine Learning Framework for Bubble Characterization in Two-Phase Flows

Abstract

Understanding the three-dimensional motion of bubbles is essential for interpreting transport and mixing in multiphase flows, especially when bubbles deform under shear or move rapidly through the flow field. In many laboratory setups, only a single high-speed camera is available, which limits measurements to two dimensions. Traditional image-processing tools can identify bubbles only when they appear circular and isolated, but they struggle with irregularly shaped bubbles, shear-induced deformations, strong blurring, and partial overlaps. Multi-camera systems could overcome these issues, but require significant hardware additions and calibration effort. In this work, we introduce a new machine-learning framework that can detect bubbles and estimate their depth using only a single 20 kHz high-speed camera with 3 \textmu m resolution. The method first uses a large unlabeled dataset and clusters the bubbles with an unsupervised algorithm to reveal their underlying structure. These clusters provide pseudo labels, which are combined with a small set of true in-plane bubble labels to train a semi-supervised model that generalizes across different bubble appearances. These components produce a continuous depth-proxy score that indicates how close each bubble is to the imaging plane, even when bubbles are distorted or irregularly shaped. In parallel, we perform robust bubble identification using instance segmentation, which separates touching, overlapping, and elongated bubbles generated by high-velocity shear. Quantitatively, the in-plane segmentation baseline achieves strong held-out performance with Average Precision (AP) = 0.818, implying stable detection across thresholds, clutter, bubble detection Precision of 0.901, and a False-Positive Rate (FPR) near 6.1\%, hence low spurious bubbles and cleaner statistics under the tested acquisition conditions.