Bubble Size Modeling and Characterization in Flotation Using Image Processing and Machine Learning

In this study, an intelligent framework was developed for modeling bubble size and evaluating its relationship with flotation performance using image processing and machine learning techniques. Experiments were conducted on a silica sample with 96–97% purity in a Plexiglas column cell (50 mm diameter, 3.5 m height). Three operating variables—air flow rate (0.1–0.4 L/min), collector concentration (0.5–1.5 g/kg), and frother concentration (0.3–0.7 mL/L)—were investigated using a full factorial design. High-speed video data were processed using histogram-based intensity mapping, CLAHE-based local contrast enhancement, adaptive thresholding, frame-to-frame tracking, edge enhancement, and geometric calibration. Bubble instances were manually localized using bounding boxes, followed by pixel-level polygon annotation of visible boundaries; these masks served as ground truth, while solid particles, strong reflections, and other non-bubble artifacts were treated as negative/background examples. A supervised YOLO11n-based model was integrated with the image-processing pipeline for bubble identification and segmentation, followed by boundary characterization and geometric diameter estimation. The effect of image enhancement was assessed using the same model configuration and data partitioning for original and enhanced image sets. For clear and isolated bubbles, the original-image workflow achieved a mean intersection-over-union (IoU) of 0.91 and a Dice coefficient of 0.95, whereas the enhanced-image workflow achieved a mean IoU of 0.96 and a Dice coefficient of 0.98. The mean absolute relative error in equivalent bubble diameter, calculated against diameters derived from manually delineated ground-truth polygon masks, decreased from 3.4% to 1.8% after image enhancement. The average rising velocity of bubble–particle aggregates was approximately 20% lower than that of free bubbles, with a Gaussian velocity distribution centered at 16 pixels per frame. At a constant air flow rate of 0.25 L/min and collector dosage of 1.00 g/kg, increasing frother dosage from 0.30 to 0.70 mL/L was associated with a decrease in Sauter mean bubble diameter (D32) from 1.20 to 0.70 mm. Under these conditions, the feed grade was 96.50% SiO₂, the concentrate grade increased from 98.63% to 99.21% SiO₂, and the calculated tailings grade changed from 95.08% to 94.10% SiO₂. Silica recovery increased from 40.88% to 48.24%, corresponding to an approximately 18% relative increase. The ML-based segmentation and geometric post-processing stage required approximately 0.244 s per bubble image crop on an Intel Core i7-6600U CPU. Overall, the framework links bubble characteristics with flotation performance and provides a basis for future real-time monitoring and control.