A stochastic approach for measuring bubble size distribution via image analysis

• A method is proposed to process images and determining bubble size distribution.
• The method accounts for bubbles in clusters, isolated and truncated by image edges.
• The importance of considering bubbles in clusters and truncated is established.

Gas dispersion properties are key parameters in flotation performance. Flotation rate constant has been reported to be strongly influenced by the bubble surface area flux (Sb). In order to determine Sb, both superficial gas velocity (Jg) and the bubble size distribution (BSD) have to be measured. The superficial gas velocity can be easily measured using the inverted probe method. On the other hand, measuring the bubble size distribution is an intricate process. Among the available methods for measuring BSD, image analysis is the most popular; nevertheless, it has some limitations, especially when bubbles appear touching each other in the image (bubble clusters). From a classical image analysis point of view, it is usually assumed that bubble clusters occur as a non-selective process and that not considering them does not bias the measurement.In this work, an alternative method for measuring BSD is presented. The image is represented as a coverage stochastic process, namely a Boolean model with circular objects, which allows determining statistical diameters, d10 and d32, and the complete BSD directly from the binary image. Both the classical image analysis and the Boolean modelling were tested first with a series of images generated at a laboratory flotation cell, and later with a series of simulated images where the actual BSD was known. In both cases, the stochastic approach proved to be better than classical image analysis in the determination of BSD and statistical diameters. The results show that even if bubble clusters are non-selective (which was imposed on the simulated images) large bubbles are more likely to be in a cluster, which implies that clusters must be considered in the measurement to avoid biased estimations.