An image analysis approach to determine average bubble sizes using one-dimensional Fourier analysis

This paper presents a methodology based on the one-dimensional Discrete Fourier Transform to estimate the Sauter mean diameter, D32, of a bubble population sampled from the collection zone of flotation machines. Binary images, recorded by means of a bubble viewer, were represented as a set of pulse trains. The spectral properties of the trains were then exploited to correlate the pulse widths of the square waves with the spectral bandwidth, BW, which was determined from their power spectral densities. As the pulse widths are indirect measures of the bubble size, a correlation between D32 and BW was obtained from simulated images, D32 = 3.7/BW1.1, in which known D32 values were set. This correlation was tested with three different datasets, which included different gas dispersion mechanisms (pneumatic and mechanical), type and concentration of reagents (frothers and synthetic seawater), superficial gas rates and image resolution. The results were in good agreement with those obtained by means of conventional image analysis. In addition, no special treatment was required for cluster analysis with the proposed methodology. The technique showed advantages in terms of robustness under a low number of analysed pulse trains as well as lower processing times to estimate the D32 for relatively small images.