where σ is the surface tension and ∆pcapis the differential pressure measured across the sparger at the onset of bubbling. Equation (1) was adopted from Houghton et al.,42 which explains that the∆pcap measured in the aforementioned fashion represents the average capillary pressure at the onset of bubbly. In the current work the average pore size was 85μm ± 10μm.
The refraction index mismatch as well as the round geometry of the acrylic column introduced a significant optical distortion. Thus a refractive index matching box (water-box) was used to mitigate this problem. The water-box was 0.2m × 0.15m × 0.15m, made from casted acrylic, and filled with water. Spatial calibration was performed with a custom calibration plate, and the residual image distortion after mounting the water-box was negligible relative to the bubble sizes measured.

2.2 Bubble size measurement

A camera (EOS 70D DSLR, Canon) was used to capture monochrome still images of the bubbles. This camera had an APS-C CMOS image sensor (22.5mm × 15mm) with a maximum resolution of 5472 × 3648 pixels. The camera pixel size was 4.1μm × 4.1μm with a 14-bit depth. The camera was fitted with a 60 mm 1:2.8 lens (Canon) to produce a nominal field-of-view of 120 mm by 80 mm. The column was backlit with an LED panel (Daylight 1200, Fovigtec StudioPRO) that delivered up to 13,900-illumination flux (5600 K color temperature) at one meter. Backlighting was uniformly diffused using a 3 mm thick white acrylic sheet. Homogenous backlighting simplifies image-processing as well as improves the measurement accuracy. Bubble images were processed for bubble size measurements using ImageJ (1.49v, National Institutes of Health (NIH), Bethesda, MD, USA),43-46 a common open access image-processing program. Within ImageJ, an edge detection algorithm was used to sharpen the bubble edges, subtract the background, and apply a grayscale threshold to convert the 14-bit images to binary images. A subset of images from each condition were manually processed and then used to determine the appropriate grayscale threshold. It is worth mentioning that the bubble images become darker in background as the number of bubbles per image increases. Therefore, a range of acceptable threshold values were explored for each condition and produced a 2% variation in measured bubble size. Interested readers are referred to the previous studies from the current research group47-49 for more details on the image processing scheme. Including uncertainty from the spatial calibration and image processing procedures, the measurement uncertainty was less than 8%. In the current work, the imaging system and processing scheme could resolve bubbles as small as 0.2 mm in diameter. Figure 2 provides an example of a bubble image with the identified bubbles using the appropriate threshold outlined. Figure 2 also depicts that the processing algorithm can identify in-focus bubbles and exclude out-of-focus bubbles, which minimizes the impact of out-of-plane bubble locations on the spatial calibration. In addition, Figure 2 shows that, even with a proper threshold, overlapping and defective bubbles can contaminate the size distributions. Consequently, each image was manually inspected for the aforementioned problems and impacted bubbles were removed from the population sample.