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.