So far it was discussed that the homogenous operation regime exhibits
Gaussian-like characteristics and heterogeneous regime features a spike
shape distribution; this was inspected using PDF plots of BSD from the
range tested (see Table 1). Figure 4 shows the bubble size distribution
from G1 plotted on probability coordinates. Figure 4a shows that in
homogenous range (based on gas superficial velocity) the BSD exhibits
linearity on a normal distribution probability plot. The near-Gaussian
behavior in the homogenous regime was also discussed above by means of
the PDF shape and higher order statistics. BSD from heterogeneous
operation cases (41.4 mm/s ≥ USG ≥ 69 mm/s) in G1
was plotted on a lognormal probability plot (see Figure 4b). It is
interesting to see the strong linear behavior of BSD on a lognormal
probability plot. Figure 4b also shows that the range at which the BSD
exhibit linear trend on a lognormal probability plot starts at the mode
of the PDF (thick solid vertical line) and ends at the Sauter mean
diameter (d32 , vertical lines). The mode of the
PDF corresponds to the most frequent bubble size,dmf , interested reader can refer to Mohagheghian
and Elbing47 for analysis ofdmf . The present study shows that only a portion
of the right leg of the BSD PDF within heterogeneous regime is
lognormal. The PDF exhibits a linear trend betweendmin and dmf ; furthermore,
the PDF can be modeled with a second order polynomial curve betweend32 and dmax .