Figure 4. Comparison of the result of DBFF between the
experiment and calculation based on the regressed DIFT.
We have presented in the above section that the DBFF changes
monotonically with DIFT. To determine DIFT, the quantitative
relationship between the DBFF and the interfacial tension is required.
We have presented such a correlation between the DBFF and the static
interfacial tension in our previous research 37, as
shown in Eq. 3. This equation provides a bridge between the DIFT and the
static interfacial tension, helps us quantitatively characterize the
DIFT with a serials of known static
interfacial tension.
Based on the experimental data in Figure 3(a), the interfacial tension
in Eq. 3 was regressed by nonlinear
least square fitting. The obtained
values of DIFT at different height are shown in Table 2. With these
DIFT, the calculated DBFFs are shown in Figure 3(a) as curves. Figure 4
also shows the comparison between the calculated results and the
experimental results for DBFF. Considering that there is an error of
about 0.05 in the statistical process 36, 37, the
experimental results below 0.1 are useless for evaluating the calculated
results. We can see from Figure 4 that the prediction error of this
correlation is within ±25% when the DBFF is greater than 0.1. The
correlation in our previous work with different static interfacial
tensions fits well with the experimental data of this work with DIFTs.
As a comparison, the static interfacial tension was also regressed from
the DBFFs measured in the blank experiments. The results were also
listed in Table 2. We can see that the obtained interfacial tensions are
almost the same at different height of the column. Furthermore, the
result is approximately equal to that measured by pendent drop method
(14.98 mN/m). These results furtherly proved the feasibility of the
regression method. Moreover, we can see from Table 2 that the DIFT
increases from the column top to bottom, and almost reaches the value of
equilibrium interfacial tension (12.8 mN/m, measured by pendent drop
method) at the height of 590 mm. The variation of DIFT along the column
will be discussed in detail in the next section.