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.