*4.1. The E*ff*ects of Ca and La1*

After the parameters such as the injection velocity of the upper side nozzle and the lower side nozzle are respectively substituted into Equation (14), the data of multiple linear regression are shown in the Table 6:

**Table 6.** Value and standard error of lg Ca and lg La1 by multiple linear regression for the upper side nozzle and lower side nozzle.


From Table 6, the equation of the mixing time of the upper side nozzle and the lower side nozzle and the similar number of Ca, La1 can be obtained, respectively:

$$\tau = \frac{D\_s}{V\_{us}} \Big( \text{Ca}^{-0.96} \text{La}\_1^{-0.65} \text{)}\tag{15}$$

$$\tau = \frac{D\_s}{V\_{ls}} \text{(Ca}^{-0.74} \text{La}\_1^{-0.67} \text{)}\tag{16}$$

where *Vus* is the injection velocity of the upper side nozzle, m·s−1, *Vls* is the injection velocity of the lower side nozzle, m·s<sup>−</sup>1.

Figure 5a,b shows the relationship between the experimental value and the calculated value of the dimensionless group of the mixing time of the upper side nozzle and the lower side nozzle, respectively, made according to the Equations (15) and (16). As can be seen from Figure 5a,b, for both the upper side nozzle and the lower side nozzle, the experimental values have a considerable linear relationship with the calculated values. At the same time, to further verify the comparison, Figure 6a–f shows the relation diagram of the experimental value and the calculated value of the mixing time dimensionless groups in three monitoring points τ1, τ<sup>2</sup> and τ<sup>3</sup> of the upper and lower side nozzle, respectively. It can also be seen that it has a higher consistency with the τ (cf. Figure 5).

**Figure 5.** Comparison of experimental lgτ*Vs*/*Ds* with calculated ones for upper side nozzle (**a**) and lower side nozzle (**b**), respectively, using proposed Equations (15) and (16).

**Figure 6.** Comparison of experimental lgτ*Vs*/*Ds* with calculated ones for upper side nozzle (**a**–**c**) and lower side nozzle (**d**–**f**), respectively, using τ1, τ2, τ3.
