*4.2. The E*ff*ects of Ca, La1 and Njm*

.

After studying the effect of Ca and La1, the N*jm* dimensionless group is added here for the purpose of investigating the relationship between the dimensionless group of the mixing time and the dimensionless groups such as density, dynamic viscosity, stirring energy, flow rate, and so on based on the variable of velocity. The following table contains the multiple linear regression data based on the three dimensionless numbers of upper side nozzle and lower side nozzle, respectively:

From Table 7, the equations between the dimensionless group of the mixing time and the three dimensionless groups of Ca, La1 and N*jm* for the upper and lower side nozzles can be obtained, respectively, as shown below:

$$\pi = \frac{D\_s}{V\_{us}} \Big( \text{Ca}^{-1.90} \text{La}\_1^{-2.61} \text{N}\_{jm}^{-5.01} \) \tag{17}$$

$$\tau = \frac{D\_s}{V\_{ls}} \left( \text{Ca}^{-1.51} \text{La}\_1^{-2.27} \text{N}\_{jm}^{-4.11} \right) \tag{18}$$


**Table 7.** Value and standard error of lg Ca, lg La1, and lgN*jm* by multiple linear regression for upper side nozzle and low side nozzle.

Similarly, by drawing the experimental values and calculated values for the dimensionless group of mixing time, we can see from Figure 7a,b that they have a good linear correlation, and the comparison chart (cf. Figure 8a–f) of τ1, τ2, τ<sup>3</sup> is also shown a high consistency with τ (cf. Figure 7), respectively.

**Figure 7.** Comparison of experimental lgτ*Vs*/*Ds* with calculated ones for upper side nozzle (**a**) and lower side nozzle (**b**), respectively, using proposed Equations (17) and (18).

**Figure 8.** 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.
