Figure 2 Comparison of the predicted results with experimental data in the literature^1,3,6,35

Combining the above parameters with the physical data provided in the literature, we nondimensionalized the experimental data and plotted them in Figure 2. It can be seen that the predicted results of the model are in good agreement with the experimental data of Andersson and Maaß, which further validates the accuracy and generalizability of the theoretical model. However, Figure 2 shows that the predicted results of the model are in relatively poor agreement with the experimental data of Ashar et al., especially at the lower We_L , which we analyze as a result of the higher drop viscosity of the experimental system in Ashar et al. Moreover, the high spatial inhomogeneity of the turbulent energy dissipation rate in their experimental device can also cause deviations between the model predictions and experimental results.

As is discussed in Section 2, most breakup frequency models in the literature are based on limited modeling frameworks. Particularly，frameworks based on the eddy-particle collision and based on the statistical description are mostly adopted by researchers. Breakup frequency models proposed by Coulaloglou and Tavlarides¹⁸ (CT model, as shown in Eq.) and proposed by Luo and Svendsen¹⁵ (Luo model, as shown in Eq.) are the most representative and well-known models under the above two frameworks, respectively.

CT model:

Luo model:

In such a scenario, the two models are also analyzed in the present work. To intuitively compare the experimental data of drop breakup frequency obtained by different researchers, the method recommended by Lehr et al. ³⁶ to dimensionless the drop size and drop breakup frequency is introduced, that is:

Where L ^* and T ^* have length and time dimensions respectively:

In the original model of Coulaloglou and Tavlarides¹⁸, the drop breakup frequency depends on the dispersed phase density, that is, the density ρ_f in Eq. and Eq. takes the value of the dispersed phase density ρ_d . Firstly, we compared the predicted results of the CT model with the experimental data, as shown in Figure 3a. It can be seen that by changing the specific values of the adjustable parameters, the original CT model can conform to the experimental data under different experimental facilities, but the accurate prediction of the breakup frequency under different facilities cannot be achieved by a fixed combination of the parameters. From the original literature of Coulaloglou and Tavlarides, it can be seen that the density term comes from the estimation of the turbulent stress. According to the current cognition of most researchers, the magnitude of the turbulent stress should be related to the continuous phase density, which means that the dispersed phase density in the CT model should be replaced by the continuous phase density, and thus, the density ρ_f in Eq. and Eq. is taken as the continuous phase density ρ_c in the following analysis. And then, we compare the predicted results of the density-corrected CT model with the experimental data, and the result is shown in Figure 3b. It can be seen that by adjusting the adjustable parameters combination, the modified CT model can better match the experimental data of different researchers relative to the original model. Also, we plot the predicted results of the Luo model in Figure 3b, and it shows that the Luo model overestimates the actual magnitude of the breakup frequency.