## 3 Results and Discussion
### Comparison of Secondary Atomization Methods
Such models should factor in the whole complex of processes identified in the conducted experiments with droplet-particle collisions. A special emphasis is placed here on the calculation of energies in the droplet-particle interaction zone. To calculate the kinetic dissipation energy (\(E_{\text{c}}\)) in the droplet-particle collision zone, the following equations [8] are applied:  
\[E_{\text{P}}=(\int_{\text{hc}}^{\text{h0}}F_{\text{P}}\text{ dh}+\int_{\text{h0}}^{\text{hrupt}}F_{\text{P}}\text{ dh})/E_{\text{i}};\;F_{\text{P}}=-\int_{\text{S}}\rho\text{i}_{\text{z}}\cdot \text{nds}, \tag{1}\]  
\[E_{\text{vis}}=(\int_{\text{hc}}^{\text{h0}}F_{\text{vis}}\text{ dh}+\int_{\text{h0}}^{\text{hrupt}}F_{\text{vis}}\text{ dh})/E_{\text{i}};\;F_{\text{vis}}=\mu\int_{\text{S}}\
abla u\cdot\text{nds}, \tag{2}\]  
\[E_{\text{sf}}=F_{\text{sf}}\cdot(\text{hrupt}-\text{h}_{\text{c}})/E_{\text{i }};\;F_{\text{sf}}=2\alpha F_{\text{p}}\text{sin}(\alpha)\text{sin}(\alpha+ \theta), \tag{3}\]  
\[E_{\text{c}}=(0.5m_{\text{d}}{U_{\text{d}}}^{2}-0.5m_{\text{cd}}{U_{\text{cd} }}^{2})/E_{\text{i}}, \tag{4}\]  
where h\({}_{\text{c}}\), h\({}_{\text{0}}\), h\({}_{\text{rupt}}\) are the heights of the particle center at the moment of the droplet-particle contact, \(U_{\text{d}}\), \(U_{\text{cd}}\) are the initial droplet velocity and child droplet velocity. \(F_{\text{P}}\), \(F_{\text{vis}}\), \(F_{\text{sf}}\) are the projections of the pressure, viscous drag and surface tension forces in the normal direction. \(E_{\text{P}}\), \(E_{\text{vis}}\), \(E_{\text{sf}}\) are the proportions of the kinetic dissipation energy caused by external forces. \(E_{\text{i}}\) is the initial kinetic energy. For the transition from agglomeration to stretching separation to occur, the kinetic dissipation energy must be greater than or equal to 1. At \(E_{\text{c}}>1\), stretching separation is bound to occur, which is one of the prerequisites of using liquid in industrial applications. Figure 11: Effect of liquid properties on the transition boundary between agglomeration and stretching separation during the collision of a droplet with a solid particle (**a**), with another droplet (**b**) [45] and with a solid substrate (**c**): 1, 2—water; 3, 4—50 vol% water and 50 vol% glycerol; 5, 6—10 vol% water and 90 vol% diesel; 1, 3, 5—stretching separation; 2, 4, 6—agglomeration. A decrease in the surface tension and an increase in the viscosity of liquid lead to lower kinetic energy (\(E_{\rm i}\)) and, thus, higher kinetic dissipation energy (\(E_{\rm c}\)). This brings about stretching separation. The Equations (1)-(4) can be used to find the critical ratios of energies in the droplet-particle collision zone, at which the transition between the regimes occurs in the experiments with droplets colliding with particles and with each other. Since most technologies involve multicomponent and multiphase flows, it is important to differentiate between the regimes and critical conditions for the collisions of droplets with each other and droplets with solid particles. This research presents the experimental results for developing the existing models to take this differentiation into account.