## 3 Results and Discussion
### Effect of Liquid Viscosity  
Figure 4 shows the interaction of particles with droplets at varying dynamic viscosities of liquid. Video S1 contains the corresponding video-grams. It is clear in Figure 4 that, at identical sizes and velocities of droplets before the collision, a lower number of secondary fragments with larger sizes were generated with a higher dynamic viscosity of liquid. For example, for the 50 vol% and 10 vol% glycerol solutions, there were 8 and 14 child droplets, respectively. These results are consistent with the findings [45]. An increase in viscosity leads to greater viscous friction forces in the near-wall boundary the liquid layer. These prevent its spreading over the particle surface. Hence, the liquid-particle contact area is smaller. As a result, a liquid layer with a smaller volume is entrained from the particle surface. The viscous forces prevent its significant deformation during floating. Thus, fewer child droplets result from its breakup. With highly viscous liquids, the newly formed child droplets quickly assumed a spherical shape. That was caused by high internal friction forces that changed the standard deformation cycles of droplets during free fall (prolate ellipsoid--sphere--oblate ellipsoid--sphere, etc.) and by surface tension forces of liquid, preventing its deformation. The observed effects also led to a smaller area of separation of child droplets after a highly viscous liquid contacted a particle compared to the equivalent characteristic in the experiments with water droplets. More viscous liquids spend greater  
Figure 3: Images illustrating the collisions of water droplets with a particle: (**a**)—agglomeration (\(R_{\rm d}\) = 2.15 mm; \(R_{\rm p}\) = 3 mm, \(U_{\rm d}\) = 2.67 m/s); (**b**)—stretching separation (\(R_{\rm d}\) = 2.2 mm; \(R_{\rm p}\) = 3 mm, \(U_{\rm d}\) = 3.2 m/s). energy on overcoming viscous friction. Thus, the child droplets had lower velocity when breaking off from the spherical particle. Figure 5a presents a collision regime map for water and glycerol solution droplets interacting with a metal particle approx. 3 mm in diameter. A dimensionless linear impact parameter (\(B\)) was used to construct the regime maps. This allowed for the radii of droplets and particles, the centricity of droplet-particle interaction and the Weber number, related to inertia and surface tension, droplet velocity and sizes. An increase in the liquid viscosity was found to significantly shift the boundary between agglomeration and stretching separation towards higher Weber numbers (Figure 5a). Thus, at identical \(R_{\text{d}}\), \(B\), \(\alpha\) and ambient gas temperature, the boundary of stretching separation for water droplets corresponds to We = 20 and for the 50 vol% glycerol solution  
Figure 4: Images illustrating the collisions of water droplets with a particle in the stretching separation regime at varying liquid viscosities. Figure 5: Collision regime maps for liquid droplets interacting with solid particles (**a**) and ratios of free surface areas after (\(S_{1}\)) and before (\(S_{0}\)) the head-on collision with \(B\) = 0 (**b**) at varying viscosities of liquid and constant size of droplets: 1—distilled water; 2—10 vol% glycerol solution; 3—25 vol % glycerol solution; 4—50 vol % glycerol solution. to 75. Consistent occurrence of stretching separation for the composition with higher viscosity is provided by increasing the droplet velocity. Changes in the viscous forces due to varying concentrations of glycerol in the aqueous solution cannot significantly change the balance of forces. Forces caused by surface tension remain dominant. An increase in the liquid viscosity generally increases the critical Weber number by 20-30%. For boundaries of transition plotted for agglomeration and stretching separation, approximations were obtained like \(B=\text{a}\cdot\text{We}^{2}+\text{b}\cdot\text{We}+\text{c}\).