## 2 Materials and Methods  
### Materials  
In the experiments, a group of liquid compositions was used to understand the impact of liquid properties on the characteristics of droplet-particle collisions. Their properties are listed in Table 1. The viscosity of liquids was determined by means of a Brookfield DV3T LV visometer [46] at room temperature (20-23 \({}^{\circ}\)C). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name of** & **Density** & **Surface Tension** & **Dynamic** & **Interfacial** \\
**Composition** & **\(\rho\), kg/m\({}^{3}\)** & **\(\sigma\), mN/m** & **Viscosity \(\mu\), mPa-s** & **Tension \(\sigma_{0}\), N/m** \\ \hline Water & 998 & 72.69 & 1 & – \\ \hline \hline \multicolumn{5}{c}{Compositions to vary \(\mu\)} \\ \hline Glycerol solution & \multirow{2}{*}{1022} & \multirow{2}{*}{71.3} & \multirow{2}{*}{1.371} & \multirow{2}{*}{–} \\ (10 vol\%) & & & & \\ \hline Glycerol solution & \multirow{2}{*}{1060} & \multirow{2}{*}{69.3} & \multirow{2}{*}{2.239} & \multirow{2}{*}{–} \\ (25 vol\%) & & & & \\ \hline Glycerol solution & \multirow{2}{*}{1126} & \multirow{2}{*}{66.1} & \multirow{2}{*}{6.301} & \multirow{2}{*}{–} \\ (50 vol\%) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of liquids under study. Viscosity was measured using a spindle complete with a heat-insulated cylindrical jacket (150 mm high, with an aperture 20 mm in diameter to fit a 50-mL test tube) and a SC4-34 spindle (measurement range 24-600 \(\times\) 10\({}^{3}\) mPa-s) operating with a Small Sample Adapter (SSA) (heat-insulated with a cylindrical jacket with a built-in chamber for samples with a volume of less than 16 mL). The viscometer with dedicated software measured the shear rate of liquid that was used to calculate its dynamic viscosity. The accuracy of the shear rate measurement was \(\pm\)1% in compliance with ASTM D445 [47]. To determine the influence of liquid viscosity on the characteristics of atomization of droplets due to their collisions with a solid particle, solutions with varying concentrations of glycerol (10 vol%; 25 vol%; 50 vol%) and distilled water were used. Such solutions made it possible to vary the liquid viscosity (1-6.301 mPa-s). To explore the impact of liquid surface tension on the regimes and outcomes of the interaction of a droplet with a solid particle, aqueous solutions of surfactants were prepared: 99.5 vol% distilled water and 0.5 vol% Tween-20; 99.5 vol% distilled water and 0.5 vol%. Such solutions made it possible to vary the surface tension of liquid in the range of 36.1-72.69 mN/m. Du [PERSON] ring method (K6 tensiometer, KRUSS) [48] was used to measure the surface tension of the investigated liquids at 20-23 \({}^{\circ}\)C. It ranged from 1.0 to 90.0 mN/m. To determine the liquid interfacial tension, an ST-2 stalagmometer was used. Its operating principle is based on determining the volume of water droplets forced onto the diesel-with-emulsifier/water interface [49]. D\({}_{\text{c}}\)D emulsifier was selected to vary the interfacial tension [50]. Summer diesel fuel, distilled tall oil (DTO), triethanolamine (TEA) and diethylamine (DEA) were mixed to produce the emulsifier. The diesel emulsion was prepared in a Sapfir 2.8 ultrasonic bath at a frequency of 35 kHz. At the first stage, D\({}_{\text{c}}\)D emulsifier was added to diesel fuel at a concentration of 0.08 g/L and 1.60 g/L. The choice of these concentrations was justified in [45]. After that, the components were stirred for 2 min and 10 vol% water was added. The emulsion was stirred for 300 s. The emulsions involved in the research and their preparation procedure are identical to those used in [45]. Spherical metal balls 2-4 mm in diameter were used as solid particles. This size of spherical particle was chosen by varying the surface curvature and determining the size of particles at which the collision of a droplet with a particle was close to that of a droplet with a flat substrate. Metal substrates in the form of a 10-mm-thick cylindrical disc 80 mm in diameter were also used.