# Rates of High-Temperature Evaporation of Promising Fire-Extinguishing Liquid Droplets
## 1 Introduction
The theoretical results obtained for the case of homogeneous concentration illustrated a higher evaporation rate at the end of the droplet lifetime. The change in droplet density was shown to be a more important and dominant factor, which affects the evaporation rate of the electrolyte solution droplet. It was found that the evaporation and crystallization affect the surface of the droplet, which limits the diffusion of the solute. This effect maintains a high concentration of solute near the free surface of the droplet. These regularities explain the differences in the results for radius changes in water without impurities and solutions. The paper [27] presented the results of studies of evaporation of droplets (radius \(\approx\) 10 mm) on the substrates of extrusion polystyrene, plexiglass, and stainless steel at 24 \({}^{\circ}\)C and a relative humidity of 30%. It was assumed that the transport of water vapor and trapped air mainly moves upward due to the low molar mass of the water vapor. Simulation results using finite plane sources and semi-infinite solids served to estimate the droplet temperature and evaporation rate. The main dependence of the evaporation on the substrate material and droplet sizes was established. It was shown that, in the experiments, there was natural convection, which provides evaporation rates significantly exceeding the rates of diffusion into stagnant air. The effect of the thermocouple junction on the characteristics of the evaporation of a droplet of a binary solution of n-Dodecane and n-Hexadecane has been experimentally and theoretically investigated. The corresponding droplets with an initial diameter of 900 \(\upmu\)m were placed on the thermocouple junction or on the end of the quartz fiber to record the values of the integral evaporation characteristics [24]. At low ambient temperatures (200 \({}^{\circ}\)C), the conductivity of the fiber mainly affects the early evaporation stage. At a high temperature (500 \({}^{\circ}\)C), it affects the entire evaporation process. The influence of the fiber diameter on droplet evaporation has also been investigated. The evaporation rate of droplets is shown to vary nonlinearly with an increasing fiber diameter. Features of heating and internal convective flows were theoretically studied to estimate the mobility of droplets on a hydrophobic surface [28]. Temperature and velocity fields of intra-droplet convection were modeled against the background of experimental conditions. The acceleration of the liquid inside the droplet was predicted for droplets of different sizes. The results of theoretical studies of convection were compared with measurements of particle velocities recorded by the Particle Image Velocimetry (PIV) method. Adhesion, inertia, and shear forces were determined for the case of droplet slip on a hydrophobic surface. It was found that the calculated velocities were in good agreement with the PIV data. Two vortices were formed in the droplet with circulating flows, rotating in opposite directions due to the interaction of Marangoni flows and buoyancy. The Bond number was found to be less unified (in particular, in the range of 0.03-0.2) for all droplet sizes (15-100 \(\upmu\)L). This indicated that the Marangoni flow dominated over the buoyancy flow within the drop. The inertia force of the droplet became greater than the adhesion and shear forces of the liquid when heating. Hence, the droplet slid onto a hydrophobic surface, which was also observed in the experiments. The values of the Nusselt and Bond numbers increased with the growth of the droplet volume and reached maxima of 151 and 0.2 at a droplet size of 100 \(\upmu\)L.  
Evaporation of water and ethanol droplets was experimentally studied in the paper [22]. The results of studies of the evaporation rate of droplets suspended on a thermocouple under the influence of laser radiation and without it were presented. Laser excitation was shown to lead to a significant temperature increase in the droplets.