# The Impact of Single- and Multicomponent Liquid Drops on a Heated Wall: Child Droplets
## 1 Introduction
[5] varied the Weber number from 50 to 1080, using water, isopropanol, and glycerin as well as four materials of a substrate, namely, smooth glass, polyvinyl chloride, wax, and rough glass. A drop of the liquid with a lower surface tension broke up at lower Weber numbers, while an increase in roughness considerably reduced the critical Weber number. [PERSON] et al. [6] used lower Weber numbers because the drop diameter was \(1.9\pm 0.03\) mm, and the average roughness of surfaces was 0.025\(-\)6.3 \(\upmu\)m. They showed that increasing the Weber number and the surface roughness promoted the drop breakup. In addition to roughness and thermophysical properties of substrate materials, the surface hydrophilicity also had a governing effect on breakup. In particular, [PERSON] et al. [6] utilized ultrahydrophilic, hydrophilic, hydrophobic, and superhydrophobic surfaces and performed the experiments at a surface temperature ranging from 125 \({}^{\circ}\)C to 415 \({}^{\circ}\)C and Weber numbers from 10 to 225. There was some mean temperature range, at which the drop broke up to form a maximum number of child droplets. [PERSON] et al. [7] generated a sequence of drops to impinge on a surface, so that each successive droplet contacted with a liquid film of a different thickness. They presented the outcomes of two successively moving drops impinging on a surface, varying their diameter from 0.39 mm to 0.65 mm and velocity from 2 m/s to 5 m/s. Metal surface temperatures were 25 \({}^{\circ}\)C, 300 \({}^{\circ}\)C, and 500 \({}^{\circ}\)C, whereas the glass surface temperature remained 25 \({}^{\circ}\)C. When two drops fell on the surface one after another, a corona was formed upon the impingement of the second drop. Both drops coalesced, and the resulting rim spread over the surface in a corona-like shape. If the first drop impinged on the surface heated up to 300 \({}^{\circ}\)C, it then deformed, forming a thin lamella, and then broke up into smaller fragments. At a surface temperature of 500 \({}^{\circ}\)C, a moderate number of child droplets emerged. In addition, surface temperature has a significant effect on drop cooling. [PERSON] [10] studied the efficiency of cooling water drops falling on the metal disks heated up to 85-400 \({}^{\circ}\)C. They used stainless steel and aluminum disks with a surface roughness Ra of 0.4 and 3, respectively. The drop impact velocity was 2.2 m/s. The drop cooling efficiency substantially depended on the surface temperature and was practically independent of the surface roughness. [PERSON] et al. [11] studied the impact of a nanofluid drop onto a surface (aluminum sheet) with a magnetic field. The effect of surface properties on the dynamic behavior of the drop was analyzed. The behavior of drops on both treated and untreated surfaces had the same tendency: the drops expanded to the maximum diameter (stretch) and then narrowed. However, the treated surface provided a larger drop size, which is explained by the degree of adhesion between the drop and surface. Experimental findings [1; 2; 3; 4; 5; 6; 7; 8] are the basis for developing the models of drop impact on solid walls. Some interesting results in this area were obtained, for instance, by [PERSON] et al. [9], who proposed a model of fuel film formation when impinging a diesel aerosol on a low-temperature wall. The model described the mechanism of fuel film emergence, its breakup and the interaction between the drop having spread over the surface and the drop impinging on it. The theoretical results produced an acceptable fit with experimental data. An important factor was the formation of a thin liquid film on the surface and the contact of all successive droplets with this film. Thus, for instance, [PERSON] [10] described theoretically the non-stationary laminar viscous flow in a thin layer of a Newtonian fluid. Such a flow appears during the drop impact on a dry surface at high Weber and Reynolds numbers. As a result, [PERSON] [10] solved the Navier-Stokes equation theoretically for the viscous flow in an expanding drop.