## 3 Results and Discussion
### Instantaneous Velocity Fields in a Horizontal Section of Sessile Drop  
It is quite difficult to measure the velocity field directly at the moment of the fall (for example, at \(t=0.01\)-\(0.1\) s) because of the extremely fast change in the direction of the vectors in time and because of the rapid change in the velocity in time. In Figure 9, time \(t=0\) s corresponds to the time of drops' contact. Accordingly, when \(t\) is less than zero, there is no drop impact, and for \(t>0\), the image after the interaction of drops is given. After the fall of the droplet, on the surface a predominant direction of velocity appears, resulting in a single main vortex (\(t=0.75\) s), the size and energy of which substantially exceed those of other smaller vortices (\(t=0.25\)-\(0.5\) s). In the vicinity of the wall (\(t=0.75\) s), the velocity vectors (in the horizontal plane) have the same direction (parallel to each other). In this case, the diameter of the vortex coincides with the diameter of the drop. It is obvious that near the free surface of the drop, the direction of the liquid rotation will change to the opposite. This flow pattern is fundamentally different from Figure 6a, when even a very small value of _We_ leads to unstable rotation of the liquid and to fragmentation of the vortices. Already in 0.25 s, several smaller vortices are formed. It is obvious that a significant increase in the value of _We_ will lead to an increase in the number of small vortices. Thus, thermocapillary forces (Figure 9) lead, on the contrary, to stable rotation. This conclusion is very important, as the Marangoni forces will lead to the maximum convection velocity. The thermal factor has a much greater effect (compared to the dynamic factor) due to the stability of the surface flow in the presence of thermocapillary forces. It is important to emphasize some limitations related to stability. The aqueous solution of alcohol leads to instability of the surface flow and to chaotic behavior [3], i.e., in this case, surfactant in the form of alcohol forms an uneven field of concentrations on the drop surface. Below we will focus on this property, which is very important for correct modeling. In Figures 10-12, sessile drop 2 consisted of water and the falling droplet 1 consisted of an aqueous solution (water + surfactant). As can be seen from Figures 10-12, the velocity field, after the droplet fall, becomes uneven. Against the background of the main direction of motion there are individual vortexes that change their position and direction of rotation. The absence of a symmetrical toroid in the drop and the presence of many small vortices, as well as a rapidly changing pattern of the velocity  
Figure 9: Velocity field in horizontal section of drop 2; \(V_{01}=2.5\) uL; \(V_{02}=40\) uL; \(T_{w}=80\) °C; \(T_{01}=20\) °C; water (droplet 1) + water (drop 2). field in the drop section is probably due to the nonuniform distribution of surfactant concentrations on the drop 2 surface, which leads to different surface tension gradients \(d\sigma/dl\) (uneven distribution of \(\sigma\) on the free surface will result in gradients \(\Delta\sigma/\Delta l\)). For approximately 2 s after the droplet fall, the average velocity in the section continuously decreases. After \(t=1.75\) s (Figure 11) the velocity increases slightly since the amplitude of the average value is commensurate with the random pulsation value. The flow inside drop 2 is unstable, and the vortex is continuously redistributed from one area to another. Figure 10: Velocity field in horizontal section of drop 2; \(V_{01}=2.5\)\(\mu\)L; \(V_{02}=40\)\(\mu\)L; \(T_{w}=80\)\({}^{\circ}\)C; \(T_{01}=20\)\({}^{\circ}\)C; water (drop 2), water + surfactant OP-10) (droplet 1). Let us estimate the time for the spread of surfactant molecules over the surface of sessile drop 2. The diffusion coefficient \(D_{s}\) on drop 2 surface for water-SDS is assumed to be the same as in the volume \(\sim\) 10\({}^{-10}\)[59].