## 3 Results and Discussion
### Velocity and Temperature Field for Sessile Water Drop after the Fall of Another Droplet of Water
The excess of \(\Delta T_{s}\) almost three times for the initial period, in comparison with the quasi-stationary thermal regime, leads to a three-fold increase in the convection velocity for the initial period of time in contrast to \(t>7\) s.  
Figure 5a gives the temperature field of the surface of drop 2 using the thermal imager. On the basis of the thermal images (Figure 5a), the hottest area of drop 2 surface is in its center, and when moving towards the contact line \(T_{s}\) decreases (except for a very narrow area near the contact line). The direction of the temperature gradient cannot be related to the measurement error of the thermal imager, i.e., to the effect of the wall. The drop 2 height of 2-3 mm is much higher than the lowest possible height, when there is an effect of the wall on the infrared radiation for the water layer [47] (the water layer thickness should be no less than 0.3-0.5 mm). Even for the specified small  
Figure 5: (a) Thermal image of water drop 2 interface (\(Ma_{T}\)—the thermal Marangoni number, \(t=5\) s); (b) the direction of characteristic velocities for the two limiting cases of interaction of drops (the joint influence of dynamic and thermal factors); (c) velocities in the horizontal section of sessile drop 2 (\(V_{02}=40\)\(\mu\)L; \(V_{01}=2.5\)\(\mu\)L; \(T_{w}=20\)\({}^{\circ}\)C). height of the liquid, the effect will also be negligible. The direction of rotation of the liquid in the drop and the value of the average velocity depend on the ratio of forces: buoyancy (\(Ra\)), surface force due to the temperature gradient on the free surface of the drop (\(Ma_{T}\)) and the friction force. The direction of rotation will be determined by the value and the direction of \(Ra\) and \(Ma_{T}\). Then, the thermal Marangoni flow (\(Ma_{T}\)) will be directed from the center of drop 2 to the contact line (towards the greater surface tension of water \(\sigma\)) (Figure 5a). It is important to note that in this work the direction of the temperature gradient on the interface and of the \(Ma\) do not coincide with the generally accepted ones, i.e., from edge to center. The flow direction towards the center of drop 2 occurs with weak convection, i.e., when the conductive heat transfer plays a determining role. In this case, the coldest point on the surface of the sessile drop 2 will correspond to its center. Then the maximum surface tension will also take place in the central part of drop 2 surface. In the present work, convection significantly exceeds the conductive transfer and determines the direction of the liquid rotation. At the initial moment of stretching drop 2 on the surface of the hot wall, buoyancy determines a certain direction of rotation, which afterwards remains. This direction of circulation is not caused by the error of the thermal imager, as indicated above. Figure 5b shows a diagram of velocity directions for the following options: \(U_{02}\) and \(U_{\rm MT}\). The pulse from the falling droplet 1 (\(mU_{01}\)) is completely transmitted to the sessile drop 2 on a hot wall. Let us consider the factors that can lead to free convection in the sessile heated drop after the small cold drop falls. After falling, a pressure jump occurs in the bottom surface of the sessile drop [48]. The duration of the pressure surge is microseconds. In the present work, measurements of the pressure inside the drop were not performed. Further, a transition process is implemented, when an excess of pressure leads to convection inside the drop and to a change in its shape, as well as to fluctuations in the free surface of the sessile drop. These factors are called dynamic. Since the pressure jump and interaction of elastic waves inside the droplet last for microseconds, the action of viscosity forces can be neglected during this time. Changes in the shape of the large drop when two drops interact can be neglected as well, since the contact line of the drop remains stationary, and the volume of the small falling drop is much smaller than the volume of the sessile drop.