## 3 Results and Discussion
### Velocity and Temperature Field for Sessile Water Drop after the Fall of Another Droplet of Water
Figure 7 presents the magnified thermal pictures of the drop 2 interface after the fall of droplet 1. At time \(t\) = 0 s there is a symmetrical temperature field (droplet 1 did not contact the surface of drop 2, droplet 1's temperature was 20 \({}^{\circ}\)C, and for drop 2 \(T_{s}\) = 67-70 \({}^{\circ}\)C. The purpose of thermal imaging measurements is to show the time of thermal relaxation (\(t_{T}\)) after the interaction of cold and hot drops. Already in \(t\) = 0.05 s after the merging of drops, the temperature on the free surface becomes quasi-stationary, i.e., the time of thermal relaxation is less than 0.1 s. From the contact line of the drop to the center of the drop, the distance on the free surface is approximately equal to \(l_{S}\) = 5.5 mm/s. You can estimate the velocity of the liquid on a free surface as \(U_{s}\) = \(l_{S}\)/\(t_{T}\) = 5.5 (mm/s)/0.05 (s) = 110 mm/s. The maximum value for the average velocity in drop 2 (\(U_{\rm{aver}}\), Figure 2b) is 7.2 mm/s. Thus, \(U_{\rm{s}}\) exceeds \(U_{\rm{aver}}\) approximately 16 times. This strong velocity suppression is due to the vortex formation inside the droplet, as well as due to the viscosity. Estimating how many times the velocity on the liquid surface (\(U_{s}\)) at the moment of the thermal jump exceeds the thermal front velocity (\(U_{a}\)) due to the molecular temperature conductivity \(a\). \(U_{a}\) = \(a\)/\(l_{S}\) = 0.03 mm/s. Then, \(U_{\rm{s}}\)/\(U_{a}\) = 3700. These estimates demonstrate that the surface thermocapillary forces play a large role in comparison with molecular transport when the thermal boundary conditions on the free surface of the liquid change sharply. An abrupt local change in surface tension due to the temperature \(T_{s}\) or due to the surfactant will result in a sharp velocity jump (\(U_{s}\)), which will quickly attenuate in an extremely short period of time. This conclusion is extremely important for the correct modeling of a large number of fast-flowing phase transition processes when there is a phase boundary (liquid-gas). One of them is the plasma spraying of the nanosurface. Temperature inhomogeneities on the surface of the melt during crystallization will lead to high velocities on the surface of the melt (liquid). In this case, to estimate this velocity, it is necessary to take into account the thickness of the liquid layer for calculating the friction force. As it is seen from Figure 7, already after 0.05-0.1 s additional cooling of drop 2, the surface will be only by 3-5 \({}^{\circ}\)C lower than for \(t=0\) s. The temperature difference on drop 2's surface in 0.05 s will be \(\Delta T_{s}=14\) + 4 = 18 \({}^{\circ}\)C, rather than 60 \({}^{\circ}\)C. According to Equation (3), an increase of \(\Delta T_{s}\) by  
Figure 6: (**a**) Instantaneous velocity fields at the interaction of two drops (PIV measurement, starting point \(t=0\) s corresponds to droplet 1 falling time, \(V_{02}=40\)\(\mu\)L; \(V_{01}=2.5\)\(\mu\)L; \(T_{w}=20\)\({}^{\circ}\)C); (**b**) image of drop 2 before (left) and after (right) image lightening in the image editor (the red line indicates the contour of drop 2). Figure 7: Thermal imager measurements of thermal field on the surface of drop 2 (water) after the fall of droplet 1 (water). 20-30% will result in a value of \(U_{\text{aver}}\) = 1.6 mm/s. This value is about 5 times lower than the maximum experimental value for \(U_{\text{aver}}\) = 7.2-7.5 mm/s. Thus, a short-term temperature gradient for the interval \(\Delta t\) = 0.01 s has led to a four-fold increase in the velocity due to thermocapillary convection. Figure 7 also shows a dotted line for the drop. After this line, the thickness of the water layer becomes less than 0.3-0.5 mm and the \(T_{s}\) measurement is incorrect due to the influence of the substrate on the temperature measurement, i.e., the \(T_{s}\) values are underestimated.