## 3 Results and Discussion
### Instantaneous Velocity Fields in a Horizontal Section of Sessile Drop
The surface flow of the liquid, in accordance with the experimental data, is directed against a particle motion, i.e., from the center of drop towards the drop contact line (\(V_{l}<0\)). Curve (3) in Figure 13c is calculated according to Equation (4). Theoretical calculation was performed along the trajectory of the particle 1 (Figure 13a), i.e., on the shortest distance on the drop surface from the edge of the contact line to the center of drop. Since it was extremely difficult to experimentally measure the difference \(\Delta R\) due to its low value, it was necessary to base the calculation on such a value of the curvature radii difference that corresponded to the maximum particle velocity of 3-4 mm/s. The simulation shows that the agreement with the experiment is achieved when the relative difference between the values of the radii \(\Delta R_{1}=(R_{2}-R_{1})/R_{1}\) is only a fraction of a percent. Thus, the solution is very sensitive to changes in wettability and small surfactant additives can lead to a noticeable change in the particle velocity. As it is seen in Figure 13c the theoretical curve reflects the qualitative behavior of the experimental curve. The maximum value of the calculated velocity is close to the experimental values. The segment on the abscissa axis \(l/R\), corresponding to the velocity extremum and plotted from the coordinate origin, is approximately \(l/R=0.3\), the derivative \(dV_{p}/dt=\) max at \(l/R=0\), since \(\Delta R=\) max; the derivative \(dV_{p}/dt=0\) at \(l/R=1\), since \(\Delta R=0\). The difference between experiment and simulation for the section of \(0.3<l/R<0.8\) is quite obvious. The real trajectory of the drop is very different from a straight line. At the time of the trajectory half turn, the drop velocity falls several times. The specified interval has several points of turning. As a result, the velocity in this interval will be significantly less. To describe the trajectory rotation, it is necessary to take into account the three-dimensional unsteady flow inside the drop. The toroid is imposed by random circular movement. The vortices in the water drop change position and direction, thereby changing the direction of the particle. The proposed calculation model also describes the experimental data of [61], in which the velocity of a particle with a diameter of 20 \(\upmu\)m at a distance from the contact line of 250 \(\upmu\)m is approximately (2-3)\(\cdot\)10\({}^{-4}\) mm/s. The calculation by Equation (4), taking into account the area \(S_{1}\) for the specified diameter (20 \(\upmu\)m) and neglecting the Marangoni forces, also gives the maximum velocity value of (2-3)\(\cdot\)10\({}^{-4}\) mm/s. In fact, the Marangoni flow without such particles develops the liquid velocity on the drop surface of 0.001-0.01 mm/s. This velocity exceeds by 10-100 times that of capillary motion. Obviously, the particles have suppressed the Marangoni flow in [61]. Figure 14 illustrates experimental data for the average velocity \(U_{\text{aver}}\) in horizontal section of drop 2 (\(V_{02}\) = 40 \(\upmu\)L; \(T_{w}\) = 80 \({}^{\circ}\)C). For each specific type of mixture, four repeated experiments have been carried out. The time of measuring \(U_{\text{aver}}\) in 3 s after droplet 1 falls corresponds to the quasi-stationary regime, i.e., when \(U_{\text{aver}}\) does not change over time. Previous experiments have investigated the behavior of \(U_{\text{aver}}\) immediately after the fall of droplet 1 (within the first two seconds after the fall). The purpose of these experiments is to study the influence of dynamic and thermal factors. Three seconds after the drops' interaction, only the surfactant effect remains on the surface of the sessile drop 2. Experiments with drops of different compositions in Figure 14 are compared with drop 2, which consists of pure water (1). Adding of graphite particles has led to insignificant decrease in \(U_{\text{aver}}\) (2).