## 3 Results and Discussion  
### Velocity Field in Sessile Water Drop, Located on a Heated Wall  
Drop 2 evaporated in the mode of constant contact radius (CCR). The fall of the second small droplet 1 did not lead to a change in the radius \(R_{02}\) of sessile drop 2 (\(R_{02}\) = const). Figure 2a presents experimental data for velocities in the water drop 2 (initial volume of drop 2 (\(V_{02}\)) is 40 \(\mu\)L; and the wall temperature \(T_{\rm w}\) = 80 \({}^{\circ}\)C). The velocities \(U_{\rm max}\), \(U_{\rm max(20)}\), and \(U_{\rm aver}\) were measured by PIV. The time \(t\) = 0 corresponds to that when drop 2 spread along the hot wall, and the radius of the base of drop 2 \(R_{02}\) was established constant. The experimental data in Figure 2a were obtained without the small droplet 1 falling. The maximum value of the average velocity \(U_{\rm aver}\) is 7.2-7.5 mm/s and corresponds to the time close to \(t\) = 0.2-0.5 s (the initial time of placing the cold drop 2 with a temperature of 20 \({}^{\circ}\)C on a hot wall). The maximum value \(U_{\rm aver}\) was recorded at the initial moment, since this time corresponded to the maximum temperature difference (\(\Delta T_{s}\)) on the free surface of the drop (\(\Delta T_{s}\) = \(T_{w}\) - \(T_{0}\) = 80 - 20 = 60 \({}^{\circ}\)C, where \(T_{w}\) is the wall temperature, and \(T_{0}\) is the initial temperature of droplet 1). The thermal Marangoni number (Equation (1)) is:  
\[Ma_{T}=(\Delta T_{s}h/\mu a)\cdot(d\sigma/dT_{s}), \tag{1}\]  
where \(\Delta T_{s}\) is the temperature gradient on the liquid, \(\sigma\) is the surface tension coefficient for water-air, \(h\) is the drop 2 height (\(h\) = \(h_{02}\) = 2.6 mm), \(\mu\) is the dynamic viscosity of water, and \(a\) is the thermal diffusivity of water. The Rayleigh number (Equation (2)) is:  
\[Ra=g\beta\Delta T_{s}(h)^{3}/\
u a, \tag{2}\]  
where \(\
u\) is the kinematic viscosity of the water, \(\beta\) is the coefficient of thermal expansion, and \(g\) is the gravity acceleration. Indeed, the equation of motion is nonlinear. The convection introduces nonlinearity. However, within the limits of the experimental error it is possible to carry out a qualitative assessment in a linear approximation. Let us consider the total convective velocity as a sum of individual components. Let us make an approximate estimate for \(U_{\rm aver}\)[32; 33; 46] between the average velocity in drop 2 and the Marangoni and Rayleigh numbers (Equation (3)):  
\[U_{\rm aver}=U_{MT}+U_{Ra}=k_{T}(Ma_{T}+Ra)\]where the empirical constant \(k_{T}\) determined from experimental data is 0.15\(\cdot\)10\({}^{-7}\) (m/s). This linear approximation is quite justified, since the Rayleigh number is much less than the \(Ma\) number, and the nonlinear velocity term must be significantly less than the total value of \(U_{\rm aver}\). Quasi-linearity also follows from quasi-stationarity and linear superposition of forces. This does not take into account the shape of the drop, the contact angle, or the number of vortices in the drop. However, it is currently impossible to accurately model the convection field inside the drop, since the noticeable suppression of free convection due to surfactant on the liquid surface is not taken into account. The influence of surfactant leads to a tens of times underestimation of the theoretical value of the free convection velocity in the water drop, compared to the experiment [21; 22]. A decrease in the convection velocity is also observed at low concentrations of alcohol [3]. The empirical constant \(k_{T}\) is obtained by generalizing experimental data and indirectly takes into account the influence of surfactant, which allows applying Equation (3) to approximate the value of the average convection velocity not only in the drop, but also in a thin layer of a single-component liquid. For the case of solution, an additional term associated with the action the solutal Marangoni number appears. The velocity value drops rapidly and already in the first 3-5 s enters the quasi-stationary level.