## 3 Results
The droplet diffusion coefficient in gas is determined by its size and the thermodynamic parameters, such as temperature and pressure of the continuous and dispersed phases. Changes in these flow conditions translate into variations in the physical properties of both media, such as density and viscosity, on which the droplet diffusion coefficient is dependent. Additional calculations were conducted to investigate the phenomenon further by considering three values of the \(LVG\), \(\frac{dn}{dx}\), which equaled 1.93, 2.22, and 4.2 \(\frac{m}{s}\). Consequently, the calculations performed assumed variation in \(\delta_{bl}\), which ranged from 0.0245 m to 0.021 m. The characteristics of \(s_{M}\) and \(s_{ref}\) stopping distances as a function of the velocity gradient were calculated for a droplet with a diameter \(d_{d}=100\) um and are depicted in Appendix C, Figures 10 and 11. It was noticed that both \(s_{M}\) and \(s_{ref}\) had a lower value as the \(LVG\) decreased, when compared to data from Table 4. A 12% drop in velocity gradient and 5.8% decrease in boundary layer thickness resulted in a decrease of 24% and 22% in \(s_{M}\) and \(s_{ref}\), respectively. The percentage decrease in the value of \(s_{M}\) was slightly higher than in the case of \(s_{ref}\), as observed. It was noticed that the percentage decrease in the \(s_{M}\) was slightly higher than in the case of the \(s_{ref}\). This disproportion is due to the differences in definitions of both stopping distances (Equations (6) and (7)). Equation (6) has an extra member that involves the velocity gradient and the constant \(K\), which was not included in Equation (7), leading to this divergence. \begin{table}
\begin{tabular}{l c c c c} \hline \(d_{d}\) [μm] & \(s_{M}\cdot 10^{-5}\) [m] & \(s_{ref}\cdot 10^{-5}\) [m] & \(\varepsilon_{d,M}\cdot 10^{-8}\) [\(\frac{m^{2}}{s}\)] & \(\varepsilon_{d,ref}\cdot 10^{-8}\) [\(\frac{m^{2}}{s}\)] \\ \hline
1.86 & 0.0529746 & 0.052974598 & 0.0001347028 & 0.00013470278 \\
5.04 & 0.390637 & 0.3906364 & 0.00732466 & 0.00732465 \\
16.45 & 4.162 & 4.161 & 0.8314 & 0.8312 \\
50 & 38.7 & 38.4 & 72 & 71 \\
100 & 171 & 154 & 1395 & 1135 \\
150 & 687 & 346 & 22.669 & 5747 \\ \hline \end{tabular} \({}^{\dagger}\) Results of a comparative analysis are presented in Appendix B, in Figures 10 and 11.  
\end{table} 
Table 4: Droplet diffusion coefficients and stopping distances \({}^{\ddagger}\) estimated for varying \(d_{d}\), a maximum value of the \(LVG\), and \(\delta_{bl}\) = 0.026 m.  
The question of which droplet will undergo turbulent or inertial diffusion can be answered by comparing the values of the stopping distances (\(s_{M}\) and \(s_{ref}\)) of the droplets to the mixing length (\(l_{m}\)) presented in Table 4. The mixing path is a function of the thickness of the boundary layer (\(\delta_{bl}\)), unlike the stopping distances. The theoretical interpretation of the empirical findings revealed that by adding the \(M\) force, a significant increase in values \(\varepsilon_{d,M}\) and \(s_{M}\) was achieved compared to \(\varepsilon_{d,ref}\) and \(s_{ref}\), accordingly. Thus, it was deemed that the \(M\) force contributes to the increase in speed of the droplet diffusion with diameter \(d_{d}\geq 16.45\) um, which is advantageous. For droplets with diameters \(d_{d}=1.86\) um and \(d_{d}=5.04\) um, there was a difference in the seventh decimal place between the values of \(s_{M}\cdot 10^{-5}\) and \(s_{ref}\cdot 10^{-5}\). The corresponding diffusion coefficients, \(\varepsilon_{d,M}\cdot 10^{-8}\) and \(\varepsilon_{d,ref}\cdot 10^{-8}\), differed in the tenth decimal place. The data obtained stay in accordance with the literature data as airborne droplets (\(d_{d}=1.86\) um and \(d_{d}=5.04\) um), and even larger ones (\(\leq\)20 um) are impacted by a gas phase diffusion of less than about 7% [41]. Both the \(s_{M}\) and the \(s_{ref}\) estimated for the airborne droplets were far lower in value when compared to the value of the mixing path and will follow the turbulent flow of the gas.