# Rates of High-Temperature Evaporation of Promising Fire-Extinguishing Liquid Droplets
## 3 Experimental Setup and Methods  
In experiments, three schemes of heating of a drop of a fire-extinguishing liquid were applied: on a heated surface (it is traditionally called conductive), in a gas stream (convective), and in a muffle furnace (radiation) (Figure 1). Each of them meets the conditions [29; 30; 31] of real fires especially during heating on the surface of the burning material or fire-resisting walling, during motion in gas or steam-gas flow (a mixture of flue gases, air, and vapors), and when reaching the front of the flame burning. When calculating values of heat fluxes (\(q_{\rm cond},q_{\rm conv},q_{\rm rad}\)), the following expressions were used [12]: \(q_{\rm conv}=\alpha\cdot(T_{\rm a}-T_{\rm s})\), \(W/\rm m^{2}\); \(q_{\rm cond}=\lambda_{\rm d}\cdot(T_{\rm sub}-T_{\rm s})/R_{\rm d}\), \(W/\rm m^{2}\), \(q_{\rm rad}=\varepsilon_{\rm d}\cdot\cdot(T_{\rm a}{}^{4}-T_{\rm s}{}^{4})+ \varepsilon_{\rm a}\cdot\cdot T_{\rm a}{}^{4}\), \(W/\rm m^{2}\) (the approach based on the assumption that droplets are opaque grey spheres [31]), \(\alpha=\rm Nu\cdot\lambda_{\rm a}/(2R_{\rm d})\), \(W/(\rm m^{2}\cdot K)\), \(\rm Nu=(2+0.57\cdot Re^{1/2}\cdot Pr^{1/3})/(1+B_{\rm f})^{0.7}\) (for forced convection), \(\rm Nu=0.675\cdot Ra^{0.088}\) (for free convection), \(\rm Re=2R_{\rm d}\cdot L_{\rm a}/\rm v_{\rm a}\), \(\rm Ra=Pr\cdot Gr\), \(\rm Gr=(g\cdot\beta_{\rm a}\cdot d^{3}(T_{\rm a}-T_{\rm s}))/(v_{\rm a}\cdot T_{ \rm a})^{2}\), \(\rm Pr=v_{\rm a}\cdot p_{\rm a}\cdot C_{\rm a}/\lambda_{\rm a}\), \(\varepsilon_{\rm d}=0.9\), \(\varepsilon_{\rm a}=0.1\), \(\sigma=5.68\cdot 10^{-8}\), \(W/(\rm m^{2}\cdot K^{4})\). When calculating forced convection, it was assumed that there was no spatial gradient along a droplet's surface, and recirculation inside the droplets was not taken into account [31]. In Reference [30], radiation heat was calculated using the expression \(q_{\rm rad}=\pi\rm d^{2}\cdot\sigma\cdot\varepsilon\cdot(T_{\rm a}{}^{4}-T_{ \rm s}{}^{4})\) at \(\varepsilon_{\rm d}=0.95\) and equal to absorptivity. It has been found that it is accurate when compared to other tedious procedures. The result shows that the equation can predict \(q_{\rm rad}\) to within 4% [30]. The Nu expression for forced convection takes into account the evaporation of droplets \(\rm Nu=(2+0.57\cdot Re^{1/2}\cdot Pr^{1/3})/(1+B_{\rm f})^{0.7}\)[31], \(B_{\rm f}=[C_{\rm a}\cdot(T_{\rm a}-T_{\rm s})/L](1-|q_{\rm d}|/|q_{\rm c}|+|q _{\rm f}|/|q_{\rm c}|)\)--mass transfer number (\(|q_{\rm d}|\) is the rate at which heat is spent on raising the temperature of a liquid droplet, \(|q_{\rm c}|\) and \(|q_{\rm f}|\) are the heat rates supplied to droplets by convection and radiation, respectively, and \(L\)--latent heat of vaporization per unit mass). The performed calculations have shown that taking into account the parameter \(B_{\rm f}\), heat fluxes \(q_{\rm conv}\) will decrease by 2%-15% at a temperature growth from 100 to 600 \({}^{\circ}\)C. Values of thermophysical parameters of air \(\lambda_{\rm a}\), \(\rm v_{\rm a}\), \(\rm p_{\rm a}\), and \(C_{\rm a}\) were chosen according to data from Reference [29] by taking into account their dependence on temperature. When calculating values of \(q_{\rm cond}\), the registered radius of the contact spot was taken as \(R_{\rm d}\), i.e., taking into account the factor  
Figure 1: Schemes of experimental stands with droplet heating on a substrate (**a**), in an air stream (**b**), and in a muffle furnace (**c**). of significantly different conditions of the spread of droplets of the studied compositions on the substrate. Accordingly, the \(q_{\text{cond}}\) values for the studied compositions (especially when comparing the foaming agent emulsion and EA-5 solution with other liquids) differed significantly at identical heating temperatures. The choice of expressions for the calculation of Nu numbers was made in the analysis of the main conclusions [30; 32; 33; 34; 35; 36].