Mean-field kinetic theory approach to evaporation of a binary liquid into vacuum

Evaporation of a binary liquid into near-vacuum conditions has been studied using numerical solutions of a system of two coupled Enskog-Vlasov equations. Liquid-vapor coexistence curves have been mapped out for different liquid compositions. The evaporation process has been investigated at a range of liquid temperatures sufficiently lower than the critical one for the vapor not to significantly deviate from the ideal behavior. It is found that the shape of the distribution functions of evaporating atoms is well approximated by an anisotropic Maxwellian distribution with different characteristic temperatures for velocity components normal and parallel to the liquid-vapor interface. The anisotropy reduces as the evaporation temperature decreases. Evaporation coefficients are computed based on the separation temperature and the maximum concentration of the less volatile component close to the liquid-vapor interface. This choice leads to values which are almost constant in the simulation conditions.

Figure 1

Equilibrium simulations. Phase diagram of the binary mixture for different molar fractions of the $a$ component in the liquid phase. (a) Temperature vs density. (b) Temperature vs vapor molar fraction.

Figure 2

Equilibrium simulations. Density and molar fraction of the $a$ component of the mixture (which is equimolar in the liquid phase) for different temperatures. Solid lines: results provided by the numerical solution of the system of two coupled Enskog-Vlasov equations, Eqs. (4) with $N=2$. Dashed lines: predictions based on Eqs. (9). (a) Density. (b) Molar fraction.

Figure 3

Nonequilibrium simulations. Macroscopic quantities at different times for $T/T_0=0.5$. (a) Density (solid), concentration (dashed), and longitudinal velocity (dashed-dotted). (b) Full (solid), longitudinal (dashed), and transversal (dash-dotted) temperatures.

Figure 4

Nonequilibrium simulations. Time histories of the maximum molar fraction of the less volatile $a$ component and the separation temperature for different temperatures. (a) Maximum concentration. (b) Separation temperature.

Figure 5

Nonequilibrium simulations. Reduced normalized distribution functions of the evaporated atoms. Solid blue triangles up and solid red triangles down are the numerical results for the $a$ component and $b$ component, respectively. Dashed black lines are the best Maxwellian fits. Temperatures of the latter are explicitly reported and the percentage errors do not exceed 1%. (a) $T/T_0=0.4$. (b) $T/T_0=0.45$. (c) $T/T_0=0.5$. (d) $T/T_0=0.55$.

Figure 6

Nonequilibrium simulations. Reduced normalized distribution functions of the evaporated atoms for different mass component ratios. Solid blue triangles up and solid red triangles down are the numerical results for the $a$ component and $b$ component, respectively, for $m_b/m_a=1$. Solid violet triangles left and solid green triangles right are the numerical results for the $a$ component and $b$ component, respectively, for $m_b/m_a=5$. Dashed black lines are the best Maxwellian fits. Temperatures of the latter are explicitly reported and the percentage errors do not exceed 1%. (a) $a$ component. (b) $b$ component.

Figure 7

Nonequilibrium simulations. Time histories of the number of evaporated atoms for the two components at different temperatures. Solid lines are the numerical results. Dashed straight lines are included to guide the eyes. (a) Less volatile $a$ component. (b) More volatile $b$ component.

Figure 8

Nonequilibrium simulations. Evaporation coefficients of the $a$ component (blue symbols and lines) and of the $b$ component (red symbols and lines) for different temperatures as a function of the interface composition. The accuracy of the results is within 5%.