Velocity distribution function of spontaneously evaporating atoms

Numerical solutions of the Enskog-Vlasov equation are used to determine the velocity distribution function of atoms spontaneously evaporating into near-vacuum conditions. It is found that an accurate approximation is provided by a half-Maxwellian including a drift velocity combined with different characteristic temperatures for the velocity components normal and parallel to the liquid-vapor interface. The drift velocity and the temperature anisotropy reduce as the liquid bulk temperature decreases but persist for relatively low temperatures corresponding to a vapor behavior which is only slightly nonideal. Deviations from the undrifted isotropic half-Maxwellian are shown to be consequences of collisions in the liquid-vapor interface which preferentially backscatter atoms with lower normal-velocity component.

Figure 1

Schematic of the computational setup. The simulation domain is a finite symmetric interval with perfectly absorbing boundary conditions at $z=\pm 60a$. The initial condition consists of a liquid slab in equilibrium with its vapor placed in the middle of the simulation domain.

Figure 2

Dimensionless density, $n{a}^3$, mean velocity in the $z$ direction, $V_z/{\left(R{T}_0\right)}^{1/2}$, normal, $T_{\perp }/T_c$, parallel, $T_{\parallel }/T_c$, and total, $T/T_c$, temperatures for (a) the lowest and (b) the highest liquid bulk temperatures considered in the simulation campaign.

Figure 3

(a) Reduced normal molecular fluxes normalized to unity of evaporated molecules, (b) residual distribution, and (c) corresponding $Q\text{−}Q$ plots of the residuals for the lowest liquid bulk temperature considered in the simulation campaign ($T_{\ell }/T_c=0.53$). Dashed-dotted line: fitted undrifted anisotropic half-Maxwellian; dashed: fitted isotropic drifted half-Maxwellian; solid line: fitted drifted anisotropic half-Maxwellian. Inset of (a) tail of the distributions in logarithmic scale, with $x$-axis tick values matched to the ticks of the plot.

Figure 4

(a) Reduced normal molecular fluxes normalized to unity of evaporated molecules, (b) residual distribution, and (c) corresponding $Q\text{−}Q$ plots of the residuals for the highest liquid bulk temperature considered in the simulation campaign ($T_{\ell }/T_c=0.729$). Dashed-dotted line: fitted undrifted anisotropic half-Maxwellian; dashed: fitted isotropic drifted half-Maxwellian; solid line: fitted drifted anisotropic half-Maxwellian. Inset of (a) tail of the distributions in logarithmic scale, with $x$-axis tick values matched to the ticks of the plot.

Figure 5

Reduced velocity distribution function and molecular flux of evaporated molecules, parallel and normal to the liquid-vapor interface, respectively, at different liquid bulk temperatures. Colored histograms are the numerical results of the EV equation normalized to unity; solid and dashed lines are their best fits based on a drifted anisotropic half-Maxwellian with parameters $\xi$, ${\theta }_{\perp }$, and ${\theta }_{\parallel }$.

Figure 6

Fitted parameters of the velocity distribution function of spontaneously evaporating atoms as a function of the liquid bulk temperature.

Figure 7

Histogram of the last collision cell of evaporated atoms for the lowest and highest liquid bulk temperatures considered in the simulation campaign. The peak of the distribution is close to the separation point $z_s$ which is marked by the vertical black line.

Figure 8

Isocontours of the distribution functions of evaporated atoms (solid lines) and “potentially” evaporating atoms (dashed lines), for the lowest and highest temperatures considered in the simulation campaign. Atoms originate from locations before the separation point.

Figure 9

Isocontours of distribution functions of evaporated particles for the lowest and highest temperatures considered in the simulation campaign.