A molecular dynamics test of the Hertz-Knudsen equation for evaporating liquids

The precise determination of evaporation flux from liquid surfaces gives control over evaporation-driven self-assembly in soft matter systems. The Hertz-Knudsen (HK) equation is commonly used to predict evaporation flux. This equation states that the flux is proportional to the difference between the pressure in the system and the equilibrium pressure for liquid/vapor coexistence. We applied molecular dynamics (MD) simulations of one component Lennard-Jones (LJ) fluid to test the HK equation for a wide range of thermodynamic parameters covering more than one order of magnitude in the values of flux. The flux determined in the simulations was 3.6 times larger than that computed from the HK equation. However, the flux was constant over time while the pressures in the HK equation exhibited strong fluctuations during simulations. This observation suggests that the HK equation may not appropriately grasp the physical mechanism of evaporation. We discuss this issue in the context of momentum flux during evaporation and mechanical equilibrium in this process. Most probably the process of evaporation is driven by a tiny difference between the liquid pressure and the gas pressure. This difference is equal to the momentum flux i.e. momentum carried by the molecules leaving the surface of the liquid during evaporation. The average velocity in the evaporation flux is very small (two to three orders of magnitude smaller than the typical velocity of LJ atoms). Therefore the distribution of velocities of LJ atoms does not deviate from the Maxwell-Boltzmann distribution, even in the interfacial region.