Maximum evaporating flux of molecular fluids from a planar liquid surface.

In this work, we use the kinetic theory of gases (KTG) to develop a theoretical model to understand the role of internal motions of molecules on the maximum evaporation flux from a planar liquid surface. The kinetic theory is applied to study the evaporation of molecular fluids into a vacuum and predict the dimensionless maximum evaporation flux (J_{R,max}, i.e., the ratio of the maximum evaporation flux to the molar flux emitted from a liquid surface). The key assumptions regarding the velocity distribution function (VDF) of polyatomic molecules in the highly nonequilibrium vapor near the evaporating surface are validated by the VDF obtained directly from molecular dynamics (MD) simulations. Our KTG-based analysis shows that J_{R,max} is affected by the specific heat (c_{V,int}) associated with internal degrees of freedom of fluid molecules. When the maximum evaporation flux is reached, the isotropic evaporating vapor far from the liquid surface moves at its speed of sound regardless of whether it is a monatomic vapor or polyatomic vapor. To fundamentally understand the evaporation of a molecular fluid into a vacuum, we solve the Boltzmann transport equation (BTE) to obtain the temperature, density, and flow speed distributions in the highly nonequilibrium evaporating vapor flow. Our BTE solutions indicate that there are several universal features of the evaporating vapor when the maximum evaporation flux occurs. In particular, we find that the evaporating vapor flow speed reaches the maximum value of sqrt[1.5] times the most probable thermal speed in the vapor flow direction at the vacuum boundary, and this maximum value is independent of fluid properties. All theoretical predictions in this work are verified by the MD simulation results of the evaporation of the model liquid Ar and the model liquid n-dodecane into a vacuum, and existing experimental data.