Density distribution for the molecules of a liquid in a semi-infinite space

TL;DR

This paper derives and solves a Vlasov-type equation to predict the density distribution of a liquid near a vacuum interface, using the Sutherland approximation for intermolecular forces.

Contribution

It introduces a self-consistent Vlasov model for liquid density near a boundary, incorporating the Sutherland approximation for the first time.

Findings

Density profile near the interface predicted by the model

Numerical solutions illustrate the density variation in the vicinity of the boundary

The model provides insights into molecular distribution at the liquid-vacuum interface

Abstract

The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to predict the behavior of the density at and in the vicinity of the liquid-vacuum interface. A numerical solution to the Vlasov equation is also produced and the density profile shown and discussed.