Contact theorems for anisotropic fluids near a hard wall

TL;DR

This paper derives a general contact theorem for anisotropic fluids near a hard wall, linking the contact value of the distribution function to bulk pressure and wall interactions, with applications to nematic fluids.

Contribution

It introduces a new general expression for the contact value in anisotropic fluids, incorporating molecular orientation and wall interactions, extending previous isotropic models.

Findings

Derived a contact theorem for anisotropic fluids near a wall.

Applied the theorem to nematic fluids, illustrating its practical relevance.

Connected contact values to bulk pressure and anchoring phenomena.

Abstract

In this paper, starting from the Born-Green-Yvon (BGY) equation, we derive a general expression for the contact value of the singlet distribution function near a hard wall for anisotropic fluids. This relation includes two separate contributions. One is connected to the partial bulk pressure relative to a given orientation of the molecules. The second one is connected to the anchoring phenomena and is characterized by the direct interaction between the molecules and the wall. From this relation, we then formulate the contact theorem for the density and the order parameter profiles. The results are illustrated on the case of a nematic fluid near a hard wall.