Hard-Sphere Fluids in Contact with Curved Substrates

TL;DR

This study uses density functional theory to analyze how the surface tension of a hard-sphere fluid varies with curvature of contact surfaces, finding no evidence for a logarithmic curvature term.

Contribution

It provides an analytical expression for surface tension near convex walls and investigates curvature effects using DFT, with validation against numerical results.

Findings

No evidence of a logarithmic curvature term in surface tension.

Good agreement between analytical expression and DFT results.

Surface tension depends on curvature but lacks the logarithmic contribution.

Abstract

The properties of a hard-sphere fluid in contact with hard spherical and cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is applied to determine the density profile and surface tension $\gamma$ for wide ranges of radii of the curved walls and densities of the hard-sphere fluid. Particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to $\gamma$ that is proportional to the logarithm of the radius of curvature. Moreover, by treating the curved wall as a second component at infinite dilution we provide an analytical expression for the surface tension of a hard-sphere fluid close to arbitrary hard convex walls. The agreement between the analytical expression and DFT is good. Our results show no signs for the existence of a logarithmic term in the curvature dependence of $\gamma$.