Structure of hard particle fluids near a hard wall. I. y w(z) for hard disks

The wall-cavity correlation function yw(z) for hard disks against a hard wall is predicted accurately by yw(z)=yw(0)exp[−ΔV(z)(a1+ a2z)]; 0≤z≤σ, where ΔV(z) is the area excluded to the disk centers by a cavity at a distance z from the wall. yw(0), a1, and a2 are expressed in terms of the thermodynamic properties of the bulk fluid, for which accurate semiempirical expressions are available. To test this relation, nwo(z) and yw(z) in the range 0≤z≤σ were calculated for the first time in a computer simulation experiment.