On the determination of the structure and tension of the interface between a fluid and a curved hard wall

Abstract

The structure and tension of the interface between a fluid and a spherically shaped hard wall are studied theoretically. The authors show the equivalence of different expressions for the surface tension and Tolman length using the squared-gradient model and density functional theory with a nonlocal, integral expression for the interaction between molecules. Even though both these models yield equilibrium density profiles that do not satisfy the wall theorem, they still obey the basic requirement of mechanical equilibrium. The authors trace back the origin of the difference between these two observations to the (lack of) continuity of the cavity function at the hard wall.

Direct determination of the Tolman length from the bulk pressures of liquid drops via molecular dynamics simulations

“…This is explicitly shown in the appendix of Ref. 23. We have verified that all four expressions in Eqs.…”

Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

“…From an opposite point of view, we may concentrate in the external force and on contact properties. From the wall theorem 11,28 the total scalar force between the wall and the HS system in a pressure form is…”

“…33 The suspended drop on its vapor, 9,10,19 the bubble of vapor on its liquid, the fluid in contact with a spherical convex substrates ͑or cavity in the liquid͒, 11,12,19,20 and the fluid confined in a spherical vessel or pore 11,18,40 are different systems in which the spherical inhomogeneity of the fluid is central, and currently, the study of these systems are converging to the analysis of the curvature dependence of physical magnitudes. 11 Particularly relevant for PW are such works on HS systems 12 and hard wall spherical substrates. 11,20 PW seen on this context shows the dimensional dependence of an analytical solvable system on this up to date and relevant problem in statistical mechanics and thermodynamics.…”

“…11 Particularly relevant for PW are such works on HS systems 12 and hard wall spherical substrates. 11,20 PW seen on this context shows the dimensional dependence of an analytical solvable system on this up to date and relevant problem in statistical mechanics and thermodynamics. In PW we study a fluid in contact with a hard wall, therefore, we deal with the surface tension of a fluid-substrate interface.…”

“…9,11,12,33,43 It seems that the spherical symmetry is the simplest one, and then the principal subject of several works on curved interfaces but deviations from sphericity are also studied. 33 The suspended drop on its vapor, 9,10,19 the bubble of vapor on its liquid, the fluid in contact with a spherical convex substrates ͑or cavity in the liquid͒, 11,12,19,20 and the fluid confined in a spherical vessel or pore 11,18,40 are different systems in which the spherical inhomogeneity of the fluid is central, and currently, the study of these systems are converging to the analysis of the curvature dependence of physical magnitudes. 11 Particularly relevant for PW are such works on HS systems 12 and hard wall spherical substrates.…”