Energy of Interaction between Solid Surfaces and Liquids

Abstract

We consider the wetting transition on a planar surface in contact with a semi-infinite fluid. In the classical approach, the surface is assumed to be solid, and when interaction between solid and fluid is sufficiently short-range, the contribution of the fluid can be represented by a surface free energy with a density of the form Φ(ρ S ), where ρ S is the limiting density of the fluid at the surface.In the present paper we propose a more precise representation of the surface energy that takes into account not only the value of ρ S but also the contribution from the whole density profile ρ(z) of the fluid, where z is coordinate normal to the surface.The specific value of the functional of ρ S at the surface is expressed in meanfield approximation through the potentials of intermolecular interaction and some other parameters of the fluid and the solid wall.An extension to the case of fluid mixtures in contact with a solid surface is proposed.

Liquid nanofilms. A mechanical model for the disjoining pressure

“…Forces between liquid and solid have short range and can be simply described by adding a special energy at the surface. This is not the entire interfacial energy: another contribution comes from the distortions in the liquid density profile near the wall [18,23]. Finally, for a plane solid wall (at a molecular scale), this surface free energy is obtained in the form…”

“…, where m l et m s respectively denote the masses of liquid (fluid) and solid molecules [18]. Moreover, we have λ = 2πc ll 3σ l m 2 l .…”

“…The liquid at level z = h is situated at a distance order of two molecular diameters from the vapor bulk and the vapor has a negligible density with respect to the liquid density [25]. In our model, these two last energies can be expressed by writing a unique energy ψ per unit surface located on the mathematical surface (Σ) at z = h : by a calculation like in [18], we can write ψ in a form analogous to expression (5) and also expressed in [23] in the form ψ(ρ) = −γ 5 ρ + 1 2 γ 4 ρ 2 ; but with a wall corresponding to a negligible density, γ 5 ≃ 0 and the surface free energy ψ is reduced to…”

“…It was used by Cahn in a phenomenological form, in a well-known paper studying wetting near a critical point [17]. An asymptotic expression is obtained in [18] with an approximation of hard sphere molecules and London potentials for liquid-liquid and solid-liquid interactions: in this way, we took into account the power-law behavior which is dominant in a thin liquid film in contact with a solid. The disjoining pressure Π is a well adapted tool for a very thin liquid film of thickness h. In cases of Lifshitz analysis [19] and van der Waals theory, the disjoining pressure behaviors are respectively as Π ∼ h −3 and Π ∼ exp(−h).…”

Travelling waves of density for a fourth-gradient model of fluids

“…Starting from the classical framework of kinetic theory of gases [20], and using as basic constitutive quantities the potentials of the van der Waals forces, as done in [21,22], we consider an expansion in the density up to the fourth order and we obtain a new model for the volume energy. This new model is named a fourth-gradient fluid.…”