Scaling theory for the criticality of fluids between plates

Abstract

On the basis of a scaling hypothesis for the criticality of fluids, or fluid mixtures, held between parallel plates, we analyze the combined effects of finite wall separation and ’’symmetry breaking’’ boundary conditions at the walls (i.e., adsorption, or preferential adsorption of one component, at the surfaces). The resulting bulk (but ’’two-dimensional’’) critical point is shifted both in temperature and in density or composition (and in the conjugate field variables) by amounts described by scaling. The scaled form of the phase boundary is consistent with results from a low temperature Ising lattice gas model expansion.

Critical and near-critical phase behavior and interplay between the thermodynamic Casimir and van der Waals forces in a confined nonpolar fluid medium with competing surface and substrate potentials

“…The phase behaviour of a confined fluid medium between parallel walls exerting identical surface adsorption potentials δ µ 1 ≡ J s 1 ,l sr = δ µ 2 ≡ J s 2 ,l sr = 0 on both surface layers has been studied extensively both theoretically and experimentally [76,134,136,137,143,144,146,147,157,162,163]. So far the considerations have been made either for fluid systems governed by pure short-range interactions [134,143,144,146,147,157,163], or for systems with surface potentials strongly preferring the same phase of the fluid [76,136,137,162].…”

“…So far the considerations have been made either for fluid systems governed by pure short-range interactions [134,143,144,146,147,157,163], or for systems with surface potentials strongly preferring the same phase of the fluid [76,136,137,162]. Here we are going to consider the case when at least one of the wall-fluid potentials favor a phase of the fluid different from the one preferred by the short-ranged Fig.…”

“…We note that X sr Cas (x t , x µ = 0) is analytic for all values of x t , because the film critical point [77,143,144,157]. Obviously one has x t ≥ 0 if k ≥ 1/ √ 2 (with k = 1/ √ 2 corresponding to the bulk critical point), 0 ≥ x t ≥ −π 2 if 1/ √ 2 ≥ k ≥ 0 (with k = 0 corresponding to the actual film critical point), and x t ≤ −π 2 if −1 < k < 0 (negative k describes the region below the bulk critical point).…”

“…If the system is made finite, e.g., by the introduction of a second wall the behavior of the fluid is further enriched. When ξ becomes comparable to the characteristic system size, say L, the size dependence of thermodynamic functions enters through the ratio L/ξ , i.e., takes a scaling form given by the finite-size scaling theory [29,40,41,[140][141][142] that incorporates, inter alia, shift of the critical point of the system [143][144][145][146][147]. Be-low T c if the confining walls of the film geometry consist of the same material, one encounters the phenomenon of capillary condensation [76,134,[147][148][149] where the confinement of the fluid causes, e.g., the liquid vapor coexistence line to shift away from the coexistence line of the bulk fluid into the one-phase regime.…”

Interplay of complete wetting, critical adsorption, and capillary condensation

“…Its position as well as that of H c,L depends on L and the strength and the range of the surface fields. For large L and strong h 1 the shifts of the critical temperature and of the bulk field H c,L (h 1 , p) are given by [32,35] (see, c.f., Fig. 2)…”