The edge contact angle, capillary condensation and meniscus depinning

We study the phase equilibria of a fluid confined in an open capillary slit formed when a wall of finite length H is brought a distance L away from a second macroscopic surface. This system shows rich phase equilibria arising from the competition between two different types of capillary condensation, corner filling and meniscus depinning transitions depending on the value of the aspect ratio a = L/H. For long capillaries, with a 1, condensation is always of type II. In all regimes, capillary condensation is completely suppressed for sufficiently large contact angles. We show that there is an additional continuous, third-order phase transition in the condensed liquidlike phase, associated with the depinning of each meniscus as they round the upper open edges of the slit. Finite-size scaling predictions are developed for these transitions and phase boundaries which connect with the fluctuation theories of wetting and filling transitions. We test several of our predictions using a fully microscopic Density Functional Theory which allows us to study the two types of capillary condensation and its suppression at the molecular level

Meniscus osculation and adsorption on geometrically structured walls

We study the adsorption of simple fluids at smoothly structured, completely wet walls and show that a meniscus osculation transition occurs when the Laplace and geometrical radii of curvature of locally parabolic regions coincide. Macroscopically, the osculation transition is of fractional, 7 2 , order and separates regimes in which the adsorption is microscopic, containing only a thin wetting layer, and mesoscopic, in which a meniscus exists. We develop a scaling theory for the rounding of the transition due to thin wetting layers and derive critical exponent relations that determine how the interfacial height scales with the geometrical radius of curvature. Connection with the general geometric construction proposed by Rascón and Parry is made. Our predictions are supported by a microscopic model density functional theory for drying at a sinusoidally shaped hard wall where we confirm the order of the transition and also an exact sum rule for the generalized contact theorem due to Upton. We show that as bulk coexistence is approached the adsorption isotherm separates into three regimes: A preosculation regime where it is microscopic, containing only a thin wetting layer; a mesoscopic regime, in which a meniscus sits within the troughs; and finally another microscopic regime where the liquid-gas interface unbinds from the crests of the substrate

Critical effects and scaling at meniscus osculation transitions

We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature R w in a confining parabolic geometry. We argue that the exponent β osc characterizing the scale of the interfacial height ℓ 0 ∝ R β osc w at osculation, for large R w , falls into two regimes representing fluctuation-dominated and mean-field-like behavior, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-range forces, the exponent is related to the value of the interfacial wandering exponent ζ by β osc = 3 ζ / ( 4 − ζ ) . In contrast, in the mean-field regime, which was not previously identified and which occurs for systems with longer-range forces (and higher dimensions), the exponent β osc takes the same value as the exponent β co s for complete wetting, which is determined directly by the intermolecular forces. The prediction β osc = 3 / 7 in d = 2 for systems with short-range forces (corresponding to ζ = 1 / 2 ) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in d = 3 , based on a microscopic model density-functional theory, determines that β osc ≈ β co s ≈ 0.326 close to the predicted value of 1 / 3 appropriate to the mean-field regime for dispersion forces

Scaling behavior of thin films on chemically heterogeneous walls

We study the adsorption of a fluid in the grand canonical ensemble occurring at a planar heterogeneous wall which is decorated with a chemical stripe of width L . We suppose that the material of the stripe strongly preferentially adsorbs the liquid in contrast to the outer material which is only partially wet. This competition leads to the nucleation of a droplet of liquid on the stripe, the height h m and shape of which (at bulk two-phase coexistence) has been predicted previously using mesoscopic interfacial Hamiltonian theory. We test these predictions using a microscopic Fundamental Measure Density Functional Theory which incorporates short-ranged fluid-fluid and fully long-ranged wall-fluid interactions. Our model functional accurately describes packing effects not captured by the interfacial Hamiltonian but still we show that there is excellent agreement with the predictions h m ≈ L 1 / 2 and for the scaled circular shape of the drop even for L as small as 50 molecular diameters. For smaller stripes the droplet height is considerably lower than that predicted by the mesoscopic interfacial theory. Phase transitions for droplet configurations occurring on substrates with multiple stripes are also discussed

Capillary contact angle in a completely wet groove

We consider the phase equilibria of a fluid confined in a deep capillary groove of width L with identical side walls and a bottom made of a different material. All walls are completely wet by the liquid. Using density functional theory and interfacial models, we show that the meniscus separating liquid and gas phases at two phase capillary coexistence meets the bottom capped end of the groove at a capillary contact angle thetacap(L) which depends on the difference between the Hamaker constants. If the bottom wall has a weaker wall-fluid attraction than the side walls, then thetacap>0 even though all the isolated walls are themselves completely wet. This alters the capillary condensation transition which is now first order; this would be continuous in a capped capillary made wholly of either type of material. We show that the capillary contact angle thetacap(L) vanishes in two limits, corresponding to different capillary wetting transitions. These occur as the width (i) becomes macroscopically large, and (ii) is reduced to a microscopic value determined by the difference in Hamaker constants. This second wetting transition is characterized by large scale fluctuations and essential critical singularities arising from marginal interfacial interactions.A. O. P. wishes to thank the support of the EPSRC UK for Grant No. EP/J009636/1. A. M. thanks the Czech Science Foundation for Grant No. 13-09914S. C. R. acknowledges support from Grants No. FIS2010-22047-C05 and No. MODELICO

Surface phase diagrams for wetting with long-ranged forces

Recent Density Functional Theory and simulation studies of wetting and drying transitions in systems with long-ranged, dispersion-like forces, away from the near vicinity of the bulk critical temperature Tc, have questioned the generality of the global surface phase diagrams for wetting, due to Nakanishi and Fisher, pertinent to systems with short-ranged forces. We extend these studies deriving fully analytic results which determine the surface phase diagrams over the whole temperature range up to Tc. The phase boundaries, order of, and asymmetry between, the lines of wetting and drying transitions are determined exactly showing that they always converge to an ordinary surface critical point. We highlight the importance of lines of maximally multicritical wetting and drying transitions, for which we determine the exact critical singularities

Modified Kelvin equations for condensation in narrow and wide grooves

We consider the location and order of capillary condensation transitions occurring in deep grooves of width L and depth D. For walls that are completely wet by liquid (contact angle θ=0) the transition is continuous and its location is not sensitive to the depth of the groove. However, for walls that are partially wet by liquid, where the transition is first order, we show that the pressure at which it occurs is determined by a modified Kelvin equation characterized by an edge contact angle θE describing the shape of the meniscus formed at the top of the groove. The dependence of θE on the groove depth D relies, in turn, on whether corner menisci are formed at the bottom of the groove in the low density gaslike phase. While for macroscopically wide grooves these are always present when θ<45° we argue that their formation is inhibited in narrow grooves. This has a number of implications including that the local pinning of the meniscus and location of the condensation transition is different depending on whether the contact angle is greater or less than a universal value θ∗≈31°. Our arguments are supported by detailed microscopic density functional theory calculations that show that the modified Kelvin equation remains highly accurate even when L and D are of the order of tens of molecular diameters

Capillary condensation and depinning transitions in open slits

We study the low-temperature phase equilibria of a fluid confined in an open capillary slit formed by two parallel walls separated by a distance L which are in contact with a reservoir of gas. The top wall of the capillary is of finite length H while the bottom wall is considered of macroscopic extent. This system shows rich phase equilibria arising from the competition between two different types of capillary condensation, corner filling, and meniscus depinning transitions depending on the value of the aspect ratio a = L / H and divides into three regimes: For long capillaries, with a 1 , condensation is always of type II. In all regimes, capillary condensation is completely suppressed for sufficiently large contact angles which is determined explicitly. For long and intermediate capillaries, we show that there is an additional continuous phase transition in the condensed liquid-like phase, associated with the depinning of each meniscus as they round the upper open edges of the slit. Meniscus depinning is third-order for complete wetting and second-order for partial wetting. Detailed scaling theories are developed for these transitions and phase boundaries which connect with the theories of wedge (corner) filling and wetting encompassing interfacial fluctuation effects and the direct influence of intermolecular forces. We test several of our predictions using a fully microscopic density functional theory which allows us to study the two types of capillary condensation and its suppression at the molecular level for different aspect ratios and contact angles