We show that continuous filling or wedge-wetting transitions are possible in 3D wedge-geometries made from (angled) substrates exhibiting first-order wetting transitions and develop a comprehensive fluctuation theory yielding a complete classification of the critical behaviour. Our fluctuation theory is based on the derivation of a Ginzburg criterion for filling and also an exact transfer-matrix analysis of a novel effective Hamiltonian which we propose as a model for wedge fluctuation effects. The influence of interfacial fluctuations is shown to be very strong and, in particular, leads to a remarkable universal divergence of the interfacial roughness ξ ⊥ ∼ (TF − T ) −1/4 on approaching the filling temperature TF , valid for all possible types of intermolecular forces.PACS numbers: 68.45. Gd, 68.35.Rh, There are two reasons why it is extremely difficult to observe interfacial fluctuation effects at continuous (critical) wetting transitions in the laboratory [1]. Firstly, critical wetting is a rather rare phenomenon for which no examples are known for solid-liquid interfaces and only a limited number for fluid-fluid interfaces [2,3]. Secondly, the influence of interfacial fluctuations in three dimensions (d = 3) is believed to be rather small [1]. For example, for systems with long-ranged forces, the divergence of the wetting layer thickness ℓ on approaching the wetting temperature T w is mean-field-like, ℓ ∼ (T w − T ) −1 , and the only predicted effect of fluctuations is to induce an extremely weak divergence of the width (roughness) ξ ⊥ of the unbinding interface: ξ ⊥ ∼ − ln(T w − T ). Nonclassical critical exponents and an appreciable interfacial width are only predicted for systems with strictly shortranged forces [4], but even here the size of the asymptotic critical regime is very small and beyond the reach of current experimental and simulation methods [3,5,6].The purpose of the present article is to show that these problems do not arise for continuous (critical) filling or wedge-wetting transitions [7][8][9] occurring for fluid adsorption in three-dimensional wedges. First, we show, contrary to previous statements in the literature [8], that critical filling can occur in systems made from walls that exhibit first-order wetting transitions. Consequently, the observation of critical filling transitions is a realistic experimental prospect. Second, we argue that interfacial fluctuations have a strong influence on the character of the filling transition and, in particular, the interfacial roughness of the unbinding interface, which is shown to diverge with a universal critical exponent. The fluctuation theory we develop is based on the derivation of a Ginzburg criterion for the self-consistency of mean-field (MF) theory and also an exact transfer matrix analysis of a novel interfacial Hamiltonian model for wedge wetting which we introduce to account for the highly anisotropic soft-mode fluctuations. This model leads to a complete classification of the critical behaviour in d = 3 and predicts some remarkable...

The shape and chemical composition of solid surfaces can be controlled at a mesoscopic scale. Exposing such structured substrates to a gas that is close to coexistence with its liquid phase can produce quite distinct adsorption characteristics compared to those of planar systems, which may be important for technologies such as super-repellent surfaces or micro-fluidics. Recent studies have concentrated on the adsorption of liquids on rough and heterogeneous substrates, and the characterization of nanoscopic liquid films. But the fundamental effect of geometry on the adsorption of a fluid from the gas phase has hardly been addressed. Here we present a simple theoretical model which shows that varying the shape of the substrate can exert a profound influence on the adsorption isotherms of liquids. The model smoothly connects wetting and capillary condensation through a number of examples of fluid interfacial phenomena, and opens the possibility of tailoring the adsorption properties of solid substrates by sculpting their surface shape.

Phys. Rev. Lett. 83, 5535 (1999) We study 2D wedge wetting using a continuum interfacial Hamiltonian model which is solved by transfer-matrix methods. For arbitrary binding potentials, we are able to exactly calculate the wedge free-energy and interface height distribution function and, thus, can completely classify all types of critical behaviour. We show that critical filling is characterized by strongly universal fluctuation dominated critical exponents, whilst complete filling is determined by the geometry rather than fluctuation effects. Related phenomena for interface depinning from defect lines in the bulk are also considered.PACS numbers: 68.45. Gd, 68.35.Rh, At present, experimental methods allow the shape of solid surfaces to be controlled at a nanoscopic level [1].Fluids confined by such structured substrates can exhibit quite distinct adsorption characteristics compared to that occuring for planar systems [2]. This includes new types of interfacial phase transitions and critical phenomena which are not only of fundamental interest but may well play an important role in developing technologies such as super-repellent surfaces [3], self assembly of three-dimensional structures [4] or micro-fluidics [5], among others [6]. An interesting example of these phenomena which is recently attracting new interest is the so called filling or wedge wetting transition of a fluid adsorbed in a wedge [7,8], formed by the junction of two flat walls tilted at angles ±α to the horizontal as shown in Fig. 1. Thermodynamic arguments predict that a wedge-gas interface is completely filled by a liquid phase (at bulk liquid-gas coexistence) for temperatures T > T α , where the filling temperature T α is lower than the wetting temperature T w of the planar (α = 0) wall [9]. In fact, according to these macroscopic arguments, the location of the filling transition phase boundary is beautifully expressed in terms of the contact angle Θ π (T ) of the liquid drop on the planar substrate [9]:Thus, the liquid completely wets the wedge when the contact angle is smaller than the tilted angle α. Interestingly, this macroscopic result was predicted and confirmed experimentally [10] eight years before the seminal paper by Cahn on wetting in planar surfaces [11].Recently, the macroscopic prediction (1) has been supported by mean-field analysis of a model system which also suggest that the qualitative order of the filling transition (first-order or continuous) follows that of the planar wetting transition [7]. Thus, for planar substrates exhibiting critical wetting transitions, the wedge offers two new examples of interfacial-like critical phenomena in which the interface height ℓ 0 (measured from the bottom of the wedge) diverges as the temperature and chemical potential are varied. Borrowing from the vocabulary used for wetting, we refer to the wedge filling transition ocurring as T → T − α (at bulk coexistence) as critical filling. In contrast, by complete filling, we refer to the divergence of ℓ 0 for temperatures T > T α as the bul...

We derive a non-local effective interfacial Hamiltonian model for short-ranged wetting phenomena using a Green's function method. The Hamiltonian is characterized by a binding potential functional and is accurate to exponentially small order in the radii of curvature of the interface and the bounding wall. The functional has an elegant diagrammatic representation in terms of planar graphs which represent different classes of tube-like fluctuations connecting the interface and wall. For the particular cases of planar, spherical and cylindrical interfacial (and wall) configurations, the binding potential functional can be evaluated exactly. More generally, the non-local functional naturally explains the origin of the effective position-dependent stiffness coefficient in the smallgradient limit.

Interfacial fluctuation effects occurring at wedge- and cone-filling transitions are investigated and shown to exhibit very different characteristics. For both geometries we argue that the conditions for observing critical (continuous) filling are much less restrictive than for critical wetting, which is known to require the fine tuning of the Hamaker constants. Wedge filling is critical if the wetting binding potential does not exhibit a local maximum, whilst conic filling is critical if the line tension is negative. This latter scenario is particularly encouraging for future experimental studies. Using mean-field and effective Hamiltonian approaches, which allow for breather-mode fluctuations which translate the interface up and down the sides of the confining geometry, we are able to completely classify the possible critical behaviours (for purely thermal disorder). For the three-dimensional wedge, the interfacial fluctuations are very strong and characterized by a universal roughness critical exponent ν⊥W = 1/4 independent of the range of the forces. For the physical dimensions d = 2 and d = 3, we show that the effect of the cone geometry on the fluctuations at critical filling is to mimic the analogous interfacial behaviour occurring at critical wetting in the strong-fluctuation regime. In particular, for d = 3 and for quite arbitrary choices of the intermolecular potential, the filling height and roughness show the same critical properties as those predicted for three-dimensional critical wetting with short-ranged forces in the large-wetting-parameter (ω>2) regime.