Crossover scaling of apparent first-order wetting in two dimensional systems with short-ranged forces

Recent analyses of wetting in the semi-infinite two dimensional Ising model, extended to include both a surface coupling enhancement and a surface field, have shown that the wetting transition may be effectively first-order and that surprisingly the surface susceptibility develops a divergence described by an anomalous exponent with value $\gamma_{11}^{\rm eff}=\frac{3}{2}$. We reproduce these results using an interfacial Hamiltonian model making connection with previous studies of two dimensional wetting and show that they follow from the simple crossover scaling of the singular contribution to the surface free-energy which describes the change from apparent first-order to continuous (critical) wetting due to interfacial tunnelling. The crossover scaling functions are calculated explicitly within both the strong-fluctuation and intermediate-fluctuation regimes and determine uniquely and more generally the value of $\gamma_{11}^{\rm eff}$ which is non-universal for the latter regime. The location and the rounding of a line of pseudo pre-wetting transitions occurring above the wetting temperature and off bulk coexistence, together with the crossover scaling of the parallel correlation length, is also discussed in detail

Condensation and evaporation transitions in deep capillary grooves

We study the order of capillary condensation and evaporation transitions of a simple fluid adsorbed in a deep capillary groove using a fundamental measure density functional theory (DFT). The walls of the capillary interact with the fluid particles via long-ranged, dispersion, forces while the fluid-fluid interaction is modelled as a truncated Lennard-Jones-like potential. We find that below the wetting temperature $T_w$ condensation is first-order and evaporation is continuous with the metastability of the condensation being well described by the complementary Kelvin equation. In contrast above $T_w$ both phase transitions are continuous and their critical singularities are determined. In addition we show that for the evaporation transition above $T_w$ there is an elegant mapping, or covariance, with the complete wetting transition occurring at a planar wall. Our numerical DFT studies are complemented by analytical slab model calculations which explain how the asymmetry between condensation and evaporation arises out of the combination of long-ranged forces and substrate geometry

Bridging transitions for spheres and cylinders

We study bridging transitions between spherically and cylindrically shaped particles (colloids) of radius $R$ separated by a distance $H$ that are dissolved in a bulk fluid (solvent). Using macroscopics, microscopic density functional theory and finite-size scaling theory we study the location and order of the bridging transition and also the stability of the liquid bridges which determines spinodal lines. The location of the bridging transitions is similar for cylinders and spheres, so that for example, at bulk coexistence the distance $H_b$ at which a transition between bridged and unbridged configurations occurs, is proportional to the colloid radius $R$. However all other aspects, and, in particular, the stability of liquid bridges, are very different in the two systems. Thus, for cylinders the bridging transition is typically strongly first-order, while for spheres it may be first-order, critical or rounded as determined by a critical radius $R_c$. The influence of thick wetting films and fluctuation effects beyond mean-field are also discussed in depth

The Influence of Intermolecular Forces at Critical Point Wedge Filling

We use microscopic density functional theory to study filling transitions in systems with long-ranged wall-fluid and short-ranged fluid-fluid forces occurring in a right-angle wedge. By changing the strength of the wall-fluid interaction we can induce both wetting and filling transitions over a wide range of temperatures and study the order of these transitions. At low temperatures we find that both wetting and filling transitions are first-order in keeping with predictions of simple local effective Hamiltonian models. However close to the bulk critical point the filling transition is observed to be continuous even though the wetting transition remains first-order and the wetting binding potential still exhibits a small activation barrier. The critical singularities for adsorption for the continuous filling transitions depend on whether retarded or non-retarded wall-fluid forces are present and are in excellent agreement with predictions of effective Hamiltonian theory even though the change in the order of the transition was not anticipated

Filling transitions in acute and open wedges

We present numerical studies of first-order and continuous filling transitions, in wedges of arbitrary opening angle $\psi$, using a microscopic fundamental measure density functional model with short-ranged fluid-fluid forces and long-ranged wall-fluid forces. In this system the wetting transition characteristic of the planar wall-fluid interface is always first-order regardless of the strength of the wall-fluid potential $\varepsilon_w$. In the wedge geometry however the order of the filling transition depends not only on $\varepsilon_w$ but also the opening angle $\psi$. In particular we show that even if the wetting transition is strongly first-order the filling transition is continuous for sufficient acute wedges. We show further that the change in the order of the transition occurs via a tricritical point as opposed to a critical-end point. These results extend previous effective Hamiltonian predictions which were limited only to shallow wedges

Edge contact angle and modified Kelvin equation for condensation in open pores

We consider capillary condensation transitions occurring in open slits of width $L$ and finite height $H$ immersed in a reservoir of vapour. In this case the pressure at which condensation occurs is closer to saturation compared to that occurring in an infinite slit ($H=\infty$) due to the presence of two menisci which are pinned near the open ends. Using macroscopic arguments we derive a modified Kelvin equation for the pressure, $p_{cc}(L;H)$, at which condensation occurs and show that the two menisci are characterised by an edge contact angle $\theta_e$ which is always larger than the equilibrium contact angle $\theta$, only equal to it in the limit of macroscopic $H$. For walls which are completely wet ($\theta=0$) the edge contact angle depends only on the aspect ratio of the capillary and is well described by $\theta_e\approx \sqrt{\pi L/2H}$ for large $H$. Similar results apply for condensation in cylindrical pores of finite length. We have tested these predictions against numerical results obtained using a microscopic density functional model where the presence of an edge contact angle characterising the shape of the menisci is clearly visible from the density profiles. Below the wetting temperature $T_w$ we find very good agreement for slit pores of widths of just a few tens of molecular diameters while above $T_w$ the modified Kelvin equation only becomes accurate for much larger systems

Phase transitions, interfacial fluctuations and hidden symmetries for fluids near structured walls

Fluids adsorbed at micro-patterned and geometrically structured substrates can exhibit novel phase transitions and interfacial fluctuation effects distinct from those characteristic of wetting at planar, homogeneous walls. We review recent theoretical progress in this area paying particular attention to filling transitions pertinent to fluid adsorption near wedges, which have highlighted a deep connection between geometrical and contact angles. We show that filling transitions are not only characterized by large scale interfacial fluctuations leading to universal critical singularities but also reveal hidden symmetries with short-ranged critical wetting transitions and properties of dimensional reduction. We propose a non-local interfacial model which fulfills all these properties and throws light on long-standing problems regarding the order of the 3D short-range critical wetting transition