Wetting, Algebraic Curves, and Conformal Invariance.

Recent studies of wetting in a two-component square-gradient model of interfaces in a fluid mixture, showing three-phase bulk coexistence, have revealed some highly surprising features. Numerical results show that the density profile paths, which form a tricuspid shape in the density plane, have curious geometric properties, while conjectures for the analytical form of the surface tensions imply that nonwetting may persist up to the critical end points, contrary to the usual expectation of critical point wetting. Here, we solve the model exactly and show that the profile paths are conformally invariant quartic algebraic curves that change genus at the wetting transition.

Critical-point wedge filling and critical-point wetting.

For simple fluids adsorbed at a planar solid substrate (modeled as an inert wall) it is known that critical-point wetting, that is, the vanishing of the contact angle θ at a temperature T_{w} lying below that of the critical point T_{c}, need not occur. While critical-point wetting necessarily happens when the wall-fluid and fluid-fluid forces have the same range (e.g.

Critical behaviour of the contact angle within nonwetting gaps.

Recent density functional theory and simulation studies of fluid adsorption near planar walls in systems where the wall-fluid and fluid-fluid interactions have different ranges, have shown that critical point wetting may not occur and instead nonwetting gaps appear in the surface phase diagram, separating lines of wetting and drying transitions, that extend up to the critical temperature. Here we clarify the features of the surface phase diagrams that are common, regardless of the range and balance of the forces, showing, in particular, that the lines of temperature driven wetting and drying transitions, as well as lines of constant contact angleπ>θ>0, always converge to an ordinary surface phase transition at. When nonwetting gaps appear the contact angle either vanishes or tends toast≡(Tc-T)/Tc→0.

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, dispersionlike forces, away from the near vicinity of the bulk critical temperature T_{c}, 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 T_{c}. 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.

Correction: Abrupt onset of the capillary-wave spectrum at wall-fluid interfaces.

Correction for 'Abrupt onset of the capillary-wave spectrum at wall-fluid interfaces' by Andrew O. Parry , , 2023, , 5668-5673, https://doi.org/10.

Abrupt onset of the capillary-wave spectrum at wall-fluid interfaces.

Surfaces between 3D solids and fluids exhibit a wide variety of phenomena both at equilibrium, such as roughening transitions, interfacial fluctuations and wetting, and also out-of-equilibrium, such as the surface growth of driven interfaces. These phenomena are described very successfully using lower dimensional (2D) effective models which focus on the physics associated with emergent mesoscopic lengths scales, parallel to the interface, where the 2D-like behaviour is physically transparent. However, the precise conditions under which this dimensional reduction is justifiable have remained unclear.

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_{w}^{β_{osc}} 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.

Intermittent attractive interactions lead to microphase separation in nonmotile active matter.

Nonmotile active matter exhibits a wide range of nonequilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria Neisseria meningitidis in which diffusive agents feel intermittent attractive forces. Through a formal coarse-graining procedure, we show that this truly scalar model of active matter exhibits the time-reversal-symmetry breaking terms defining the Active Model B+ class.

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.

Casimir Contribution to the Interfacial Hamiltonian for 3D Wetting.

Previous treatments of three-dimensional (3D) short-ranged wetting transitions have missed an entropic or low-temperature Casimir contribution to the binding potential describing the interaction between the unbinding interface and wall. This we determine by exactly deriving the interfacial model for 3D wetting from a more microscopic Landau-Ginzburg-Wilson Hamiltonian. The Casimir term changes the interpretation of fluctuation effects occurring at wetting transitions so that, for example, mean-field predictions are no longer obtained when interfacial fluctuations are ignored.

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<2/π, the condensation is of type I involving menisci which are pinned at the top edges at the ends of the capillary.

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<2/π, the condensation is of type I involving menisci which are pinned at the top edges at the ends of the capillary characterized by an edge contact angle.

Breaking Cassie's Law for Condensation in a Nanopatterned Slit.

We study the phase transitions of a fluid confined in a capillary slit made from two adjacent walls, each of which are a periodic composite of stripes of two different materials. For wide slits the capillary condensation occurs at a pressure which is described accurately by a combination of the Kelvin equation and the Cassie law for an averaged contact angle. However, for narrow slits the condensation occurs in two steps involving an intermediate bridging phase, with the corresponding pressures described by two new Kelvin equations.

Three-Phase Fluid Coexistence in Heterogenous Slits.

We study the competition between local (bridging) and global condensation of fluid in a chemically heterogeneous capillary slit made from two parallel adjacent walls each patterned with a single stripe. Using a mesoscopic modified Kelvin equation, which determines the shape of the menisci pinned at the stripe edges in the bridge phase, we determine the conditions under which the local bridging transition precedes capillary condensation as the pressure (or chemical potential) is increased. Provided the contact angle of the stripe is less than that of the outer wall we show that triple points, where evaporated, locally condensed, and globally condensed states all coexist are possible depending on the value of the aspect ratio a=L/H, where H is the stripe width and L the wall separation.

Microscopic determination of correlations in the fluid interfacial region in the presence of liquid-gas asymmetry.

In a recent article, we showed how the properties of the density-density correlation function and its integral, the local structure factor, in the fluid interfacial region, in systems with short-ranged forces, can be understood microscopically by considering the resonances of the local structure factor [A. O. Parry and C.

Scaling of wetting and prewetting transitions on nanopatterned walls.

We consider a nanopatterned planar wall consisting of a periodic array of stripes of width L, which are completely wet by liquid (contact angle θ=0), separated by regions of width D which are completely dry (contact angle θ=π). Using microscopic density functional theory, we show that, in the presence of long-ranged dispersion forces, the wall-gas interface undergoes a first-order wetting transition, at bulk coexistence as the separation D is reduced to a value D_{w}∝lnL, induced by the bridging between neighboring liquid droplets. Associated with this is a line of prewetting transitions occurring off coexistence.

Correlation-function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations.

In a recent article, we described how the microscopic structure of density-density correlations in the fluid interfacial region, for systems with short-ranged forces, can be understood by considering the resonances of the local structure factor occurring at specific parallel wave vectors q [Nat. Phys. 15, 287 (2019)1745-247310.

Bridging of liquid drops at chemically structured walls.

Using mesoscopic interfacial models and microscopic density functional theory we study fluid adsorption at a dry wall decorated with three completely wet stripes of width L separated by distances D_{1} and D_{2}. The stripes interact with the fluid with long-range forces inducing a large finite-size contribution to the surface free energy. We show that this nonextensive free-energy contribution scales with lnL and drives different types of bridging transition corresponding to the merging of liquid drops adsorbed at neighboring wetting stripes when the separation between them is molecularly small.

Curvature corrections to the nonlocal interfacial model for short-ranged forces.

In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double-parabola potential, we reformulate the derivation of the interfacial model using a rigorous boundary integral approach. This is done for three scenarios: a single fluid phase in contact with a nonplanar substrate (i.

Modified Kelvin Equations for Capillary 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 θ_{E} describing the shape of the meniscus formed at the top of the groove.

First-order wedge wetting revisited.

We consider a fluid adsorbed in a wedge made from walls that exhibit a first-order wetting transition and revisit the argument as to why and how the pre-filling and pre-wetting coexistence lines merge when the opening angle is increased approaching the planar geometry. We clarify the nature of the possible surface phase diagrams, pointing out the connection with complete pre-wetting, and show that the merging of the coexistence lines lead to new interfacial transitions. These occur along the side walls and are associated with the unbinding of the thin-thick interface, rather than the liquid-gas interface (meniscus), from the wedge apex.

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.

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 vapor. In this case the pressure at which condensation occurs is closer to saturation compared to that occurring in an infinite slit (H=∞) due to the presence of two menisci that 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 characterized by an edge contact angle θ_{e} that is always larger than the equilibrium contact angle θ, only equal to it in the limit of macroscopic H.

Classical density functional study of wetting transitions on nanopatterned surfaces.

Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting.

Geometry-induced capillary emptying.

When a capillary is half-filled with liquid and turned to the horizontal, the liquid may flow out of the capillary or remain in it. For lack of a better criterion, the standard assumption is that the liquid will remain in a capillary of narrow cross-section, and will flow out otherwise. Here, we present a precise mathematical criterion that determines which of the two outcomes occurs for capillaries of arbitrary cross-sectional shape, and show that the standard assumption fails for certain simple geometries, leading to very rich and counterintuitive behavior.