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)]. Here we investigate this further by comparing approximations for the local structure factor and pair correlation function against three new examples of analytically solvable models within square-gradient theory. Our analysis further demonstrates that these approximations describe the pair correlation function and structure factor across the whole spectrum of wave vectors, encapsulating the crossover from the Goldstone mode divergence (at small q) to bulklike behavior (at larger q). As shown, these approximations are exact for some square-gradient model potentials and never more than a few percent inaccurate for the others. Additionally, we show that they describe very accurately the correlation function structure for a model describing an interface near a tricritical point. In this case, there are no analytical solutions for the correlation functions, but the approximations are nearly indistinguishable from the numerical solutions of the Ornstein-Zernike equation.

]]>The development of a molecular theory of inhomogeneous fluids and, in particular, of the liquid–gas interface has received enormous interest in recent years; however, long-standing attempts to extend the concept of surface tension in mesoscopic approaches by making it scale dependent, although apparently plausible, have failed to connect with simulation and experimental studies of the interface that probe the detailed properties of density correlations. Here, we show that a fully microscopic theory of correlations in the interfacial region can be developed that overcomes many of the problems associated with simpler mesoscopic ideas. This theory originates from recognizing that the correlation function displays, in addition to a Goldstone mode, an unexpected hierarchy of resonances that constrain severely its structural properties. Indeed, this approach allows us to identify new classes of fully integrable models for which, surprisingly, the tension, density profile and correlation function can all be determined analytically, revealing the microscopic structure of correlations in all generalized van der Waals theories.

]]>We present a numerical study of a simple density functional theory model of fluid adsorption occurring on a planar wall decorated with a narrow deep stripe of a weaker adsorbing (relatively solvophobic) material, where wall-fluid and fluid-fluid intermolecular forces are considered to be dispersive. Both the stripe and outer substrate exhibit first-order wetting transitions with the wetting temperature of the stripe lying above that of the outer material. This geometry leads to a rich phase diagram due to the interplay between the pre-wetting transition of the outer substrate and an unbending transition corresponding to the local evaporation of liquid near the stripe. Depending on the width of the stripe, the line of unbending transitions merges with the pre-wetting line inducing a two-dimensional wetting transition occurring across the substrate. In turn, this leads to the continuous pre-drying of the thick pre-wetting film as the pre-wetting line is approached from above. Interestingly we find that the merging of the unbending and pre-wetting lines occurs even for the widest stripes considered. This contrasts markedly with the scenario where the outer material has the higher wetting temperature, for which the merging of the unbending and pre-wetting lines only occurs for very narrow stripes.

]]>*C Rascón, J Pausch, AO Parry*, Soft Matter 14, 2835 (2018)

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. When fluctuation effects, together with the influence of dispersion forces are included, these transitions display strong non-universal critical singularities that depend on the opening angle itself. Similar phenomena are also shown to occur for adsorption near an apex tip.

]]>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. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.

]]>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. This opens the possibility of creating very sensitive micro-fluidic devices that respond readily to small physical changes, for instance, by triggering the sudden displacement of fluid along a capillary without the need of any external pumping.

]]>We investigate the local structure factor $S(z;q)$ at a free liquid-gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of $S(z;q)$ known to occur for parallel (i.e., measured along the interface) wavevectors $\,q\to 0$. We show from explicit solution of the inhomogeneous Ornstein-Zernike equation that for distances $z$ far from the interface, where the profile decays exponentially, $S(z;q)$ splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, $\,\sigma_l(q)\,$ and $\,\sigma_g(q)\,$, which are determined solely by the *bulk* two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of $S(z;q)$ within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for $\,\sigma_l(q)\,$ and $\,\sigma_g(q)\,$, and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended Capillary-Wave models which failed completely to describe the simulation results.

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Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector ($q$) dependent surface tension $\sigma_\text{eff}(q)$, have encountered difficulties. There is no consensus as to even the shape of $\sigma_\text{eff}(q)$. By analysing a simple density functional model of the liquid-gas interface, we identify different schemes for separating microscopic observables into background and interfacial contributions. In order for the backgrounds of the density-density correlation function and local structure factor to have a consistent and physically meaningful interpretation in terms of weighted bulk gas and liquid contributions, the background of the total structure factor must be characterised by a microscopic $q$-dependent length $\zeta(q)$ not identified previously. The necessity of including the $q$ dependence of $\zeta(q)$ is illustrated explicitly in our model and has wider implications, i.e. in typical experimental and simulation studies, an indeterminacy in $\zeta(q)$ will always be present, reminiscent of the cut-off used in capillary-wave theory. This leads inevitably to a large uncertainty in the $q$ dependence of $\sigma_\text{eff}(q)$.

]]>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 $\theta^\text{cap}(L)$ which depends on the difference between the Hamaker constants. If the bottom wall has a weaker wall-fluid attraction than the side walls, then $\theta^\text{cap}>0$ 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 $\theta^\text{cap}(L)$ 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 characterised by large scale fluctuations and essential critical singularities arising from marginal interfacial interactions.

We study the density-density correlation function $G({\bf r},{\bf r}’)$ in the interfacial region of a fluid (or Ising-like magnet) with short-ranged interactions using square gradient density functional theory. Adopting a simple double parabola approximation for the bulk free-energy density, we first show that the parallel Fourier transform $G(z,z’;q)$ and local structure factor $S(z;q)$ separate into bulk and excess contributions. We attempt to account for both contributions by deriving an interfacial Hamiltonian, characterised by a wavevector dependent surface tension $\sigma(q)$, and then reconstructing density correlations from correlations in the interface position. We show that the standard crossing criterion identification of the interface, as a surface of fixed density (or magnetization), does not explain the separation of $G(z,z’;q)$ and the form of the excess contribution. We propose an alternative definition of the interface position based on the properties of correlations between points that

“float” with the surface and show that this describes the full $q$ and $z$ dependence of the excess contributions to both $G$ and $S$. However, neither the “crossing-criterion” nor the new “floating interface” definition of $\sigma(q)$ are quantities directly measurable from the total structure factor $S^{tot}(q)$ which contains additional $q$ dependence arising from the non-local relation between fluctuations in the interfacial position and local density. Since it is the total structure factor that is measured experimentally or in simulations, our results have repercussions for earlier attempts to extract and interpret $\sigma(q)$.