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. Rascón, Nat. Phys. 15, 287 (2019)NPAHAX1745-247310.1038/s41567-018-0361-z]. Here, we illustrate, using mean-field square-gradient theory and the more microscopic Sullivan density functional model, and how this approach generalizes when there is liquid-gas asymmetry, i.e., when the bulk correlation lengths of the coexisting liquid and gas phases are different. In particular, we are able to express the correlation function exactly as a simple average of contributions arising from two effective Ising-symmetric systems referred to as the symmetric gas and symmetric liquid. When combined with our earlier results, this generates analytical approximations for the correlation function and the local structure factor, which are near indistinguishable from the numerical solution to the Ornstein-Zernike equations over the whole range of wave vectors. Our results highlight how asymmetry affects the correlation function structure and describes the crossover from a long-ranged Goldstone mode to short-ranged properties determined by the local density as the wave vector increases.

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)1745-247310.1038/s41567-018-0361-z]. 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.

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. 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.

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. 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.

The local structure factor near an interface; beyond extended capillary-wave models

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 [Formula: see text]. 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, [Formula: see text] and [Formula: see text], 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 [Formula: see text] and [Formula: see text], 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.

Liquid-gas asymmetry and the wave-vector-dependent surface tension

Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector (q)-dependent surface tension σeff(q), have encountered difficulties. There is no consensus as to even the shape of σeff(q). By analyzing 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 characterized by a microscopic q-dependent length ζ(q) not identified previously. The necessity of including the q dependence of ζ(q) is illustrated explicitly in our model and has wider implications; i.e., in typical experimental and simulation studies, an indeterminacy in ζ(q) will always be present, reminiscent of the cutoff used in capillary-wave theory. This leads inevitably to a large uncertainty in the q dependence of σeff(q).

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 θ(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 θ(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 θ(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 characterized by large scale fluctuations and essential critical singularities arising from marginal interfacial interactions.

Pair correlation functions and the wavevector-dependent surface tension in a simple density functional treatment of the liquid-vapour interface

We study the density-density correlation function G(r, 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 σ(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 σ(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 σ(q).

Capillary emptying and short-range wetting

We consider a liquid trapped in a narrow horizontal capillary, under the influence of gravity. As the slit is widened, the meniscus, separating the capillary liquid from gas, deforms and develops a long tongue extending along the bottom wall. As a critical slit width is approached, the length of the tongue diverges continuously, leading to the emptying of the capillary. We show that the critical singularities characterizing emptying are the same as those at short-ranged wetting transitions, but at a scale set by the capillary length rather than the bulk correlation length. These meso- or macroscopic versions of both complete and critical wetting are observable in the laboratory and are studied here using a colloid-polymer mixture.

[Effect of different doses of fentanyl and butylhyoscine on the rabbit's sphincter of Oddi]

BACKGROUND

It was not until the advent of endoscopic retrograde cholangiopancreatography (ERCP) that Oddi's sphincter manometry was performed directly. Use of opioids for the intravenous (IV) sedation of these patients is controversial.

OBJECTIVE

To evaluate with manometry the effect of fentanyl at different doses as well as the effect of butylhyoscine on the rabbit's Oddi's sphincter.

METHODS

This is an experimental, randomized, double-blind study conducted in New Zealand rabbits distributed in 4 groups (control, fentanyl at doses of 1, 5 and 10 μg/kg of weight) that, after laparotomy and duodenotomy, underwent direct Oddi's sphincter manometry. The analyzed variables included sphincter pressure, wave frequency, amplitude and duration.

RESULTS

The baseline measurements of the study variables did not show any differences among the groups. The administration of fentanyl at 1 μg/kg reduced Oddi's sphincter pressure compared with the baseline value (p = 0.003), while the doses of 5 and 10 μg/kg significantly increased it (p <0.0001). Butylhyoscine decreased the sphincter pressure, frequency, amplitude and duration of the waves in all the groups and antagonized the increase in pressure produced by fentanyl.

CONCLUSIONS

Fentanyl at 1 μg/kg of body weight relaxes the rabbit's Oddi's sphincter and butylhyoscine can antagonize the increased pressure of the sphincter caused by fentanyl at 5 and 10 μg/kg of weight. These finding suggest a potential beneficial for the ERCP in clinical controlled trials in humans.

Derivation of a non-local interfacial model for 3D wetting in an external field

We extend recent studies of 3D short-ranged wetting transitions by deriving an interfacial Hamiltonian in the presence of an arbitrary external field. The binding potential functional, describing the interaction of the interface and the substrate, can still be written in a diagrammatic form, but now includes new classes of diagrams due to the coupling to the external potential, which are determined exactly. Applications to systems with long-ranged (algebraically decaying) and short-ranged (exponentially decaying) external potentials are considered at length. We show how the familiar 'sharp-kink' approximation to the binding potential emerges, and determine the corrections to this arising from interactions between bulk-like fluctuations and the external field. A connection is made with earlier local effective interfacial Hamiltonian approaches. It is shown that, for the case of an exponentially decaying potential, non-local effects have a particularly strong influence on the approach to the critical regime at second-order wetting transitions, even when they appear to be sub-dominant. This is confirmed by Monte Carlo simulation studies of a discretized version of a non-local interfacial model.

3D short-range wetting and nonlocality

Analysis of a microscopic Landau-Ginzburg-Wilson model of 3D short-ranged wetting shows that correlation functions are characterized by two length scales, not one, as previously thought. This has a simple diagrammatic explanation using a nonlocal interfacial Hamiltonian and yields a thermodynamically consistent theory of wetting in keeping with exact sum rules. For critical wetting the second length serves to lower the cutoff in the spectrum of interfacial fluctuations determining the repulsion from the wall. We show how this corrects previous renormalization group predictions for fluctuation effects, based on local interfacial Hamiltonians. In particular, lowering the cutoff leads to a substantial reduction in the effective value of the wetting parameter and prevents the transition being driven first order. Quantitative comparison with Ising model simulation studies due to Binder, Landau, and co-workers is also made.

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: II. General diagrammatic structure

In our first paper, we showed how a non-local effective Hamiltonian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Green's function method with standard perturbation theory to determine the general diagrammatic form of the binding potential functional beyond the double-parabola approximation for the Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic interactions is simply to alter the coefficients of the double parabola-like zigzag diagrams and also to introduce curvature and tube-interaction corrections (also represented diagrammatically), which are of minor importance. Non-locality generates effective long-ranged many-body interfacial interactions due to the reflection of tube-like fluctuations from the wall. Alternative wall boundary conditions (with a surface field and enhancement) and the diagrammatic description of tricritical wetting are also discussed.

Condensation in a capped capillary is a continuous critical phenomenon

We show that condensation in a capped capillary slit is a continuous interfacial critical phenomenon, related intimately to several other surface phase transitions. In three dimensions, the adsorption and desorption branches correspond to the unbinding of the meniscus from the cap and opening, respectively, and are equivalent to 2D-like complete-wetting transitions. For dispersion forces, the singularities on the two branches are distinct, owing to the different interplay of geometry and intermolecular forces. In two dimensions we establish precise connection, or covariance, with 2D critical-wetting and wedge-filling transitions: i.e., we establish that certain interfacial properties in very different geometries are identical. Our predictions of universal scaling and covariance in finite capillaries are supported by extensive Ising model simulation studies in two and three dimensions.

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: I. Double-parabola approximation

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 small-gradient limit.

Signatures of non locality for short-ranged wetting at curved substrates

The binding potential for wetting near planes, spheres, and cylinders in systems with short-ranged forces is shown to have a universal geometrical structure. This arises from the nonlocal nature of the interfacial interactions and is exactly described by a recently proposed binding potential functional, which provides a systematic framework for studying wetting at arbitrarily shaped substrates. The corrections to the equilibrium wetting layer thickness induced by nonlocality are comparable to those arising from a Tolman length and lead to diverging terms in the total mass adsorption.

Extended wedge covariance for wetting and filling transitions

Fluid adsorption on nonplanar and heterogeneous substrates is studied using a simple interfacial model. For systems with short-ranged forces, we find that, by tuning the local strength of the substrate potential, it is possible to find the exact equilibrium interfacial profile as a functional of the wall shape psi x. The tuning of the local substrate potential takes the form of a gauge condition theta x=+/-psi x, where theta x can be interpreted as a local effective contact angle. For wedgelike geometries with asymptotic tilt angle alpha, the midpoint interfacial height and roughness satisfy the same covariance relations previously found for simple linear wedges. For troughlike geometries satisfying the gauge condition, covariance is also found for the two-point correlation function. Predictions for more microscopic Landau and Ising models are also discussed.

Covariance for cone and wedge complete filling

Interfacial phenomena associated with fluid adsorption in two dimensional systems have recently been shown to exhibit hidden symmetries, or covariances, which precisely relate local adsorption properties in different confining geometries. We show that covariance also occurs in three-dimensional systems and is likely to be verifiable experimentally and in Ising model simulations studies. Specifically, we study complete wetting in wedge (W) and cone (C) geometries as bulk coexistence is approached and show that the equilibrium midpoint heights satisfy l(c)(h,alpha)=l(w)(h / 2,alpha), where h measures the partial pressure and alpha is the tilt angle. This covariance is valid for both short-ranged and long-ranged intermolecular forces and identifies both leading and next-to-leading-order critical exponents and amplitudes in the confining geometries.

Local functional models of critical correlations in thin films

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free energy and scaling of one-point functions in critical thin films. This approach is extended to predict the two-point correlation function G in critical thin films with symmetric surface fields in arbitrary dimension d. In d = 2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths xi((n)) as well as the detailed position dependence of the asymptotic decay of G. In d = 3 and d>/=4 we present new numerical predictions for the universal finite-size correlation length and scaling functions determining the structure of G across the thin film. Highly accurate analytical closed form expressions for these universal properties are derived in arbitrary dimension.

Geometry-dominated fluid adsorption on sculpted solid substrates

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.

Wetting at nonplanar substrates: unbending and unbinding

We consider fluid wetting on a corrugated substrate using effective interfacial Hamiltonian theory and show that breaking the translational invariance along the wall can induce an unbending phase transition in addition to unbinding. Both first-order and second-order unbending transitions can occur at and out of coexistence. Results for systems with short-ranged and long-ranged forces establish that the unbending critical point is characterized by hyperuniversal scaling behavior. We show that, at bulk coexistence, the adsorption at the unbending critical point is a universal multiple of the adsorption for the correspondent planar system.