arXiv subjects

Andrew O. Parry

Publications and source records attributed to Andrew O. Parry.

At least 19 recordsLinked to original sources

arXiv2026

Beyond capillary condensation: Shear-induced bridging transitions in patterned slits

We study the equilibrium phase behavior of a fluid confined in a slit made from two patterned walls. Shearing the walls frustrates the fluid, due to a competition between capillary condensation and interface delocalization, forcing the formation of bridging phases with different pinning properties. This leads to an unusually rich phase diagram, displaying first-order and continuous phase transitions, depending sensitively on the slit width and shear. Generalized Kelvin equations determine the phase boundaries, while the bridging phases are characterized by large correlation lengths, predictions for which are tested using a microscopic density functional model.

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arXiv2025

The influence of the Casimir effect on the binding potential for 3D wetting

We provide comprehensive details of how a previously overlooked entropic, or low temperature Casimir contribution, $W_C$, to the total binding potential for 3D short-ranged wetting may be determined from a microscopic Landau-Ginzburg-Wilson Hamiltonian. The entropic contribution comes from the many microscopic configurations corresponding to a given interfacial one, which arise from bulk-like fluctuations about the mean-field (MF) constrained profile, and adds to the usual MF contribution $W_{MF}$. We determine the functional dependence of $W_C$ on the interface (and wall) shape using a boundary integral method which can be cast as a diagrammatic expansion with each diagram corresponding to successively higher-order exponentially decaying contributions. The decay of $W_C$ is qualitatively different for first-order and critical wetting with the change in form occurring at the MF tricritical point. Including the Casimir contribution to the binding potential preserves the global surface phase diagram but changes, radically, predictions for fluctuation effects at first-order and tricritical wetting, even when capillary-wave fluctuations are not considered.

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arXiv2024

The Casimir effect in wetting layers

For a long time, the study of thermal effects at three-dimensional (3D) short-ranged wetting transitions considered only the effect of interfacial fluctuations. We show that an entropic Casimir contribution, missed in previous treatments, produces significant effects when it is included; in particular, mean-field predictions are no longer obtained when interfacial fluctuations are ignored. The Casimir term arises from the many different microscopic configurations that correspond to a given interfacial one. By employing a coarse-graining procedure, starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian, we identify the interfacial model for 3D wetting and the exact form of the Casimir term. The Casimir contribution does not alter the Nakanishi-Fisher surface phase diagram; it significantly increases the adsorption near a first-order wetting transition and completely changes the predicted critical singularities of tricritical wetting, including the nonuniversality occurring in 3D arising from interfacial fluctuations. We illustrate how the Casimir term leads to a reappraisal of the critical singularities at wetting transitions.

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arXiv2024

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. Being harmonic, the profile paths can be represented by an analytic function in the complex plane which then conformally maps the paths onto straight lines. Using this, we derive the conjectured form of the surface tensions and explain the geometrical properties of the tricuspid and its relation to the Neumann triangle for the contact angles. The exact solution confirms that critical point wetting is absent in this square-gradient model.

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arXiv2022

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. While the Casimir contribution does not alter the surface phase diagram, it significantly increases the adsorption near a first-order wetting transition and changes completely the predicted critical singularities of tricritical wetting, including the non-universality occurring in 3D arising from interfacial fluctuations. Using the numerical renormalization group we show that, for critical wetting, the asymptotic regime is extremely narrow with the growth of the parallel correlation length characterised by an effective exponent in quantitative agreement with Ising model simulations, resolving a longstanding controversy.

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arXiv2022

Intermittent Attractive Interactions Lead to Microphase Separation in Non-motile Active Matter

Non-motile active matter exhibits a wide range of non-equilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria {\it 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 {\it Active Model B+} class. In particular, we confirm the presence of microphase separation by solving the kinetic equations numerically. We show that the switching rate controlling the interactions provides a regulation mechanism tuning the typical cluster size, e.g. in populations of bacteria interacting via type IV pili.

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arXiv2021

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. For intermediate capillaries, with $2/π 1$, condensation is always of type II. In all regimes, capillary condensation is completely suppressed for sufficiently large contact angles which is determined explicitly. For long and intermediate capillaries, we show that there is an additional continuous phase transition in the condensed liquid-like phase, associated with the depinning of each meniscus as they round the upper open edges of the slit. Meniscus depinning is third-order for complete wetting and second-order for partial wetting. Detailed scaling theories are developed for these transitions and phase boundaries which connect with the theories of wedge (corner) filling and wetting encompassing interfacial fluctuation effects and the direct influence of intermolecular forces.

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arXiv2021

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. For intermediate capillaries, with $2/π 1$, condensation is always of type II. In all regimes, capillary condensation is completely suppressed for sufficiently large contact angles. We show that there is an additional continuous phase transition in the condensed liquid-like phase, associated with the depinning of each meniscus as they round the upper open edges of the slit. Finite-size scaling predictions are developed for these transitions and phase boundaries which connect with the fluctuation theories of wetting and filling transitions. We test several of our predictions using a fully microscopic Density Functional Theory which allows us to study the two types of capillary condensation and its suppression at the molecular level.

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arXiv2021

Breaking Cassie's law for condensation in a nano-patterned 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. These are characterised by different contact angles due to interfacial pinning, with one larger and one smaller than the Cassie angle. We determine the triple point and predict two types of dispersion force induced Derjaguin-like corrections due to mesoscopic volume reduction and the singular free-energy contribution from nano-droplets and bubbles. We test these predictions using a fully microscopic density functional model which confirms their validity even for molecularly narrow slits. Analogous mesoscopic corrections are also predicted for two dimensional systems arising from thermally induced interfacial wandering.

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arXiv2019

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 [Nat.Phys.~{\bf 15}, 287 (2019)]. Here we illustrate, using mean-field square-gradient theory and the more microscopic Sullivan density functional model, how this approach generalises 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 \textit{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.

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arXiv2019

Scaling of wetting and pre-wetting transitions on nano-patterned walls

We consider a nano-patterned 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 $D_w\propto\ln L$, induced by the bridging between neighboring liquid droplets. Associated with this is a line of pre-wetting transitions occurring off coexistence. By varying the stripe width $L$ we show that the pre-wetting line shows universal scaling behaviour and data collapse. This verifies predictions based on mesoscopic models for the scaling properties associated with finite-size effects at complete wetting including the logarithmic singular contribution to the surface free-energy.

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arXiv2019

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 $q$. Here, we investigate this further by comparing approximations for the local structure factor and correlation function against three new examples of analytically solvable models within square-gradient theory. Our analysis further demonstrates that these approximations describe the correlation function and structure factor across the whole spectrum of wave-vectors, encapsulating the cross-over from the Goldstone mode divergence (at small $q$) to bulk-like behaviour (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 very accurately describe 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 near indistinguishable from the numerical solutions of the Ornstein-Zernike equation.

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arXiv2018

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.e., wall); a free interface separating coexisting fluid phases (say, liquid and gas); and finally a liquid-gas interface in contact with a nonplanar confining wall, as is applicable to wetting phenomena. For the first two cases our approaches identifies the correct form of the curvature corrections to the free energy and, for the case of a free interface, it allows us to recast these as an interfacial self-interaction as conjectured previously in the literature. When the interface is in contact with a substrate our approach similarly identifies curvature corrections to the nonlocal binding potential, describing the interaction of the interface and wall, for which we propose a generalized and improved diagrammatic formulation.

cond-mat.soft↗

arXiv2017

Scaling behaviour of thin films on chemically heterogenous 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. We test these predictions using a microscopic Fundamental Measure Density Functional Theory which incorporates short-ranged fluid-fluid and fully long-ranged wall-fluid interactions. Our model functional accurately describes packing effects not captured by the interfacial Hamiltonian but still we show that there is excellent agreement with the predictions $h_m\approx L^{1/2}$ and for the scaled circular shape of the drop even for $L$ as small as $50$ molecular diameters. For smaller stripes the droplet height is considerably lower than that predicted by the mesoscopic interfacial theory. Phase transitions for droplet configurations occurring on substrates with multiple stripes are also discussed.

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arXiv2017

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 $θ_e$ which is always larger than the equilibrium contact angle $θ$, only equal to it in the limit of macroscopic $H$. For walls which are completely wet ($θ=0$) the edge contact angle depends only on the aspect ratio of the capillary and is well described by $θ_e\approx \sqrt{πL/2H}$ 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.

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arXiv2016

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 $γ_{11}^{\rm eff}=\frac{3}{2}$. 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 $γ_{11}^{\rm eff}$ 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.

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arXiv2016

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.

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arXiv2015

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.

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