## Publications

133 results found

Parry AO, Rascón C, 2023, Correction: Abrupt onset of the capillary-wave spectrum at wall-fluid interfaces., *Soft Matter*

Correction for 'Abrupt onset of the capillary-wave spectrum at wall-fluid interfaces' by Andrew O. Parry et al., Soft Matter, 2023, 19, 5668-5673, https://doi.org/10.1039/D3SM00761H.

Parry A, Malijevsky A, 2023, Surface phase diagrams for wetting with long-ranged forces, *Physical Review Letters*, ISSN: 0031-9007

Recent Density Functional Theory and simulation studies of wetting and drying transitions in systems with long-ranged, dispersion-like forces, away from the near vicinity of the bulk critical temperature Tc, 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 Tc. 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. We highlight the importance of lines of maximally multicritical wetting and drying transitions, for which we determine the exact critical singularities.

Parry A, rascon C, 2023, Abrupt onset of the capillary-wave spectrum at wall-fluid interfaces, *Soft Matter*, Vol: 19, Pages: 5668-5673, ISSN: 1744-683X

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, suchas the surface growth of driven interfaces. These phenomena are described very successfully usinglower 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 remainedunclear. Here we show that, for a wall-fluid interface, a dimensional reduction from 3D-like to 2D-likebehaviour – identified via the decay of density correlations – occurs abruptly at a specific value of thecontact angle, and indicates the beginning of interfacial-like 2D behaviour and the spontaneous onsetof the capillary-wave spectrum. The reduction from 3D to 2D is characterised by the divergence ofa correlation length perpendicular to the interface revealing a morphological change in the nature ofdensity correlations. Counter-intuitive effects occur, including that 3D behaviour can persist up tothe wetting temperature and also that 2D behaviour can begin when no wetting layer is present andthe adsorption is negative.

Parry A, Malijevsky A, Pospisil M, 2023, Phase transitions and droplet shapes above a wetting stripe, *Journal of Molecular Liquids*, ISSN: 0167-7322

Parry A, malijevsky A, pospisil M, 2023, phase transitions and droplet shapes above a wetting stripe, *Journal of Molecular Liquids*, ISSN: 0167-7322

Squarcini A, Romero-Enrique JM, Parry A, 2023, Derivation of the Casimir contribution to the binding potential for 3D wetting, *Molecular Physics: An International Journal at the Interface Between Chemistry and Physics*, Pages: 1-10, ISSN: 0026-8976

The renormalisation group theory of critical and tri-critical wetting transitions in three-dimensional systems with short-ranged forces, based on analysis of an effective Hamiltonian with an interfacial binding potential w(ℓ), predicts very strong non-universal critical singularities. These, however, have famously not been observed in extensive Monte Carlo simulations of the transitions in the simple cubic Ising model. Here, we show that previous treatments have missed an entropic, or low-temperature Casimir, contribution to the binding potential, arising from the many different microscopic configurations which correspond to a given interfacial one. We derive the full binding potential, including the Casimir correction term, starting from a microscopic Landau–Ginzburg–Wilson Hamiltonian, using a continuum transfer-matrix (path-integral) method. This is illustrated first in one dimension before generalising to arbitrary dimension. The Casimir contribution is qualitatively different for first-order, critical and tri-critical wetting transitions and substantially alters previous predictions for critical singularities bringing them much closer to the simulation results.

Parry A, Malijevsky A, Pospisil M, 2022, Critical effects and scaling at meniscus osculation transitions, *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, Vol: 106, Pages: 1-8, ISSN: 1539-3755

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 Rw in a confining parabolic geometry. We argue that the exponent βosc characterizing the scale of the interfacial height ℓ0∝Rβoscw at osculation, for large Rw, 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. In the fluctuation-dominated regime, representing the universality class of systems with short-range forces, the exponent is related to the value of the interfacial wandering exponent ζ by βosc=3ζ/(4−ζ). In contrast, in the mean-field regime, which was not previously identified and which occurs for systems with longer-range forces (and higher dimensions), the exponent βosc takes the same value as the exponent βcos for complete wetting, which is determined directly by the intermolecular forces. The prediction βosc=3/7 in d=2 for systems with short-range forces (corresponding to ζ=1/2) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in d=3, based on a microscopic model density-functional theory, determines that βosc≈βcos≈0.326 close to the predicted value of 1/3 appropriate to the mean-field regime for dispersion forces.

Alston H, Parry AO, Voituriez R,
et al., 2022, Intermittent attractive interactions lead to microphase separation in nonmotile active matter, *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, Vol: 106, ISSN: 1539-3755

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. 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.

Parry A, Malijevsky A, Pospisil M, 2022, Meniscus osculation and adsorption on geometrically structured walls, *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, Vol: 105, Pages: 1-13, ISSN: 1539-3755

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, 72, 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. Connection with the general geometric construction proposed by Rascón and Parry is made. Our predictions are supported by a microscopic model density functional theory for drying at a sinusoidally shaped hard wall where we confirm the order of the transition and also an exact sum rule for the generalized contact theorem due to Upton. We show that as bulk coexistence is approached the adsorption isotherm separates into three regimes: A preosculation regime where it is microscopic, containing only a thin wetting layer; a mesoscopic regime, in which a meniscus sits within the troughs; and finally another microscopic regime where the liquid-gas interface unbinds from the crests of the substrate.

Squarcini A, Romero-Enrique JM, Parry A, 2022, Casimir contribution to the interfacial Hamiltonian for 3D wetting, *Physical Review Letters*, Vol: 128, ISSN: 0031-9007

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 nonuniversality 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 characterized by an effective exponent in quantitative agreement with Ising model simulations, resolving a long-standing controversy.

Parry A, malijevsky A, 2021, Capillary condensation and depinning transitions in open slits, *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, Vol: 104, Pages: 1-19, ISSN: 1539-3755

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<a<1, depending on the value of the contact angle the condensation may be of type I or of type II, in which the menisci overspill into the reservoir and there is no pinning. For short capillaries, with a>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. 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 for different aspect ratios and contact angles.

Parry A, Malijevsky A, 2021, The edge contact angle, capillary condensation and meniscus depinning, *Physical Review Letters*, Vol: 127, Pages: 1-5, ISSN: 0031-9007

We study the phase equilibria of a fluid confined in an open capillary slit formed when a wallof finite length H is brought a distance L away from a second macroscopic surface. This systemshows rich phase equilibria arising from the competition between two different types of capillarycondensation, corner filling and meniscus depinning transitions depending on the value of the aspectratio a = L/H. For long capillaries, with a < 2/π, the condensation is of type I involving menisciwhich are pinned at the top edges at the ends of the capillary characterized by an edge contactangle. For intermediate capillaries, with 2/π < a < 1, depending on the value of the contact anglethe condensation may be of type I or of type II, in which the menisci overspill into the reservoirand there is no pinning. For short capillaries, with a > 1, condensation is always of type II. In allregimes, capillary condensation is completely suppressed for sufficiently large contact angles. Weshow that there is an additional continuous, third-order phase transition in the condensed liquidlike phase, associated with the depinning of each meniscus as they round the upper open edges ofthe slit. Finite-size scaling predictions are developed for these transitions and phase boundarieswhich connect with the fluctuation theories of wetting and filling transitions. We test several of ourpredictions using a fully microscopic Density Functional Theory which allows us to study the twotypes of capillary condensation and its suppression at the molecular level.

Láska M, Parry AO, Malijevský A, 2021, Breaking Cassie's Law for condensation in a nanopatterned slit, *Physical Review Letters*, Vol: 126, Pages: 1-1, ISSN: 0031-9007

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 nanodroplets 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.

Parry A, laska M, Malijevsky A, 2020, Three-phase fluid coexistence in heterogeneous slits, *Physical Review Letters*, Vol: 124, ISSN: 0031-9007

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. In particular, for a capillary made from completely dry walls patterned with completely wet stripes the condition for the triple point occurs when the aspect ratio takes its maximum possible value 8 /π. These predictions are tested using a fully microscopic classical density functional theory and shown to be remarkably accurate even for molecularly narrow slits. The qualitative differences with local and global condensation in heterogeneous cylindrical pores are also highlighted.

Parry A, Rascon C, 2019, Microscopic determination of correlations in the fluid interfacial region in the presence of liquid-gas asymmetry, *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, Vol: 100, ISSN: 1539-3755

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)]. 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.

Parry A, Malijevsky A, pospisil M,
et al., 2019, Scaling of wetting and pre-wetting transitions on nano-patterned walls, *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, Vol: 100, Pages: 032801-1-032801-5, ISSN: 1539-3755

We consider a nanopatterned planar wall consisting of a periodic array of stripes of width L, which arecompletely 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-rangeddispersion forces, the wall-gas interface undergoes a first-order wetting transition, at bulk coexistence as theseparation D is reduced to a value Dw ∝ ln L, induced by the bridging between neighboring liquid droplets.Associated with this is a line of prewetting transitions occurring off coexistence. By varying the stripe width L,we show that the prewetting line shows universal scaling behavior and data collapse. This verifies predictionsbased on mesoscopic models for the scaling properties associated with finite-size effects at complete wettingincluding the logarithmic singular contribution to the surface free energy

Parry A, rascon C, 2019, Correlation function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations., *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, Vol: 110, Pages: 022803-1-022803-12, ISSN: 1539-3755

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.

Malijevsky A, Parry AO, Pospisil M, 2019, Bridging of liquid drops at chemically structured walls, *PHYSICAL REVIEW E*, Vol: 99, ISSN: 2470-0045

Using mesoscopic interfacial models and microscopic density functional theory we study fluid ad-sorption at a dry wall decorated with three completely wet stripes of widthLseparated by distancesD1andD2. The stripes interact with the fluid with long-range forces inducing a large finite-sizecontribution to the surface free-energy. We show that this non-extensive free-energy contributionscales with lnLand drives different types of bridging transition corresponding to the merging ofliquid drops adsorbed at neighbouring wetting stripes when the separation between them ismolecu-larlysmall. We determine the surface phase diagram and show that this exhibits two triple points,where isolated drops, double drops and triple drops coexist. For the symmetric case,D1=D2≡D,our results also confirm that the equilbrium droplet configuration always has the symmetry of thesubstrate corresponding to either three isolated drops whenDis large or a single triple drop whenDis small; however, symmetry broken configurations do occur in a metastable part of the phasediagram which lies very close to the equilibrium bridging phase boundary. Implications for phasetransitions on other types of patterned surface are considered.

Parry A, Rascon C, 2019, The Goldstone mode and resonances in the fluid interfacial region, *Nature Physics*, Vol: 15, Pages: 287-292, ISSN: 1745-2473

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.

Romero-Enrique JM, Squarcini A, Parry AO,
et al., 2018, Curvature corrections to the nonlocal interfacial model for short-ranged forces, *Physical Review E*, Vol: 97, ISSN: 1539-3755

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.

Parry AO, Romero-Enrique JM, Squarcini A,
et al., 2018, The non-local interfacial model for short-ranged forces revisited, *Physical Review E*, ISSN: 1539-3755

Yatsyshin P, Parry AO, Rascon C,
et al., 2018, Wetting of a plane with a narrow solvophobic stripe, *Molecular Physics*, Vol: 116, Pages: 1990-1997, ISSN: 0026-8976

We present a numerical study of a simple density functional theory model of fluidadsorption occurring on a planar wall decorated with a narrow deep stripe of aweaker adsorbing (relatively solvophobic) material, where wall-fluid and fluid-fluidintermolecular forces are considered to be dispersive. Both the stripe and outersubstrate exhibit first-order wetting transitions with the wetting temperature ofthe stripe lying above that of the outer material. This geometry leads to a richphase diagram due to the interplay between the pre-wetting transition of the outersubstrate and an unbending transition corresponding to the local evaporation ofliquid near the stripe. Depending on the width of the stripe the line of unbendingtransitions merges with the pre-wetting line inducing a two-dimensional wettingtransition 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 occurseven for the widest stripes considered. This contrasts markedly with the scenariowhere the outer material has the higher wetting temperature, for which the mergingof the unbending and pre-wetting lines only occurs for very narrow stripes.

Rascon C, Pausch J, Parry AO, 2018, First order wedge wetting revisited, *Soft Matter*, Vol: 14, Pages: 2835-2845, ISSN: 1744-683X

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.

Parry AO, Malijevsky A, 2018, Modified Kelvin equations for condensation in narrow and wide grooves, *Physical Review Letters*, Vol: 120, ISSN: 0031-9007

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 θE describing the shape of the meniscus formed at the top of the groove. The dependence of θE on the groove depth D relies, in turn, on whether corner menisci are formed at the bottom of the groove in the low density gaslike phase. While for macroscopically wide grooves these are always present when θ<45° we argue that their formation is inhibited in narrow grooves. This has a number of implications including that the local pinning of the meniscus and location of the condensation transition is different depending on whether the contact angle is greater or less than a universal value θ∗≈31°. Our arguments are supported by detailed microscopic density functional theory calculations that show that the modified Kelvin equation remains highly accurate even when L and D are of the order of tens of molecular diameters.

Parry AO, malijevsky A, Pospisil M, 2017, Scaling behavior of thin films on chemically heterogeneous walls, *Physical Review E*, Vol: 96, ISSN: 1539-3755

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 hmand 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 hm≈L1/2 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.

malijevsky A, Parry AO, Pospisil M, 2017, Edge contact angle and modified Kelvin equation for condensation in open pores, *Physical Review E*, Vol: 96, ISSN: 1539-3755

We consider capillary condensation transitions occurring in open slits of width L and finite height Himmersed 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 pcc(L;H) at which condensation occurs and show that the two menisci are characterized by an edge contact angle θe that is always larger than the equilibrium contact angle θ, only equal to it in the limit of macroscopic H. For walls that are completely wet (θ=0) the edge contact angle depends only on the aspect ratio of the capillary and is well described by θe≈√πL/2H for large H. Similar results apply for condensation in cylindrical pores of finite length. We test these predictions against numerical results obtained using a microscopic density-functional model where the presence of an edge contact angle characterizing the shape of the menisci is clearly visible from the density profiles. Below the wetting temperature Tw we find very good agreement for slit pores of widths of just a few tens of molecular diameters, while above Tw the modified Kelvin equation only becomes accurate for much larger systems.

Yatsyshin P, Parry AO, Rascón C,
et al., 2017, Classical density functional study of wetting transitions on nanopatterned surfaces., *Journal of Physics: Condensed Matter*, Vol: 29, ISSN: 0953-8984

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.

Rascón C, Parry AO, Aarts DGAL, 2016, Geometry induced capillary emptying, *Proceedings of the National Academy of Sciences of USA*, Vol: 113, Pages: 12633-12636, ISSN: 0027-8424

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 microfluidic 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.

Parry AO, Kalliadasis S, Yatsyshin P, 2016, Complete prewetting, *Journal of Physics: Condensed Matter*, Vol: 28, Pages: 1-12, ISSN: 0953-8984

We study continuous interfacial transitions, analagous to two-dimensional complete wetting, associated with the first-order prewetting line, which can occur on steps, patterned walls, grooves and wedges, and which are sensitive to both the range of the intermolecular forces and interfacial fluctuation effects. These transitions compete with wetting, filling and condensation producing very rich phase diagrams even for relatively simple prototypical geometries. Using microscopic classical density functional theory to model systems with realistic Lennard-Jones fluid–fluid and fluid–substrate intermolecular potentials, we compute mean-field fluid density profiles, adsorption isotherms and phase diagrams for a variety of confining geometries.

Parry AO, Malijevsky A, 2016, Crossover scaling of apparent first-order wetting in two dimensional systems with short-ranged forces, *Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, Vol: 93, ISSN: 1063-651X

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 transitionmay be effectively first-order and that surprisingly the surface susceptibility develops a divergence described by an anomalous exponent with value eff11 = 3 2 . We reproduce these results using aninterfacial 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 surfacefree-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 eff11 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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