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We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature $R_w$ in a confining parabolic geometry. We argue that the exponent $\beta_{\rm osc}$ characterising the scale of the interfacial height $\ell_0 \propto R_w^{\beta_{\rm osc}}$ at osculation, for large $R_w$, falls into two regimes representing fluctuation-dominated and mean-field like behaviour, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and which depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-ranged forces, the exponent is related to the value of the interfacial wandering exponent $\zeta$ by $\beta_{\rm osc}=3\zeta/(4-\zeta)$. In contrast, in the mean-field regime, which has not been previously identified, and which occurs for systems with longer ranged forces (and higher dimensions), the exponent $\beta_{\rm osc}$ takes the same value as the exponent $\beta_s^{\rm co}$ for complete wetting which is determined directly by the intermolecular forces. The prediction $\beta_{\rm osc}=3/7$ in $d=2$ for systems with short-ranged forces (corresponding to $\zeta=1/2$) 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 $\beta_{\rm osc} \approx \beta_s^{\rm co}\approx 0.326$ close to the predicted value $1/3$ appropriate to the mean-field regime for dispersion forces.

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., 7 pages (4 figures) of main text plus 12 pages (2 figures) of supplementary information

We study the adsorption of simple fluids at smoothly structured, completely wet, walls and show that a meniscus osculation transition occurs when the Laplace and geometrical radii of curvature of locally parabolic regions coincide. Macroscopically, the osculation transition is of fractional, $7/2$, order and separates regimes in which the adsorption is microscopic, containing only a thin wetting layer, and mesoscopic, in which a meniscus exists. We develop a scaling theory for the rounding of the transition due to thin wetting layers and derive critical exponent relations that determine how the interfacial height scales with the geometrical radius of curvature. Connection with the general geometric construction proposed by Rasc\'on and Parry is made. Our predictions are supported by a microscopic model density functional theory (DFT) 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 pre-osculation 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.

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., 5 pages, 2 figures, and 2 pages of supplementary material

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 $al2/\ensuremath{\pi}$, 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 $2/\ensuremath{\pi}lal1$, 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 $ag1$, 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.

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 $al2/\ensuremath{\pi}$, 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 $2/\ensuremath{\pi}lal1$, 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 $ag1$, 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 liquidlike 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.

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.

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. Accurately capturing both microscopic and mesoscopic properties of fluid–gas interfaces is a long-standing challenge. Now, a microscopic theory of correlation functions that can be scaled up to explain mesoscopic surface tension phenomena is put forward.

ObjectiveTo compare normothermic (35°C–36°C) versus hypothermic (28°C) cardiopulmonary bypass (CPB) in paediatric patients undergoing open heart surgery to test the hypothesis that normothermic CPB perfusion maintains the functional integrity of major organ systems leading to faster recovery.MethodsTwo single-centre, randomised controlled trials (known as Thermic-1 and Thermic-2, respectively) were carried out to compare the effectiveness and acceptability of normothermic versus hypothermic CPB in children with congenital heart disease undergoing open heart surgery. In both studies, the co-primary clinical outcomes were duration of inotropic support, intubation time and postoperative hospital stay.ResultsIn total, 200 participants were recruited; 59 to the Thermic-1 study and 141 to the Thermic-2 study. 98 patients received normothermic CPB and 102 patients received hypothermic CPB. There were no significant differences between the treatment groups for any of the co-primary outcomes: inotrope duration HR=1.01, 95% CI (0.72 to 1.41); intubation time HR=1.14, 95% CI (0.86 to 1.51); postoperative hospital stay HR=1.06, 95% CI (0.80 to 1.40). Differences favouring normothermia were found in urea nitrogen at 2 days geometric mean ratio (GMR)=0.86 95% CI (0.77 to 0.97); serum creatinine at 3 days GMR=0.89, 95% CI (0.81 to 0.98); urinary albumin at 48 hours GMR=0.32, 95% CI (0.14 to 0.74) and neutrophil gelatinase-associated lipocalin at 4 hours GMR=0.47, 95% CI (0.22 to 1.02), but not at other postoperative time points.ConclusionsNormothermic CPB is as safe and effective as hypothermic CPB and can be routinely adopted as a perfusion strategy in low-risk infants and children undergoing open heart surgery.Trial registration numberISRCTN93129502.

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 $8/\pi$. 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., Comment: 5 pages

We consider a nanopatterned planar wall consisting of a periodic array of stripes of width $L$, which are completely wet by liquid (contact angle $\ensuremath{\theta}=0$), separated by regions of width $D$ which are completely dry (contact angle $\ensuremath{\theta}=\ensuremath{\pi}$). 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 ${D}_{w}\ensuremath{\propto}ln\phantom{\rule{0.16em}{0ex}}L$, 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 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.

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., Comment: 18 pages, 5 figures, 1 table

Using mesoscopic interfacial models and microscopic density functional theory we study fluid adsorption at a dry wall decorated with three completely wet stripes of width $L$ separated by distances $D_1$ and $D_2$. The stripes interact with the fluid with long-range forces inducing a large finite-size contribution to the surface free-energy. We show that this non-extensive free-energy contribution scales with $\ln L$ and drives different types of bridging transition corresponding to the merging of liquid drops adsorbed at neighbouring wetting stripes when the separation between them is molecularly small. 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, $D_1=D_2\equiv D$, our results also confirm that the equilbrium droplet configuration always has the symmetry of the substrate corresponding to either three isolated drops when $D$ is large or a single triple drop when $D$ is small; however, symmetry broken configurations do occur in a metastable part of the phase diagram which lies very close to the equilibrium bridging phase boundary. Implications for phase transitions on other types of patterned surface are considered.

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. We thank Eduardo Colorado for insightful comments. C.R. acknowledges the support of the Spanish Ministerio de Economía y Competitividad under Grant FIS2015 66523 P.

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 sub-strate 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 sub-strate 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 transi-tions merges with the pre-wetting line inducing a 2D 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. We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. through Grants No. EP/L027186, EP/L020564 and EP/K503733 (EPSRC-Imperial College Pathways to Impact-Impact Acceleration Award), by the European Research Council (ERC) through Advanced Grant No. 247031 and FIS2015-66523-P (MINECO/FEDER, UE).

We consider a fluid adsorbed in a wedge made from was 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 was 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. This work was partly funded by the EPSRC UK grant EP/L020564/1, "Multiscale Analysis of Complex Interfacial Phenomena". C.R. also acknowledges the support of the grant FIS2015-66523-P (MINECO/FEDER, UE).

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 $\theta=0$) the transition is continuous and its location is not sensitive to the depth of the groove. However for walls which 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 $\theta_E$ describing the shape of the meniscus formed at the top of the groove. The dependence of $\theta_E$ on the groove depth $D$ relies, in turn, on whether corner menisci are formed at the bottom of the groove in the low density gas-like phase. While for macroscopically wide grooves these are always present when $\theta

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 ${h}_{m}\ensuremath{\approx}{L}^{1/2}$ 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.

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

Hybrid procedures performed by cardiac surgeons and interventional cardiologists are becoming increasingly preferred for the treatment of adult patients with complex congenital heart disease (CHD). We report 3 cases of adult patients previously operated for CHD and recently treated with a hybrid approach in our institution. Case 1: A 76 year old woman with permanent atrial fibrillation, lung disease, chronic kidney disease, microcytic anemia and type II diabetes mellitus, previously operated for ASD closure and pulmonary valvotomy, presented with severe pulmonary regurgitation and advanced right ventricular failure. In order to minimize the surgical risk, a hybrid approach was used: an extensive right ventricular outflow tract (RVOT) plication was followed by implantation of an Edwards Sapien XT prosthesis in the RVOT through the right ventricular apex, without cardiopulmonary bypass. Case 2: A 64 year old man with previous atrial septum excision and pericardial baffle for partial anomalous pulmonary venous drainage with intact interatrial septum, presented with worsening dyspnoea, right ventricular failure and pulmonary hypertension caused by baffle stenosis. His comorbidities included coronary artery disease, atrial flutter and previous left pneumonectomy. After performing a redo longitudinal median sternotomy, a 20 mm stent was implanted in the baffle with access through the superior vena cava. Case 3: A 50 year old man, with previous atrioventricular septal defect repair, followed by mitral valve replacement with a mechanical prosthesis, subsequently developed a paravalvular leak with severe mitral regurgitation and severe left ventricular dysfunction. He underwent a transapical paravalvular leak device closure with two Amplatzer Vascular Plugs. The treatment strategy choice for the management of adult patients with CHD often represents a challenge for cardiac surgeons and cardiologists due to complex anatomy, wide range of clinical presentations and a high risk profile. In our opinion, hybrid surgery is a safe and promising therapeutic modality that increases the available treatment options for this patient population. A multidisciplinary and patient-tailored approach is crucial in these complex clinical scenarios.

IntroductionPatients with congenital heart disease often need repeated operations throughout life to replace the pulmonary valve. Valve replacement with ‘injectable’ self-expanding valves (which is performed ‘off pump’ without the use of cardiopulmonary bypass, CPB) may result in quicker recovery and lower risk of major complications than valve replacement with conventional valves (which is performed ‘on pump’ with the use of CPB).Methods and analysisWe are conducting a multicentre, single-blind randomised controlled trial in patients with congenital heart disease and aged between 12 and 80 years. We will randomise participants in a 1:1 ratio to receive either ‘off pump’ injectable pulmonary valve replacement or ‘on pump’ conventional pulmonary valve replacement. The primary outcome will be the difference between the groups with respect to post-surgery blood loss (as measured by chest drain volume) in the first 24 hours. Secondary outcomes will include in-hospital outcomes (intensive care unit stay, inotropic/vasodilator support, chest drain volume in the first 12 hours post-surgery, time of readiness for extubation, blood products used in the first 24 hours post-surgery, time of fitness for discharge, valve and heart function 6 months post-surgery (assessed using cardiovascular magnetic resonance and ECHOCARDIOGRAPHY) and health-related quality of life 6 weeks and 6 months post-surgery.Ethics and disseminationThis trial has been approved by the South West Exeter Research Ethics Committee. Findings will be shared with participating hospitals and disseminated to the academic community through peer reviewed publications and presentation at national and international meetings. Patients will be informed of the results through patient organisations and newsletters to participants.Trial registration numberISRCTN23538073

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. PY is grateful to Dr Miguel A Durán-Olivencia from the Chemical Engineering Department of Imperial College London for numerous stimulating discussions. We acknowledge financial support from the Engineering and Physical Sciences Research Council of the UK through Grants No. EP/L027186 and EP/L020564 and by the European Research Council through Advanced Grant No. 247031. CR also acknowledges the support of the Spanish Ministerio de Economía y Competitividad under grant FIS2015-66523-P.

We have obtained the complete finite-size structure of energy-density correlation functions at all temperatures defined for two-dimensional Ising models on cylindrical lattices, extending the original results of Hecht. This reveals novel structure in terms of winding numbers and confirms predictions from conformal invariance theory to leading order.

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 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 H\"ofling 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., Comment: 20 pages, 9 figures (submitted to J. Phys: Condens. Matter)

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.

We study the influence of wetting films on (density–density) correlations for a fluid in a slit-like geometry near capillary condensation. We show that, for systems with short-ranged forces, the interaction between the wetting films strongly enhances the amplitude of the exponential decay of correlations and, unlike the interfacial roughness, is independent of a high-momentum cut-off. The correlation function shows scaling behaviour near condensation arising from the equality of two characteristic length scales: the parallel correlation length (associated with the complete wetting films) and a length scale related to the non-local interaction between the wetting films on either side of the slit. We introduce a dimensionless amplitude ratio associated with the decay of correlations which allows us to distinguish between local and non-local effective Hamiltonian theories. Only the latter is fully consistent with microscopic density functional descriptions of correlation functions. The influence of long-rang...

We use a model Density Functional, based on the White-Bear version of Fundamental Measure theory, to test recent predictions, due to Evans and co-workers, that capillary condensation in a capped capillary-slit is a continuous interfacial critical phenomenon related to the complete wetting transition. Using a model with a square-well intermolecular fluid–fluid attraction we first determine accurately the location of the first-order capillary evaporation transition in an infinite (open) hard-wall capillary slit. Extending the density functional model to allow for a two-dimensional order-parameter profile, we then study the adsorption as the chemical potential is reduced to capillary evaporation but now in a capillary-slit that is capped at one end. The equilibrium density profiles obtained show that, sufficiently close to the phase boundary, a meniscus separating liquid-like and vapour-like phases forms near the capped end, and that as capillary evaporation is approached, continuously unbinds from the cappe...

Tricuspid atresia and common truncus arteriosus are rare forms of congenital heart disease; the coexistence of both anomalies is therefore an extremely uncommon event. Without treatment, early mortality is the natural course so diagnostic and therapeutic management must be performed without delay. We report a case of a newborn with a postnatal diagnosis of coexistent tricuspid atresia and common arterial trunk in whom successful palliation was performed using a staged surgical approach.

A long-standing problem in condensed-matter physics concerns the nature of the critical wetting transition in three-dimensional systems with short-ranged forces. The controversy focused originally on the discrepancy between predictions of strongly non-universal critical effects, based on renormalization group analysis of an interfacial Hamiltonian, and Monte Carlo studies of wetting in the 3D Ising model, which are instead broadly consistent with mean-field expectations. This gulf between theory and simulation was widened further by subsequent refinements of the interfacial model which appeared to show that fluctuations should necessarily drive the transition first-order. This prediction is in qualitative disagreement with the simulation studies and would radically alter the anticipated structure of the global surface phase diagram.

Isothermal–isobaric NPT and Gibbs ensemble Monte Carlo (GEMC) computer simulations of N = 1500 and N = 3000 hard cut spheres of aspect ratio L/D = 0.1, respectively, are carried out in order to investigate the effects of confinement on the isotropic (I)–nematic (N) phase transition. We first consider the free system, and confirm the stabilisation of isotropic (I), nematic (N) and columnar (Col) states. We examine in detail the I–N transition and find coexistence densities of ρI*=0.355 and ρN*=0.368. A slab geometry is then considered for two types of walls: a hard wall, which excludes the particles entirely, and an ‘adsorbent’ wall which excludes the centre of mass of the particles. The adsorbent wall is found to favour planar (edge-on) alignment, which results in the formation of a first layer of adsorbed molecules, which then acts as a rough hard wall for subsequent particles, and promotes disordered states. Using Gibbs ensemble simulations we determine the capillary phase diagram of the system, and the adsorption as a function of pore width. The capillary phase diagram obtained from Gibbs ensemble simulations corresponds to one with a first-order capillary isotropisation transition, with an associated capillary critical point for a wall separation of ∼3D. The hard walls are seen to promote homeotropic (face-on) alignment of the cut spheres, and promote the stabilisation of the nematic phase. In this case the capillary phase diagram obtained from the GEMC simulations exhibits a first-order capillary nematisation transition, and a capillary critical point for a wall separation of ∼4D.

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.

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 $\sigma_\text{eff}(q)$., Comment: 5 pages,1 figure + Supplementary Material (3 pages, 1 figure)

We present numerical studies of first-order and continuous filling transitions, in wedges of arbitrary opening angle $\psi$, using a microscopic fundamental measure density functional model with short-ranged fluid-fluid forces and long-ranged wall-fluid forces. In this system the wetting transition characteristic of the planar wall-fluid interface is always first-order regardless of the strength of the wall-fluid potential $\varepsilon_w$. In the wedge geometry however the order of the filling transition depends not only on $\varepsilon_w$ but also the opening angle $\psi$. In particular we show that even if the wetting transition is strongly first-order the filling transition is continuous for sufficient acute wedges. We show further that the change in the order of the transition occurs via a tricritical point as opposed to a critical-end point. These results extend previous effective Hamiltonian predictions which were limited only to shallow wedges.

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.

Fluids adsorbed at micro-patterned and geometrically structured substrates can exhibit novel phase transitions and interfacial fluctuation effects distinct from those characteristic of wetting at planar, homogeneous walls. We review recent theoretical progress in this area paying particular attention to filling transitions pertinent to fluid adsorption near wedges, which have highlighted a deep connection between geometrical and contact angles. We show that filling transitions are not only characterized by large scale interfacial fluctuations leading to universal critical singularities but also reveal hidden symmetries with short-ranged critical wetting transitions and properties of dimensional reduction. We propose a non-local interfacial model which fulfills all these properties and throws light on long-standing problems regarding the order of the 3D short-range critical wetting transition.

A comprehensive theory of interfacial fluctuation effects occurring at two-dimensional wedge (corner) filling transitions in pure (thermal disorder) and impure (random bond disorder) systems is presented. Scaling theory and the explicit results of transfer matrix and replica trick studies of interfacial Hamiltonian models reveal that, for almost all examples of intermolecular forces, the critical behaviour at filling is fluctuation dominated, characterized by universal critical exponents and scaling functions that depend only on the wandering exponent ζ. Within this filling-fluctuation (FFL) regime, the critical behaviour of the midpoint interfacial height, probability distribution function, local compressibility and wedge free energy are identical to corresponding quantities predicted for the strong-fluctuation (SFL) regime for critical wetting transitions at planar walls. In particular the wedge free energy is related to the SFL regime point tension, which is calculated for systems with random bond disorder using the replica trick. The connection with the SFL regime for all these quantities can be expressed precisely in terms of special wedge covariance relations, which complement standard scaling theory and restrict the allowed values of the critical exponents for both FFL filling and SFL critical wetting. The predictions for the values of the exponents in the SFL regime recover earlier results based on random walk arguments. The covariance of the wedge free energy leads to a new, general relation for the SFL regime point tension, which derives the conjectured Indekeu-Robledo critical exponent relation and also explains the origin of the logarithmic singularity for pure systems known from exact Ising studies due to Abraham and co-workers. Wedge covariance is also used to predict the numerical values of critical exponents and position dependence of universal one-point functions for pure systems.

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 thetacap(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 thetacap>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 thetacap(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. A. O. P. wishes to thank the support of the EPSRC UK for Grant No. EP/J009636/1. A. M. thanks the Czech Science Foundation for Grant No. 13-09914S. C. R. acknowledges support from Grants No. FIS2010-22047-C05 and No. MODELICO.

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 $\sigma(q)$., Comment: 11 pages, 1 figure

We consider fluids adsorbed at generalised wedges described by shape functions xγ in one direction (x), and translationally invariant in the other. For the limiting cases γ=0 and ∞, the substrate corresponds to a planar wall and a capillary slit, respectively. In this way, we show how wetting-like adsorption isotherms become capillary-like as γ is increased from 0 to ∞. The mechanism for the cross-over to condensation is shown to involve several intermediate regimes corresponding to novel examples of adsorption isotherms.

We review recent advances concerning the nature of fluctuation effects occurring at continuous filling transitions pertinent to fluid adsorption in wedge geometries. Unlike continuous (critical) wetting transitions for planar interfaces which are an extremely rare experimental phenomena, continuous filling transitions should be easily observable in the laboratory since they can occur even if the underlying wetting transition is first-order. We argue that interfacial fluctuation effects at filling transitions are extremely strong and lead to a remarkable universal divergence of the interfacial roughness ξ ⊥ ∼( T F − T ) −1/4 on approaching the transition temperature T F , valid for all types of intermolecular forces. The results of renormalisation group and transfer matrix calculations of a novel interfacial model yielding a complete classification of the critical exponents for all dimensions and ranges of forces are given.

We study a continuum interfacial Hamiltonian model of fluid adsorption in a (1+1)-dimensional wedge geometry, which is known to exhibit a filling transition when the contact angle θπ = α, with α the wedge angle. We extend the transfer matrix analysis of the model to calculate the interfacial height probability distribution function P(l;x), for arbitrary positions x along the wedge. The asymptotics of this function reveal a fluctuation-induced disorder point (non-thermodynamic singularity) that occurs prior to filling when θπ = 2α, where there is a change of length scales determining the decay of P(l;x).

We consider filling or wedge-wetting transitions occurring in a (1 + 1)-dimensional wedge geometry with both thermal and random-bond disorder using effective interfacial Hamiltonian models. For ordered systems the problem may be solved using transfer-matrix methods for quite arbitrary choices of interfacial binding potential and gives a complete classification of the possible critical behaviours. For random bonds the transition is studied for short-ranged forces using the replica trick and the wedge-wetting critical exponents are identified. Our results establish a remarkable relation between the mid-point height probability distribution PF(l0) at filling transitions and the appropriately defined height distribution function Pπ(l;θπ) at planar wetting transitions. We observe that provided the wetting specific heat component αs = 0, then, in the scaling limit, PF(l0) = Pπ(l;θπ-α) where θπ is the contact angle and α is the tilt angle of the wedge. This relation completely determines the allowed values of the filling critical exponents in the fluctuation-dominated regimes. Conjectures regarding interfacial fluctuation effects in finite-size two-dimensional systems are also made.

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 characterised by hyperuniversal scaling behaviour. 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., Comment: To be published in Physical Review E (14 pages, 4 figures)

Ideally one would like to analyse the properties of inhomogeneous fluids/Ising-like magnets (e.g., wetting of a fluid phase at a wall or confinement in thin film geometries) using a microscopic Hamiltonian H[m], with m(r) the local order-parameter (number density/magnetization). For many problems, however, this is too difficult and traditionally one has to introduce effective interfacial models based on a collective coordinate l(y) measuring the position of the fluid interface. We review progress made in unifying these approaches using multi-field effective Hamiltonian theory which is a powerful new investigative tool. We emphasize: (i) a systematic method for recovering order-parameter correlations G(r1,r2) from collective coordinate theory, (ii) the role of coupled fluctuations at three dimensional wetting transitions leading to (a) an observable increment to the value of the wetting parameter at complete wetting and (b) an inflation of the mean field regime for local surface response functions at critical wetting, (iii) the derivation of new identities relating moments of G at different positions in the fluid, and (iv) the development of a linear response theory of fluid adsorption at a non-planar wall which predicts roughness-induced first-order wetting transitions. The relevance of these predictions for long-standing controversies surrounding Ising model simulation studies is discussed.

In order to satisfy exact sum-rule requirements for correlation function structure at complete wetting, a two-field Hamiltonian , modelling the coupling of order-parameter fluctuations near the wall and unbinding interface, has been introduced. The model is characterized by a stiffness matrix, , whose bare (unrenormalized) elements are related to the mean-field free energy. We extend previous renormalization group studies to include the position dependence of the matrix elements and derive an elegant operator relationship which shows that the flow of the cross-coupling term parallels that of the free energy. This establishes the validity of a stiffness matrix - free-energy relation in the presence of fluctuation effects at the marginal dimension d = 3 for systems with short-ranged forces. We further show that an analogous relation exists for systems with long-ranged molecular interactions.

Critical effects at complete and critical wetting in three dimensions are studied using a coupled effective Hamiltonian H[s(y),\ell]. The model is constructed via a novel variational principle which ensures that the choice of collective coordinate s(y) near the wall is optimal. We highlight the importance of a new wetting parameter \Omega(T) which has a strong influence on critical properties and allows the status of long-standing Monte-Carlo simulation controversies to be re-examined., Comment: 4 pages RevTex, 2 encapsulated postscript figures, to appear in Europhys. Lett

We present numerical studies of complete, first-order and critical wedge filling transitions, at a right angle corner, using a microscopic fundamental measure density functional theory. We consider systems with short-ranged, cut-off Lennard-Jones, fluid-fluid forces and two types of wall-fluid potential: a purely repulsive hard wall and also a long-ranged potential with three different strengths. For each of these systems we first determine the wetting properties occurring at a planar wall, including any wetting transition and the dependence of the contact angle on temperature. The hard wall corner is completely filled by vapour on approaching bulk coexistence and the numerical results for the growth of the meniscus thickness are in excellent agreement with effective Hamiltonian predictions for the critical exponents and amplitudes, at leading and next-to-leading order. In the presence of the attractive wall-fluid interaction, the corresponding planar wall-fluid interface exhibits a first-order wetting transition for each of the interaction strengths considered. In the right angle wedge geometry the two strongest interactions produce first-order filling transitions while for the weakest interaction strength, for which wetting and filling occur closest to the bulk critical point, the filling transition is second-order. For this continuous transition the critical exponent describing the divergence of the meniscus thickness is found to be in good agreement with effective Hamiltonian predictions.

We present results of an extensive molecular dynamics simulation of the structure and fluctuations of a liquid-gas interface, close to its triple point, in a system with cutoff Lennard-Jones interactions. The equilibrium density profile, averaged and (shape dependent) constrained intrinsic density profiles together with the fluctuations of the interfacial shape are extracted using an intrinsic sampling method. The correlation between fluctuations in the interfacial shape and in the intrinsic density show that the latter is not due to rigid translations of some underlying profile, as is most commonly assumed. Instead, over the whole range of wavelengths from the system size down to the molecular diameter, we see wave-vector dependent behavior in good agreement with a nonlocal interfacial Hamiltonian theory specifying the shape dependence of the intrinsic profiles. © 2013 American Physical Society., A. O. P. acknowledges the support of the bank of Santander and UCIIIM for a Chair of Excellence. E. M. F., E. C., P. T., and C. R. acknowledge support from grants MODELICO (Comunidad de Madrid) and FIS2010-22047-C05 (Ministerio de Educación y Ciencia).

We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group (RG) calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying $2-\alpha_s = \infty$) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with $\beta_s = -1$) of the wetting layer thickness are not modified as long as $\omega < 2$, with $\omega$ the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with $\nu_{\perp} = 1/2$). In contrast, the non-universal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate and strong fluctuation regimes., Comment: 2 figures