Adsorption on a periodically corrugated substrate

Mean field analysis of the effective interfacial Hamiltonian shows that with increasing temperature the adsorption on a periodically corrugated substrate can proceed in two steps: first, there is the filling transition in which the depressions of the substrate become partially or completely filled; then there is the wetting transition at which the substrate as a whole becomes covered with a macroscopically thick wetting layer. The actual order and location of both transitions are related to the wetting properties of the corresponding planar substrate and to the form of corrugation. Certain morphological properties of the liquid-vapor interface in the case of a saw-like corrugated substrate are discussed analyticallyComment: 20 pages, 9 Postscript figure

Filling transition for a wedge

We study the formation and the shape of a liquid meniscus in a wedge with opening angle $2\phi$ which is exposed to a vapor phase. By applying a suitable effective interface model, at liquid-vapor coexistence and at a temperature $T_{\phi}$ we find a filling transition at which the height of the meniscus becomes macroscopically large while the planar walls of the wedge far away from its center remain nonwet up to the wetting transition occurring at $T_w>T_{\phi}$. Depending on the fluid and the substrate potential the filling transition can be either continuous or discontinuous. In the latter case it is accompanied by a prefilling line extending into the vapor phase of the bulk phase diagram and describing a transition from a small to a large, but finite, meniscus height. The filling and the prefilling transitions correspond to nonanalyticities in the surface and line contributions to the free energy of the fluid, respectively.Comment: 48 pages (RevTex), 14 figures (ps), submitted to PR

The problem of uniqueness in the reduced description of adsorption on the wedge-shaped substrate

In the reduced one-dimensional description of the adsorption on the wedge-shaped substrate the mid-point interface height serves as the order parameter. We point at the ambiguity which appears in the transfer-matrix approach to this problem. We also propose how to avoid this problem by introducing the appropriate order parameter.Comment: 7 pages, 4 Postscript figures, uses psfrag.sty; double reference remove

Edge wetting of an Ising three-dimensional system

The effect of edge on wetting and layering transitions of a three-dimensional spin-1/2 Ising model is investigated, in the presence of longitudinal and surface magnetic fields, using mean field (MF) theory and Monte Carlo (MC) simulations. For T=0, the ground state phase diagram shows that there exist only three allowed transitions, namely: surface and bulk transition, surface transition and bulk transition. However, there exist a surface intra-layering temperature $T_{L}^{s}$, above which the surface and the intra-layering surface transitions occur. While the bulk layering and intra-layering transitions appear above an other finite temperature $T_{L}^{b} (\ge T_{L}^{s})$. These surface and bulk intra-layering transitions are not seen in the perfect surfaces case. Numerical values of $T_{L}^{s}$ and $T_{L}^{b}$, computed by Monte Carlo method are found to be smaller than those obtained using mean field theory. However, the results predicted by the two methods become similar, and are exactly those given by the ground state phase diagram, for very low temperatures. On the other hand, the behavior of the local magnetizations as a function of the external magnetic field, shows that the transitions are of the first order type. $T_{L}^{s}$ and $T_{L}^{b}$ decrease when increasing the system size and/or the surface magnetic field. In particular, $T_{L}^{b}$ reaches the wetting temperature $T_{w}$ for sufficiently large system sizes.Comment: 11 Pages latex, 12 Figures P

Interfacial fluctuations near the critical filling transition

We propose a method to describe the short-distance behavior of an interface fluctuating in the presence of the wedge-shaped substrate near the critical filling transition. Two different length scales determined by the average height of the interface at the wedge center can be identified. On one length scale the one-dimensional approximation of Parry et al. \cite{Parry} which allows to find the interfacial critical exponents is extracted from the full description. On the other scale the short-distance fluctuations are analyzed by the mean-field theory.Comment: 13 pages, 3 figure

Phase diagram for morphological transitions of wetting films on chemically structured substrates

Using an interface displacement model we calculate the shapes of thin liquidlike films adsorbed on flat substrates containing a chemical stripe. We determine the entire phase diagram of morphological phase transitions in these films as function of temperature, undersaturation, and stripe widthComment: 15 pages, RevTeX, 7 Figure

Geometry dominated fluid adsorption on sculptured substrates

Experimental methods allow the shape and chemical composition of solid surfaces to be controlled at a mesoscopic level. Exposing such structured substrates to a gas close to coexistence with its liquid can produce quite distinct adsorption characteristics compared to that occuring for planar systems, which may well play an important role in developing technologies such as super-repellent surfaces or micro-fluidics. Recent studies have concentrated on adsorption of liquids at rough and heterogeneous substrates and the characterisation of nanoscopic liquid films. However, the fundamental effect of geometry has hardly been addressed. Here we show that varying the shape of the substrate can exert a profound influence on the adsorption isotherms allowing us to smoothly connect wetting and capillary condensation through a number of novel and distinct examples of fluid interfacial phenomena. This opens the possibility of tailoring the adsorption properties of solid substrates by sculpturing their surface shape.Comment: 6 pages, 4 figure

Universality for 2D Wedge Wetting

We study 2D wedge wetting using a continuum interfacial Hamiltonian model which is solved by transfer-matrix methods. For arbitrary binding potentials, we are able to exactly calculate the wedge free-energy and interface height distribution function and, thus, can completely classify all types of critical behaviour. We show that critical filling is characterized by strongly universal fluctuation dominated critical exponents, whilst complete filling is determined by the geometry rather than fluctuation effects. Related phenomena for interface depinning from defect lines in the bulk are also considered.Comment: 4 pages, 1 figur

Critical adsorption near edges

Symmetry breaking surface fields give rise to nontrivial and long-ranged order parameter profiles for critical systems such as fluids, alloys or magnets confined to wedges. We discuss the properties of the corresponding universal scaling functions of the order parameter profile and the two-point correlation function and determine the critical exponents eta_parallel and eta_perpendicular for the so-called normal transition.Comment: 22 pages, 5 figures, accepted for publication in PR

Mediation and the Best Interests of the Child from the Child Law Perspective

What is the best interests of the child in family mediation and is mediation in the best interests of the child? In this article, I use child law and the United Nations Convention on the Rights of the Child combined with mediation theory to discuss these questions. Both mediation and the best interests of the child are open for multiple interpretations. Using facilitative and evaluative mediation theory and the legal concept ‘the best interests of the child’, I explore and compare the understandings of these concepts as they apply to family mediation. This includes a discussion of the advantages and disadvantages of facilitative as well as evaluative mediation orientations in terms of protecting the best interests of the child. Finnish court-connected family mediation is a combination of both mediation orientations, and the mediator is obliged to secure the best interests of the child. From a theoretical point of view, this seems to be a challenging combination.Peer reviewe