We consider wetting of a one-dimensional random walk on a half-line $x\ge 0$ in a short-ranged potential located at the origin $x=0$. We demonstrate explicitly how the presence of a quenched chemical disorder affects the pinning-depinning transition point. For small disorders we develop a perturbative technique which enables us to compute explicitly the averaged temperature (energy) of the pinning transition. For strong disorder we compute the transition point both numerically and using the renormalization group approach. Our consideration is based on the following idea: the random potential can be viewed as a periodic potential with the period $n$ in the limit $n\to\infty$. The advantage of our approach stems from the ability to integrate exactly over all spatial degrees of freedoms in the model and to reduce the initial problem to the analysis of eigenvalues and eigenfunctions of some special non-Hermitian random matrix with disorder--dependent diagonal and constant off-diagonal coefficients. We show that even for strong disorder the shift of the averaged pinning point of the random walk in the ensemble of random realizations of substrate disorder is indistinguishable from the pinning point of the system with preaveraged (i.e. annealed) Boltzmann weight.
We present a precise equivalence of the Lifson-Poland-Scheraga model with wetting models. Making use of a representation of the former model in terms of random matrices, we obtain, in the limit of weak disorder, a mean--field approximation, that shows a change of the critical behavior due to disorder.
It is established that roughness and chemistry play a crucial role in the wetting properties of a substrate. Yet, few studies have analyzed systematically the effect of the non-uniformity in the distribution of texture and surface tension of substrates on its wetting properties. In this work we investigate this issue theoretically and numerically. We propose a continuous model that takes into account the total energy required to create interfaces of a droplet in two possible wetting states: Cassie-Baxter(CB) with air pockets trapped underneath the droplet; and the other characterized by the ho…
The wetting transition is studied in the McCoy-Wu Ising model in which the random bonds are perfectly correlated in the direction parallel to the walls . The model is solved numerically on finite size lattices up to $200 \times 200^2$. It is shown that the wetting transition is first-order. For a fixed surface field, the distribution of wetting transition temperature is obtained from $1000$ samples. The results show that the deviation of the wetting transition temperature does not decreases as the lattice size increases. It is shown that for a fixed surface field the wetting transition tempera…
The wetting transition of the Blume-Capel model is studied by a finite-size scaling analysis of $L \times M$ lattices where competing boundary fields $\pm H_1$ act on the first row or last row of the $L$ rows in the strip, respectively. We show that using the appropriate anisotropic version of finite size scaling, critical wetting in $d=2$ is equivalent to a "bulk" critical phenomenon with exponents $α=-1$, $β=0$, and $γ=3$. These concepts are also verified for the Ising model. For the Blume-Capel model it is found that the field strength $H_{1c} (T)$ where critical wetting occurs goes to zero…
An ultralow-temperature binary mixture of Bose-Einstein condensates adsorbed at an optical wall can undergo a wetting phase transition in which one of the species excludes the other from contact with the wall. Interestingly, while hard-wall boundary conditions entail the wetting transition to be of first order, using Gross-Pitaevskii theory we show that first-order wetting as well as critical wetting can occur when a realistic exponential optical wall potential (evanescent wave) with a finite turn-on length $λ$ is assumed. The relevant surface excess energies are computed in an expansion in $λ…
Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E_c. Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transiti…
A lattice model for active matter is studied numerically, showing that it displays wettings transitions between three distinctive phases when in contact with an impenetrable wall. The particles in the model move persistently, tumbling with a small rate $α$, and interact via exclusion volume only. When increasing the tumbling rates $α$, the system transits from total wetting to partial wetting and unwetting phases. In the first phase, a wetting film covers the wall, with increasing heights when $α$ is reduced. The second phase is characterized by wetting droplets on the wall with a periodic spa…
We consider a nano-patterned planar wall consisting of a periodic array of stripes of width $L$, which are completely wet by liquid (contact angle $θ=0$), separated by regions of width $D$ which are completely dry (contact angle $θ=π)$. Using microscopic Density Functional Theory we show that in the presence of long-ranged dispersion forces, the wall-gas interface undergoes a first-order wetting transition, at bulk coexistence, as the separation $D$ is reduced to a value $D_w\propto\ln L$, induced by the bridging between neighboring liquid droplets. Associated with this is a line of pre-wettin…
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 $2-α_s = \infty$) of the surface free energy excess at infinite-order wetting as well as the precise …
Four on-lattice and six off-lattice models for active matter are studied numerically, showing that in contact with a wall, they display universal wetting transitions between three distinctive phases. The particles, which interact via exclusion volume only, move persistently and, depending on the model, change their direction either via tumble processes or rotational diffusion. When increasing the turning rate $ν_T$, the systems transit from total wetting, to partial wetting and dewetted phases. In the first phase, a wetting film covers the wall, with increasing heights while decreasing $ν_T$. …
Critical wetting transition for short-range forces in three dimensions ($d=3$) is reinvestigated by means of Monte Carlo simulation. Using anisotropic finite size scaling approach, as well as approaches that do not rely on finite size scaling, we show that the critical wetting transition shows clear deviation from mean-field behaviour. We estimate that the effective critical exponent $ν_{\|}^{\textrm{eff}}=1.76\pm 0.08$ for $J/kT=0.35$ and $ν_{\|}^{\textrm{eff}}=1.85\pm 0.07$ for $J/kT=0.25$. These values are in accord with predictions of Parry {\it et al.} [Phys. Rev. Lett. {\bf 100}, 136105 …
Using fundamental-measure density functional theory we investigate entropic wetting in an asymmetric binary mixture of hard spheres with positive non-additivity. We consider a general planar hard wall, where preferential adsorption is induced by a difference in closest approach of the different species and the wall. Close to bulk fluid-fluid coexistence the phase rich in the minority component adsorbs either through a series of first-order layering transitions, where an increasing number of liquid layers adsorbs sequentially, or via a critical wetting transition, where a thick film grows conti…
Models with a nonequilibrium wetting transition display a transition also in finite systems. This is different from nonequilibrium phase transitions into an absorbing state, where the stationary state is the absorbing one for any value of the control parameter in a finite system. In this paper, we study what kind of transition takes place in finite systems of nonequilibrium wetting models. By solving exactly a microscopic model with three and four sites and performing numerical simulations we show that the phase transition taking place in a finite system is characterized by the average interfa…
We consider two-dimensional ($d=2$) systems with short-ranged microscopic interactions, where interface unbinding (wetting) transitions occur in the limit of vanishing temperature $T$. For $T=0$ the transition is characterized by non-universal critical properties analogous to those established for thermal wetting transitions in $d=3$, albeit with a redefined capillary parameter $\tildeω$. Within a functional renormalization-group treatment of an effective interfacial model, we compute the finite temperature phase diagram, exhibiting a line of interface unbinding transitions, terminating at $T=…
We study the solid-on-solid interface model above a horizontal wall in three dimensional space, with an attractive interaction when the interface is in contact with the wall, at low temperatures. The system presents a sequence of layering transitions, whose levels increase with the temperature, before the complete wetting above a certain value of this quantity.
We study non-equilibrium analogues of surface phase transitions in a minimal model of active particles in contact with a purely repulsive potential barrier that mimics a thin porous membrane. Under conditions of bulk motility-induced phase separation, the interaction strength $\varepsilon_w$ of the barrier controls the affinity of the dense phase for the barrier region. We uncover clear signatures of a wetting phase transition as $\varepsilon_w$ is varied. In common with its equilibrium counterpart, the character of this transition depends on the system dimensionality: a continuous transition …
Clarifying the factors that control the contact angle of a liquid on a solid substrate is a long-standing scientific problem pertinent across physics, chemistry and materials science. Progress has been hampered by the lack of a comprehensive and unified understanding of the physics of wetting and drying phase transitions. Using various theoretical and simulational techniques applied to realistic fluid models, we elucidate how the character of these transitions depends sensitively on both the range of fluid-fluid and substrate-fluid interactions and the temperature. Our calculations uncover pre…
We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay, or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly …
The wetting and filling properties of a fluid adsorbed on a solid grooved substrate are studied by means of a microscopic density functional theory. The grooved substrates are modelled using a solid slab, interacting with the fluid particles via long-range dispersion forces, to which a one-dimensional array of infinitely long rectangular grooves is sculpted. By investigating the effect of the groove periodicity and the width of the grooves and the ridges, a rich variety of different wetting morphologies is found. In particular, we show that for a saturated ambient gas, the adsorbent can occur …
The irreversible growth of magnetic films is studied in three-dimensional confined geometries of size $L\times L\times M$, where $M\gg L$ is the growing direction. Competing surface magnetic fields, applied to opposite corners of the growing system, lead to the observation of a localization-delocalization (weakly rounded) transition of the interface between domains of up and down spins on the planes transverse to the growing direction. This effective transition is the precursor of a true far-from-equilibrium corner wetting transition that takes place in the thermodynamic limit. The phenomenon …
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…
Cross-over between first-order and critical wetting at the liquid-vapour interface of n-alkane/methanol mixtures: tricritical wetting and critical prewetting
Hydrodynamic theory of wetting by active particles
Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）；Yusuf Hamied Department of Chemistry, University of Cambridge（剑桥大学尤素福·哈米德化学系）
The wetting of a charged wedge-like wall by an electrolyte solution is investigated by means of classical density functional theory. As in other studies on wedge wetting, this geometry is considered as the most simple deviation from a planar substrate, and it serves as a first step towards more complex confinements of fluids. By focusing on fluids containing ions and surface charges, features of real systems are covered which are not accessible within the vast majority of previous theoretical studies concentrating on simple fluids in contact with uncharged wedges. In particular, the filling tr…
The wetting properties of solid substrates with macroscopic random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. It is shown that Wenzel prewetting, which has been recently predicted for a rather wide class of roughness profiles derived from Gaussian random processes by a general distortion procedure, should in fact be ubiquitous and prevail under even much milder conditions. The well-known transition occurring at Wenzel's angle is accompanied by a prewetting transition, at which a jump in th…
The global phase diagram of wetting in the two-dimensional (2d) Ising model is obtained through exact calculation of the surface excess free energy. Besides a surface field for inducing wetting, a surface-coupling enhancement is included. The wetting transition is critical (second order) for any finite ratio of surface coupling J_s to bulk coupling J, and turns first order in the limit J_s/J to infinity. However, for J_s/J much larger than 1 the critical region is exponentially small and practically invisible to numerical studies. A distinct pre-asymptotic regime exists in which the transition…
When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied trough Langevin equations or discrete growth models. In the first case, the Kardar-Parisi-Zhang equation, which defines a very robust universality class for nonequilibrium moving interfaces, with a soft-wall potential is considered. While in the second, microscopic models, in the corresponding universality class, with evaporation and deposition of particles in the presence of hard-wall are studied. Equilibrium wetting is related to a…
