arXiv subjects

Alexandr Malijevský

Publications and source records attributed to Alexandr Malijevský.

At least 19 recordsLinked to original sources

arXiv2026

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

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

cond-mat.soft↗

arXiv2026

Uniform distributions in nonuniform systems: Wall potentials generating constant density profiles in classical density functional theory

We study the inverse problem of classical density functional theory for inhomogeneous fluids: finding the wall potential that produces a constant equilibrium density profile, i.e., a perfectly flat density distribution in the accessible region adjacent to a substrate. Within Rosenfeld's fundamental measure theory, we solve this problem for a one-component fluid in planar, spherical, and cylindrical geometries, considering both a hard-sphere fluid and a fluid with an additional truncated Lennard-Jones attraction treated at the mean-field level. Explicit analytical expressions are obtained for planar walls, while spherical walls also admit an analytical treatment in a more cumbersome form. The cylindrical case is treated numerically. The construction provides an explicit microscopic realization of structure-cancelling wall fields, related to flat-profile conditions that occur under special matching conditions in interfacial theories of wetting and drying. The theory also yields a compact collection of formulae for weighted densities and one-body direct correlation functions in the three fundamental geometries, providing useful reference expressions for density-functional implementations. The resulting analytic wall potentials are validated in independent density functional calculations, which confirm that the prescribed flat profiles are recovered within numerical accuracy.

cond-mat.soft↗

arXiv2025

Complete Wetting and Drying at Sinusoidal Walls

We investigate complete wetting and drying at sinusoidally corrugated solid walls, focusing on the effects of wall geometry and interaction range. Two distinct interaction models are considered: one incorporating only short-ranged (SR) forces (applied to drying), and another including long-ranged (LR) van der Waals interactions (applied to wetting). The SR model is analyzed within the framework of nonlocal Hamiltonian theory by Parry et al., while the LR model is treated using a sharp-kink approximation. In both cases, we derive scaling relations that describe the dependence of the adsorbed layer's width and morphology on the wall's geometric parameters as the system approaches two-phase coexistence. We identify distinct scaling regimes determined by the degree of wall corrugation and highlight the contrasting effects of SR and LR interactions. Theoretical predictions are corroborated by numerical results from classical density functional theory.

cond-mat.soft↗

arXiv2025

Capillary condensation between parallel walls of unequal length

We present a macroscopic theory of capillary condensation in slits formed by parallel walls of unequal length. Using the concept of an edge contact angle, we identify four distinct condensation states and derive Kelvin-like relations for their onset. The resulting phase diagrams, expressed in terms of wall geometry and contact angle, reveal two central organizing features: a geometric separatrix that divides distinct condensation regimes, and the wedge-filling threshold at $θ=π/4$, which separates a rich four-state scenario from a simpler two-state one. These results demonstrate how geometry dictates the onset and suppression of condensation in confined systems.

cond-mat.soft↗

arXiv2025

Three types of condensation in open wedges

Condensation in linear wedges formed by semi-infinite walls is a well-established critical phenomenon characterized by the continuous growth of an adsorbed liquid layer as bulk two-phase coexistence is approached. In this study, we investigate condensation in finite-length wedges open at both ends, demonstrating that the process becomes first-order. The open boundaries and finite geometry induce a remarkably rich phase behavior of the confined fluid, exhibiting three distinct types of condensation, reentrant phenomena, and continuous higher-order transitions between condensation states. Through a detailed macroscopic analysis, we derive the conditions for each type of condensation, classify the global phase diagrams, and explore asymptotic behavior in specific limiting cases. The asymptotic predictions are confirmed by a detailed comparison with the numerical solutions of the governing equations.

cond-mat.soft↗

arXiv2024

Asymptotic properties of bridging transitions in sinusoidally-shaped slits

We study bridging transitions that emerge between two sinusoidally-shaped walls of amplitude $A$, wavenumber $k$, and mean separation $L$. The focus is on weakly corrugated walls to examine the properties of bridging transitions in the limit when the walls become flat. The reduction of walls roughness can be achieved in two ways which we show differ qualitatively: a) By decreasing $k$, (i.e., by increasing the system wavelength), which induces a continuous phenomenon associated with the growth of bridging films concentrated near the system necks, the thickness of with the thickness of these films diverging as $\sim k^{-2/3}$ in the limit of $k\to0$. Simultaneously, the location of the transition approaches that of capillary condensation in an infinite planar slit of an appropriate width as $\sim k^{2/3}$; b) in contrast, the limit of vanishing walls roughness by reducing $A$ cannot be considered in this context, as there exists a minimal value $A_{\rm min}(k,L)$ of the amplitude below which bridging transition does not occur. On the other hand, for amplitudes $A>A_{\rm min}(k,L)$, the bridging transition always precedes global condensation in the system. These predictions, including the scaling property $A_{\rm min}\propto kL^2$, are verified numerically using density functional theory.

cond-mat.soft↗

arXiv2024

Capillary condensation between non-parallel walls

We study the condensation of fluids confined by a pair of non-parallel plates of finite height $H$. We show that such a system experiences two types of condensation, termed single- and double-pinning, which can be characterized by one (single-pinning) or two (double-pinning) edge contact angles describing the shape of menisci pinned at the system edges. For both types of capillary condensation we formulate the Kelvin-like equation and determine the conditions under which the given type of condensation occurs. We construct the global phase diagram revealing a reentrant phenomenon pertinent to the change of the capillary condensation type upon varying the inclination of the walls. Asymptotic properties of the system are discussed and a link with related phase phenomena in different systems is made. Finally, we show that the change from a single- to a double-pinned state is a continuous transition, the character of which depends on the wetting properties of the walls.

cond-mat.mes-hall↗

arXiv2024

Kelvin equation for bridging transitions

We study bridging transitions between a pair of non-planar surfaces. We show that the transition can be described using a generalized Kelvin equation by mapping the system to a slit of finite length. The proposed equation is applied to analyze the asymptotic behaviour of the growth of the bridging film, which occurs when the confining walls are gradually flattened. This phenomenon is characterized by a power-law divergence with geometry-dependent critical exponents that we determine for a wide class of walls' geometries. In particular, for a linear-wedge model, a covariance law revealing a relation between a geometric and Young's contact angle is presented. These predictions are shown to be fully in line with the numerical results obtained from a microscopic (classical) density functional theory.

cond-mat.mes-hall↗

arXiv2022

Phase behaviour of fluids in undulated nanopores

The geometry of walls forming a narrow pore may qualitatively affect the phase behaviour of the confined fluid. Specifically, the nature of condensation in nanopores formed of sinusoidally-shaped walls (with amplitude $A$ and period $P$) is governed by the wall mean separation $L$ as follows. For $L>L_t$, where $L_t$ increases with $A$, the pores exhibit standard capillary condensation similar to planar slits. In contrast, for $L<L_t$, the condensation occurs in two steps, such that the fluid first condenses locally via bridging transition connecting adjacent crests of the walls, before it condenses globally. For the marginal value of $L=L_t$, all the three phases (gas-like, bridge and liquid-like) may coexist. We show that the locations of the phase transitions can be described using geometric arguments leading to modified Kelvin equations. However, for completely wet walls, to which we focus on, the phase boundaries are shifted significantly due to the presence of wetting layers. In order to take this into account, mesoscopic corrections to the macroscopic theory are proposed. The resulting predictions are shown to be in a very good agreement with a density functional theory even for molecularly narrow pores. The limits of stability of the bridge phase, controlled by the pore geometry, is also discussed in some detail.

cond-mat.soft↗

arXiv2021

Capillary Condensation and Depinning Transitions in Open Slits

We study the low temperature phase equilibria of a fluid confined in an open capillary slit formed by two parallel walls separated by a distance $L$ which are in contact with a reservoir of gas. The top wall of the capillary is of finite length $H$ while the bottom wall is considered of macroscopic extent. This system shows rich phase equilibria arising from the competition between two different types of capillary condensation, corner filling and meniscus depinning transitions depending on the value of the aspect ratio $a=L/H$ and divides into three regimes: For long capillaries, with $a<2/π$, the condensation is of type I involving menisci which are pinned at the top edges at the ends of the capillary. For intermediate capillaries, with $2/π 1$, condensation is always of type II. In all regimes, capillary condensation is completely suppressed for sufficiently large contact angles which is determined explicitly. For long and intermediate capillaries, we show that there is an additional continuous phase transition in the condensed liquid-like phase, associated with the depinning of each meniscus as they round the upper open edges of the slit. Meniscus depinning is third-order for complete wetting and second-order for partial wetting. Detailed scaling theories are developed for these transitions and phase boundaries which connect with the theories of wedge (corner) filling and wetting encompassing interfacial fluctuation effects and the direct influence of intermolecular forces.

cond-mat.soft↗

arXiv2021

Edge Contact Angle, Capillary Condensation, and Meniscus Depinning

We study the phase equilibria of a fluid confined in an open capillary slit formed when a wall of finite length $H$ is brought a distance $L$ away from a second macroscopic surface. This system shows rich phase equilibria arising from the competition between two different types of capillary condensation, corner filling and meniscus depinning transitions depending on the value of the aspect ratio $a=L/H$. For long capillaries, with $a<2/π$, the condensation is of type I involving menisci which are pinned at the top edges at the ends of the capillary characterized by an edge contact angle. For intermediate capillaries, with $2/π 1$, condensation is always of type II. In all regimes, capillary condensation is completely suppressed for sufficiently large contact angles. We show that there is an additional continuous phase transition in the condensed liquid-like phase, associated with the depinning of each meniscus as they round the upper open edges of the slit. Finite-size scaling predictions are developed for these transitions and phase boundaries which connect with the fluctuation theories of wetting and filling transitions. We test several of our predictions using a fully microscopic Density Functional Theory which allows us to study the two types of capillary condensation and its suppression at the molecular level.

cond-mat.soft↗

arXiv2021

Breaking Cassie's law for condensation in a nano-patterned slit

We study the phase transitions of a fluid confined in a capillary slit made from two adjacent walls each of which are a periodic composite of stripes of two different materials. For wide slits the capillary condensation occurs at a pressure which is described accurately by a combination of the Kelvin equation and the Cassie law for an averaged contact angle. However, for narrow slits the condensation occurs in two steps involving an intermediate bridging phase, with the corresponding pressures described by two new Kelvin equations. These are characterised by different contact angles due to interfacial pinning, with one larger and one smaller than the Cassie angle. We determine the triple point and predict two types of dispersion force induced Derjaguin-like corrections due to mesoscopic volume reduction and the singular free-energy contribution from nano-droplets and bubbles. We test these predictions using a fully microscopic density functional model which confirms their validity even for molecularly narrow slits. Analogous mesoscopic corrections are also predicted for two dimensional systems arising from thermally induced interfacial wandering.

cond-mat.soft↗

arXiv2020

Height of a liquid drop on a wetting stripe

Adsorption of liquid on a planar wall decorated by a hydrophilic stripe of width $L$ is considered. Under the condition, that the wall is only partially wet (or dry) while the stripe tends to be wet completely, a liquid drop is formed above the stripe. The maximum height $\ell_m(δμ)$ of the drop depends on the stripe width $L$ and the chemical potential departure from saturation $δμ$ where it adopts the value $\ell_0=\ell_m(0)$. Assuming a long-range potential of van der Waals type exerted by the stripe, the interfacial Hamiltonian model is used to show that $\ell_0$ is approached linearly with $δμ$ with a slope which scales as $L^2$ over the region satisfying $L\lesssim ξ_\parallel$, where $ξ_\parallel$ is the parallel correlation function pertinent to the stripe. This suggests that near the saturation there exists a universal curve $\ell_m(δμ)$ to which the adsorption isotherms corresponding to different values of $L$ all collapse when appropriately rescaled. Although the series expansion based on the interfacial Hamiltonian model can be formed by considering higher order terms, a more appropriate approximation in the form of a rational function based on scaling arguments is proposed. The approximation is based on exact asymptotic results, namely that $\ell_m\simδμ^{-1/3}$ for $L\to\infty$ and that $\ell_m$ obeys the correct $δμ\to0$ behaviour in line with the results of the interfacial Hamiltonian model. All the predictions are verified by the comparison with a microscopic density functional theory (DFT) and, in particular, the rational function approximation -- even in its simplest form -- is shown to be in a very reasonable agreement with DFT for a broad range of both $δμ$ and $L$.

cond-mat.stat-mech↗

arXiv2020

Filling, depinning, unbinding: Three adsorption regimes for nanocorrugated substrates

We study adsorption at periodically corrugated substrates formed by scoring rectangular grooves into a planar solid wall which interacts with the fluid via long-range (dispersion) forces. The grooves are assumed to be macroscopically long but their depth, width and separations can all be molecularly small. We show that the entire adsorption process can be divided into three parts consisting of (i) \emph{filling} the grooves by a capillary liquid; (ii) \emph{depinning} of the liquid-gas interface from the wall edges; and (iii) \emph{unbinding} of the interface from the top of the wall, which is accompanied by a rapid but continuous flattening of its shape. Using a nonlocal density functional theory and mesoscopic interfacial models all the regimes are discussed in some detail to reveal the complexity of the entire process and subtle aspects that affect its behaviour. In particular, it is shown that the nature of the depinning phenomenon is governed by the width of the wall pillars (separating grooves), whilst the grooves width only controls the location of the depinning first-order transition, if present.

cond-mat.stat-mech↗

arXiv2019

Symmetry-breaking morphological transitions at chemically nanopatterned walls

We study the structure and morphological changes of fluids that are in contact with solid composites formed by alternating and microscopically wide stripes of two different materials. One type of the stripes interacts with the fluid via long-ranged Lennard-Jones-like potential and tends to be completely wet, while the other type is purely repulsive and thus tends to be completely dry. We consider closed systems with a fixed number of particles that allows for stabilization of fluid configurations breaking the lateral symmetry of the wall potential. These include liquid morphologies corresponding to a sessile drop that is formed by a sequence of bridging transitions that connect neighboring wet regions adsorbed at the attractive stripes. We study the character of the transitions depending on the wall composition, stripes width, and system size. Using a (classical) nonlocal density functional theory (DFT), we show that the transitions between different liquid morphologies are typically weakly first-order but become rounded if the wavelength of the system is lower than a certain critical value $L_c$. We also argue that in the thermodynamic limit, i.e., for macroscopically large systems, the wall becomes wet via an infinite sequence of first-order bridging transitions that are, however, getting rapidly weaker and weaker and eventually become indistinguishable from a continuous process as the size of the bridging drop increases. Finally, we construct the global phase diagram and study the density dependence of the contact angle of the bridging drops using DFT density profiles and a simple macroscopic theory.

cond-mat.stat-mech↗

arXiv2019

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

We consider a nano-patterned planar wall consisting of a periodic array of stripes of width $L$, which are completely wet by liquid (contact angle $θ=0$), separated by regions of width $D$ which are completely dry (contact angle $θ=π)$. Using microscopic Density Functional Theory we show that in the presence of long-ranged dispersion forces, the wall-gas interface undergoes a first-order wetting transition, at bulk coexistence, as the separation $D$ is reduced to a value $D_w\propto\ln L$, induced by the bridging between neighboring liquid droplets. Associated with this is a line of pre-wetting transitions occurring off coexistence. By varying the stripe width $L$ we show that the pre-wetting line shows universal scaling behaviour and data collapse. This verifies predictions based on mesoscopic models for the scaling properties associated with finite-size effects at complete wetting including the logarithmic singular contribution to the surface free-energy.

cond-mat.stat-mech↗

arXiv2019

Bridging of liquid drops at chemically structured walls

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.

cond-mat.stat-mech↗

arXiv2019

Geometry-induced interface pinning at completely wet walls

We study complete wetting of solid walls that are patterned by parallel nanogrooves of depth $D$ and width $L$ with a periodicity of $2L$. The wall is formed of a material which interacts with the fluid via a long-range potential and exhibits first-order wetting transition at temperature $T_w$, should the wall is planar. Using a non-local density functional theory we show that at a fixed temperature $T>T_w$ the process of complete wetting depends sensitively on two microscopic length-scales $L_c^+$ and $L_c^-$. If the corrugation parameter $L$ is greater than $L_c^+$, the process is continuous similar to complete wetting on a planar wall. For $L_c^-<L<L_c^+$, the complete wetting exhibits first-order \emph{depinning transition} corresponding to an abrupt unbinding of the liquid-gas interface from the wall. Finally, for $L<L_c^-$ the interface remains pinned at the wall even at bulk liquid-gas coexistence. This implies that nano-modification of substrate surfaces can always change their wetting character from hydrophilic into hydrophobic, in direct contrast to the macroscopic Wenzel law. The resulting surface phase diagram reveals close analogy between the depinning and prewetting transitions including the nature of their critical points.

cond-mat.stat-mech↗