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 $2/π<a<1$, depending on the value of the contact angle the condensation may be of type I or of type II, in which the menisci overspill into the reservoir and there is no pinning. For short capillaries, with $a>1$, condensation is always of type II. In all regimes, capillary condensation is completely suppressed for sufficiently large contact angles. 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.
It is usually expected that surface tension driven flow dominates at small scales. Evaporation from the meniscus of ethanol/methanol confined in a capillary induces Marangoni convection at the meniscus which has been investigated by previous researchers. However, Marangoni convection is unexpectedly absent at an evaporating water meniscus confined inside a small micro-channel which is reported in this work. The velocity near the water meniscus is studied using confocal micro-PIV. The water meniscus is formed at the end of a micro-channel filled with water keeping the meniscus exposed to atmosp…
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 $a<2/π$,…
A liquid surface touching a solid usually deforms in a near-wall meniscus region. In this work, we replace part of the free surface with a soft polymer and examine the shape of this elasto-capillary meniscus, result of the interplay between elasticity, capillarity and hydrostatic pressure. We focus particularly on the extraction threshold for the soft object. Indeed, we demonstrate both experimentally and theoretically the existence of a limit height of liquid tenable before breakdown of the compound, and extraction of the object. Such an extraction force is known since Laplace and Gay-Lussac,…
The dynamics of saturated vapor between two intersecting walls is examined. It is shown that, if the angle $ϕ$ between the walls is sufficiently small, the vapor becomes unstable, and spontaneous condensation occurs in the corner, similar to the so-called capillary condensation of vapor into a porous medium. As a result, an ever-growing liquid meniscus develops near the corner. The diffuse-interface model and the lubrication approximation are used to demonstrate that the meniscus grows if and only if $ϕ+2θ<π$, where $θ$ is the contact angle corresponding to the fluid/solid combination under co…
Molecular dynamics simulations are used to study the capillary adhesion from a nonvolatile liquid meniscus between a spherical tip and a flat substrate. The atomic structure of the tip, the tip radius, the contact angles of the liquid on the two surfaces, and the volume of the liquid bridge are varied. The capillary force between the tip and substrate is calculated as a function of their separation h. The force agrees with continuum predictions for h down to ~ 5 to 10nm. At smaller h, the force tends to be less attractive than predicted and has strong oscillations. This oscillatory component o…
We report a new first-order phase transition preceding capillary condensation and corresponding to the discontinuous formation of a curved liquid meniscus. Using a mean-field microscopic approach based on the density functional theory we compute the complete phase diagram of a prototypical two-dimensional system exhibiting capillary condensation, namely that of a fluid with long-ranged dispersion intermolecular forces which is spatially confined by a substrate forming a semi-infinite rectangular pore exerting long-ranged dispersion forces on the fluid. In the T-mu plane the phase line of the n…
We consider theoretically liquid rise against gravity in capillaries with height-dependent cross-section. For a conical capillary made from a hydrophobic surface and dipped in a liquid reservoir, the equilibrium liquid height depends on the cone opening angle $α$, the Young-Dupré contact angle $θ$, the cone radius at the reservoir's level $R_0$ and the capillary length $κ^{-1}$. As $α$ is increased from zero, the meniscus' position changes continuously until, when $α$ attains a critical value, the meniscus jumps to the bottom of the capillary. For hydrophilic surfaces the meniscus jumps to the…
We study numerically the hydrodynamics of dip coating from a suspension and report a mechanism for colloidal assembly and pattern formation on smooth and uniform substrates. Below a critical withdrawal speed of the substrate, capillary forces required to deform the meniscus prevent colloidal particles from entering the coating film. Capillary forces are overcome by hydrodynamic drag only after a minimum number of particles organize in a close-packed formation within the meniscus. Once within the film, the formed assembly moves at nearly the withdrawal speed and rapidly separates from the next …
We calculate the meniscus location in tapered capillaries under the influence of pressure difference and dielectrophoretic forces with and without gravity. We find that the meniscus location can be a discontinuous function of the pressure difference or the applied voltage and that the meniscus can ``jump'' to one end or another of the capillary. Phase diagrams are given as a function of the pressure and voltage, depending on the geometrical parameters of the system. We further consider a revision of the dielectric rise under dielectrophoretic force in wedge capillaries and in the case of elect…
We study the meniscus on the outside of a small spherical particle with radius $R$ at a liquid-vapor interface. The liquid is confined in a cylindrical container with a finite radius $L$ and has a contact angle $π/2$ at the container surface. The center of the particle is placed at various heights along the central axis of the container. By varying $L$, we are able to systematically study the crossover of the meniscus from nanometer to macroscopic scales. The meniscus rise or depression on the particle is found to grow as $\ln (2L/R)$ when $R\ll L\ll κ^{-1}$ with $κ^{-1}$ being the capillary l…
We use mesoscale simulations to study the depinning of a receding contact line on a superhydrophobic surface patterned by a regular array of posts. In order that the simulations are feasible, we introduce a novel geometry where a column of liquid dewets a capillary bounded by a superhydrophobic plane which faces a smooth hydrophilic wall of variable contact angle. We present results for the dependence of the depinning angle on the shape and spacing of the posts, and discuss the form of the meniscus at depinning. We find, in agreement with [17], that the local post concentration is a primary fa…
We show that condensation in a capped capillary slit is a continuous interfacial critical phenomenon, related intimately to several other surface phase transitions. In three dimensions (3d), the adsorption and desorption branches correspond to the unbinding of the meniscus from the cap and opening, respectively and are equivalent to 2d-like complete-wetting transitions. For dispersion forces, the singularities on the two branches are distinct, owing to the different interplay of geometry and intermolecular forces. In 2d we establish precise connection, or covariance, with 2d critical-wetting a…
We report the observation of a transition in the dynamical properties of water nano-menicus which dramatically change when probed at different time scales. Using a AFM mode that we name Force Feedback Microscopy, we observe this change in the simultaneous measurements, at different frequencies, of the stiffness G'(N/m), the dissipative coefficient G''(kg/sec) together with the static force. At low frequency we observe a negative stiffness as expected for capillary forces. As the measuring time approaches the microsecond, the dynamic response exhibits a transition toward a very large positive s…
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 $θ^{\rm cap}(L)$ which depends on the difference between the Hamaker constants. If the bottom wall has a weaker wall-fluid attraction than the side walls, then $θ^{\rm cap}>…
Flowing menisci: coupled dynamics and liquid exchange with soap films
Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；INPHYNI（物理化学与界面研究所）；Université de Rennes（雷恩大学）；IPR (Institut de Physique de Rennes)（雷恩物理研究所）；Institut Universitaire de France (IUF)（法兰西学院）
We account for the presence of surface charges towards describing variations in the dynamic contact angle of an advancing liquid-gas meniscus. Starting from the thin-film based formalism, we present closed-form analytical expressions relating the dynamic contact-angle with the capillary number (essentially normalized contact-line speed) and other interfacial parameters. Specifically, our analysis presents, within the realm of hydrodynamic paradigm, a connection between the micro- and macro-scale physics at the vicinity of the contact-line region, taking the combined confluence of viscous and c…
A molecular-dynamics type simulation method, which is suitable for investigating the dewetting dynamics of thin and viscous liquid layers, is discussed. The efficiency of the method is exemplified by studying a two-parameter depinning-like model defined on inhomogeneous solid surfaces. The morphology and the statistical properties of the contact line is mapped in the relevant parameter space, and as a result critical behavior in the vicinity of the depinning transition is revealed. The model allows for the tearing of the layer, which leads to a new propagation regime resulting in non-trivial c…
The influence of solidification on the spreading of liquids is addressed in the situation of an advancing liquid wedge on a cold substrate at $T_p < T_f$, of infinite thermal conductivity, where $T_f$ is the melting temperature. We propose a model derived from lubrication theory of contact-line dynamics, where an equilibrium between capillary pressure and viscous stress is at play, adapted here for the geometry of a quadruple line where the vapour, liquid, solidified liquid and basal substrate meet. The Stefan thermal problem is solved in an intermediate region between molecular and mesoscopic…
We investigate a possibility to regularize the hydrodynamic contact line singularity in the configuration of partial wetting (liquid wedge on a solid substrate) via evaporation-condensation, when an inert gas is present in the atmosphere above the liquid. The no-slip condition is imposed at the solid-liquid interface and the system is assumed to be isothermal. The mass exchange dynamics is controlled by vapor diffusion in the inert gas and interfacial kinetic resistance. The coupling between the liquid meniscus curvature and mass exchange is provided by the Kelvin effect. The atmosphere is sat…
We simulate dense assemblies of frictional spherical grains in steady shear flow under controlled normal stress $P$ in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci, assumed isolated (pendular regime), and to attractive forces. The system behavior depends on two dimensionless control parameters: inertial number $I$ and reduced pressure $P^*=aP/(πΓ)$, comparing confining forces $\sim a^2P$ to meniscus tensile strength $F_0=πΓa$, for grains of diameter $a$ joined by menisci with surface tension $Γ$. We pay special attention to the quasi-static li…
Porous asphalt (PA) is an open-graded porous material with a porosity of 20%, allowing fast drainage of rain and improving driving and acoustic conditions. However, the high porosity leads to significant contact with water resulting in a shorter life expectancy. To improve the durability and performance of PA, the distribution of water and its residence time have to be understood which entails capturing diverse multiphase phenomena. For these reasons, a numerical study is performed to analyze in detail the fluid transport mechanisms at play in PA, towards estimating the liquid distribution ins…
