Avoided critical behavior in dynamically forced wetting

A solid object can be coated by a nonwetting liquid since a receding contact line cannot exceed a critical speed. In this Letter we study the dynamical wetting transition at which a liquid film gets deposited by withdrawing a vertical plate out of a liquid reservoir. It has recently been predicted that this wetting transition is critical with diverging time scales and coincides with the disappearance of stationary menisci. We demonstrate experimentally and theoretically that the transition is due to the formation of a solitary wave, well below the critical point. As a consequence, relaxation times remain finite at threshold. The structure of the liquid deposited on the plate involves a capillary ridge that does not trivially match the Landau-Levich film.     

Mode selection of Lamb waves for the evaluation of solid plates with liquid loading

This paper studies the mode selection of Lamb waves for evaluating solid plates with liquid loading. For this purpose, the Lamb wave selected should have the features such as zero normal displacement components at the plate surface in contact with liquid, small dispersion, and maximum group velocity. It is found that when the phase velocity of Lamb wave is equal to the longitudinal wave velocity of the plate material, its normal displacement at the plate surface is always zero. Through the numerical analyses, the specific S₂ Lamb wave that has zero normal displacement component at the plate surface, small dispersion and maximum group velocity compared with the other Lamb waves has been found. With respect to the specific S₂ Lamb wave, some experimental examinations have been carried out. It is found that the liquid loading on the plate surface has less influence on the specific S₂ Lamb wave signal but it can effectively eliminate the other signals. Moreover, the specific S₂ Lamb wave selected exhibits the capability of detecting multiple defects in the solid plate with the liquid loading. It can be concluded that the specific S₂ Lamb wave selected is suitable for the evaluation of solid plates with liquid loading.     

Dynamic modelling of the deformed contact line under partial wetting conditions: Quasi-static approach

We study numerically the motion of contact lines in the context of the “Wilhelmy plate" experiment: a vertical solid plate is withdrawn at constant velocity from a bath of liquid. We apply the contact line dissipation quasi-static model to the relaxation of an initially periodically deformed contact line. The obtained numerical data are compared to the experimental results [1] showing a good agreement.     

Hydrodynamic theory of forced dewetting

A prototypical problem in the study of wetting phenomena is that of a solid plunging into or being withdrawn from a liquid bath. In the latter, dewetting case, a critical speed exists above which a three-phase contact line is no longer sustainable and the solid can no longer remain dry. Instead, a liquid film is being deposited on the solid. Demonstrating this transition from a dry to a wetted solid to be of hydrodynamic origin, we provide the first theoretical explanation of a classical prediction due to Derjaguin and Levi: instability occurs when the outer, static meniscus approaches the shape corresponding to a perfectly wetting fluid. Our analysis investigates the conditions under which the highly curved contact line region can be matched to the static profile far away from it.     

Contact line moving on a solid

The moving contact line problem can be summarized as follows: consider the triple line where a solid, a liquid and its vapor meet. This contact line may be the perimeter of a liquid droplet standing on a solid. Suppose now that, because of gravity for instance, the droplet and so its perimeter slides on the solid surface. The boundary conditions for viscous fluids impose that the flow velocity on an immobile solid is zero. If one assumes that the liquid/vapor surface is a material surface, i.e. that it is convected by the fluid, the contact line cannot move with respect to the solid, contrary to what is observed. Over the years many suggestions have been made to solve this problem. I show that solutions relying on the introduction of microscopic length scales are not consistent within the general framework of continuum mechanics. To get consistent solutions, one needs to introduce evaporation/condensation near the moving line, in agreement with experimental findings.     

Morphological stability analysis of partial wetting

We develop a macroscopic static theory of the morphological stability of partial wetting. The system we studied consist of a smooth horizontal solid surface and some non-volatile liquid on it. A necessary condition for the stable equilibrium of such systems is known as the Young condition on the contact angle made at the contact line where the free surface of liquid meets the solid surface. But this condition is local and is not sufficient for the stability. We present a formulation for studying the stability of systems which satisfy the Young condition. Then we apply this to several morphologies of wetting. We find that there are at least two fundamental morphologies that we call a hole and a ridge, which are thermodynamically unstable against certain infinitesimal deformations of the contact lines. The hole type instability has also been found recently [D. J. Srolovitz and S. A. Safran, J. Appl. Phyys., 60 (1986), 1]. We also derived a reduced expression for the wetting energy as a functional of the contact line positions under the assumption of almost flat free surface of the liquid. This serves us to understand the characteristic length scale which appears in the ridge type instability. Besides these instabilities there is another category of morphological instability in which the system becomes unstable against an infinitesimal deformation of the free surface of liquid. We show this by an illustrating example in which the instability is described as the so-called tangent bifureation in nonlinear systems.     

Phase field modeling of hysteresis in sessile drops

We propose a novel approach to describe wetting of plane solid surfaces by liquid drops. A two-dimensional nonconserved phase field variable is employed to distinguish between wetted and nonwetted regions on the surface. The imbalance in the Young's force provides for the exchange of relative stability of the two phases. The three-phase contact line tension arises from the gradient energy and contact angle hysteresis from the kinetic coefficient. Using this theory, we discuss contact angle hysteresis on chemically heterogeneous surfaces. We show significant departure from the classical Cassie theory, which is attributed to defect pinning of the continuous triple line.     

A mesh-dependent model for applying dynamic contact angles to VOF simulations

Typical VOF algorithms rely on an implicit slip that scales with mesh refinement, to allow contact lines to move along no-slip boundaries. As a result, solutions of contact line phenomena vary continuously with mesh spacing; this paper presents examples of that variation. A mesh-dependent dynamic contact angle model is then presented, that is based on fundamental hydrodynamics and serves as a more appropriate boundary condition at a moving contact line. This new boundary condition eliminates the stress singularity at the contact line; the resulting problem is thus well-posed and yields solutions that converge with mesh refinement. Numerical results are presented of a solid plate withdrawing from a fluid pool, and of spontaneous droplet spread at small capillary and Reynolds numbers.     

Spatial variations of the mean and statistical quantities in the thermal boundary layers of turbulent convection

We have studied the dynamics of the contact line of a viscous liquid on a solid substrate with macroscopic random defects. We have first characterized the friction force f₀ at microscopic scale for a substrate without defects; f₀ is found to be a strongly nonlinear function of the velocity U of the contact line. In presence of macroscopic defects, we find that the applied force F(U) is simply shifted with respect to f₀(U) by a constant: we do not observe any critical behavior at the depinning transition. The only observable effect of the substrate disorder is to increase the hysteresis. We have also performed realistic numerical simulation of the motion of the contact line. Using the same values of the parameters as in the experiment, we find that the experimental data is qualitatively well reproduced. In light of experimental and numerical results, we discuss the possibility of measuring a true critical behavior.Received: 6 October 2003, Published online: 19 February 2004PACS: 46.65. + g Random phenomena and media - 64.60.Ht Dynamic critical phenomena - 68.08.Bc Wetting     

Positronium decay and formation in paraffin wax from polarized and unpolarized positrons

Summary Ps formation and decay in heterogeneousn-alkane samples (paraffin waxes) have been studied both in the solid and in the liquid phase; then, in the solid phase, the positron's residual degree of polarization was measured at the instant of Ps formation. Differently from what is already known in homogeneousn-alkane samples, Ps shows, many degrees below the melting point, a mean lifetime longer than that typical of the liquid phase; furthermore, the mean lifetime's values pertaining to the transition between solid and liquid do not show a sharp variation across the melting temperature but gradually decrease over a range of temperatures of several degrees. Positronium decay in static magnetic fields indicates that o-Ps magnetic quenching in liquid phase is regular, and corresponds to a contact density value α=|ψ(0)|²/|ψ(0)|_vac ²=0.79±0.07; instead, in the solid phase, o-Ps magnetic quenching shows anomalous behaviour for fields weaker than 7kG. Positrons' residual polarization measurements do not reveal the presence of depolarization effects during the whole slowing-down process until Ps is formed.     

Pinning-depinning of the contact line on nanorough surfaces

We study the pinning-depinning phenomenon of a contact line on a solid surface decorated by a random array of nanometric structures. For this purpose, we have investigated the contact angle hysteresis behaviour of six different wetting and non-wetting fluids with surface tensions varying from 25 to 72mN m^-1. For low values of the areal density of defects φ_d, the hysteresis H increases linearly with φ_d indicating that “individual” defects pin the contact line. Then, from a given value of φ_d, the hysteresis H becomes to decrease with increasing φ_d, indicating a new kind of collective depinning. These two regimes were observed for all fluids used. In both cases, our experimental results are compared with the theoretical predictions for contact angle hysteresis induced by single or multiple topographical defects. We ascribe the decrease of H to the formation of cavities along the wetting front.     

Response of a large plate-liquid system to a moving pressure step. Transient and stationary aspects

An unbounded system of a plate in contact with a liquid is presented. The coupling equations are set, accounting for the compressibility of the liquid and the Mindlin-Reissner plate theory. A numerical solution, founded on an explicit scheme, is validated. The resolution is applied to a strip loaded by a unit pressure step spreading uniformly along the strip axis. The simulation for every speed of loading ranging among the characteristic velocities of the coupled system points out how a steady state response can emerge from the transient one. The steady state solution is theoretically established, which agrees well with the numerical prevision. The form of the response is different for every region limited by the characteristic velocities. For a load speed greater than the speed of acoustic waves in the liquid, the pressure propagates along a straight line and the existence of a steady state response is confirmed. On the contrary, for a lower load speed, no pressure front is present and the response always keeps its transient character. The solution shows that displacements obtained in the transient part increase incessantly with time and become quickly larger than in the stationary part. Concerning the stresses, the study reveals that the amplitudes are of the same order in the two parts. The solution can be extended easily to the case of a pressure spreading with a cylindrical symmetry, which can correspond to the real conditions of detonation loading.     

Line tension and the shape of nanodroplets

Various factors are discussed which might influence the equilibrium contact angle of nanodroplets placed on a solid substrate. Special emphasis is put on the possible role of the dependence of the solid-liquid interface tension g^SL \gamma^{{{\rm SL}}}_{} on the pressure in the liquid, which in nanodrops considerably exceeds the saturation pressure. We show that certain published data regarding that dependence are meaningless because these have been deduced based on an inconsistent data analysis.     

The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: A review

A sessile drop is an isolated drop which has been deposited on a solid substrate where the wetted area is limited by the three-phase contact line and characterized by contact angle, contact radius and drop height. Although, wetting has been studied using contact angles of drops on solids for more than 200 years, the question remains unanswered: Is wetting of a rough and chemically heterogeneous surface controlled by the interactions within the solid/liquid contact area beneath the droplet or only at the three-phase contact line? After the publications of Pease in 1945, Extrand in 1997, 2003 and Gao and McCarthy in 2007 and 2009, it was proposed that advancing, receding contact angles, and contact angle hysteresis of rough and chemically heterogeneous surfaces are determined by interactions of the liquid and the solid at the three-phase contact line alone and the interfacial area within the contact perimeter is irrelevant. As a consequence of this statement, the well-known Wenzel (1934) and Cassie (1945) equations which were derived using the contact area approach are proposed to be invalid and should be abandoned. A hot debate started in the field of surface science after 2007, between the three-phase contact line and interfacial contact area approach defenders. This paper presents a review of the published articles on contact angles and summarizes the views of the both sides. After presenting a brief history of the contact angles and their measurement methods, we discussed the basic contact angle theory and applications of contact angles on the characterization of flat, rough and micropatterned superhydrophobic surfaces. The weak and strong sides of both three-phase contact line and contact area approaches were discussed in detail and some practical conclusions were drawn.     

Simulation and Experiments on the Capillary Force between a Circular Disk and a Parallel Substrate

The capillary force of a liquid bridge with a pinned contact line between a small disk and a parallel plate is investigated by simulation and experiments. The numerical minimization simulation method is utilized to calculate the capillary force. The results show excellent agreement with the Young-Laplace equation method. An experimental setup is built to measure the capillary force. The experimental results indicate that the simulation results agree well with the measured forces at large separation distances, while some deviation may occur due to the transition from the advancing contact angle to the receding one at small distances. It is also found that the measured rupture distance is slightly larger than the simulation value due to the effect of the viscous interaction inside the liquid bridge.     

Dynamics and hysteresis of the contact line between liquid hydrogen and cesium substrates

We have measured both the hysteresis and the dynamics of the edge of a liquid hydrogen meniscus on several solid cesium substrates. We find that the dynamics of the contact line is thermally activated. For all substrates, we find that the activation energy is of the order of the hysteresis. We show that the pinning of the contact line on mesoscopic defects of the Cs substrate is likely to control both the hysteresis and the dynamics of the contact line at low velocity, close to the depinning threshold. Such a mechanism could be relevant also for simple room-temperature systems.     

On Young's (1805) equation and Finn's (2006) ‘counterexample’

In 1805, Thomas Young considered the balance of forces acting on the contact line formed at the intersection of a liquid-fluid interface with a solid surface and introduced a macroscopic concept of “contact angle”. From Young's reasoning it follows that in equilibrium the contact angle is a material property of the liquid/fluid/solid system independent of a particular configuration. Two centuries later, Robert Finn considered a model problem which seems to suggest that there is a fundamental flaw in Young's force diagram and the reasoning behind it. In the present note, we show that the apparent paradox in Finn's model problem disappears once Young's original concepts are applied in a correct way.     

Improvement of the magnetic properties of Nd9.5Fe81Zr3B6.5 nanocomposite magnets by semi-melt spinning

Nd_9.5Fe₈₁Zr₃B_6.5 ribbons are prepared by single roller melt-spinning technique at 1150 °C which is in the solid and liquid coexistence zone. The phase evolution and magnetic properties were studied by X-ray diffraction, differential scanning calorimetry, transmission electron microscopy observations, and magnetization measurements. The experimental results show that in comparison to the ribbons quenching at higher temperature, the thickness of ribbons prepared at 1150 °C are insensitive to the wheel speed and an uniform nanoscale structure with fine grains can be obtained directly from the semi-melt and the exchange coupling interaction between the grains was enhanced for the nanocomposite permanent alloy which can contributed to excellent magnetic properties.     

The vicinity of an equilibrium three-phase contact line using density-functional theory: density profiles normal to the fluid interface

The paper by Nold et al. [Phys. Fluids 26 (7), 072001 (2014)] examined density profiles and the micro-scale structure of an equilibrium three-phase (liquid–vapour–solid) contact line in the immediate vicinity of the wall using elements from the statistical mechanics of classical fluids, namely density-functional theory. The present research note, building on the above work, further contributes to our understanding of the nanoscale structure of a contact line by quantifying the strong dependence of the liquid–vapour density profile on the normal distance to the interface, when compared to the dependence on the vertical distance to the substrate. A recent study by Benet et al. [J. Phys. Chem. C 118 (38), 22079 (2014)] has shown that this could explain the emergence of a film-height-dependent surface tension close to the wall, with implications for the Frumkin–Derjaguin theory.     

Capillary pressure and contact line force on a soft solid

The surface free energy, or surface tension, of a liquid interface gives rise to a pressure jump when the interface is curved. Here we show that a similar capillary pressure arises at the interface of soft solids. We present experimental evidence that immersion of a thin elastomeric wire into a liquid induces a substantial elastic compression due to the solid capillary pressure at the bottom. We quantitatively determine the effective surface tension from the elastic displacement field and find a value comparable to the liquid-vapor surface tension. Most importantly, these results also reveal the way the liquid pulls on the solid close to the contact line: the capillary force is not oriented along the liquid-air interface, nor perpendicularly to the solid surface, as previously hypothesized, but towards the interior of the liquid.