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.     

Precursor films in wetting phenomena

The spontaneous spreading of non-volatile liquid droplets on solid substrates poses a classic problem in the context of wetting phenomena. It is well known that the spreading of a macroscopic droplet is in many cases accompanied by a thin film of macroscopic lateral extent, the so-called precursor film, which emanates from the three-phase contact line region and spreads ahead of the latter with a much higher speed. Such films have been usually associated with liquid-on-solid systems, but in the last decade similar films have been reported to occur in solid-on-solid systems. While the situations in which the thickness of such films is of mesoscopic size are fairly well understood, an intriguing and yet to be fully understood aspect is the spreading of microscopic, i.e. molecularly thin, films. Here we review the available experimental observations of such films in various liquid-on-solid and solid-on-solid systems, as well as the corresponding theoretical models and studies aimed at understanding their formation and spreading dynamics. Recent developments and perspectives for future research are discussed.     

Droplet suction on porous media

We study the forced aspiration of small ( mm) and large ( cm) liquid drops, deposited on prewetted porous membranes, and pumped mechanically with a constant current J. Two kinds of membranes are used where the pores are i) disconnected, cylindrical and calibrated or ii) interconnected “sponge-like”. Whatever the size of the drops and the intensity J of the current, two suction regimes are observed versus time: 1) a “locked” regime, when the drop is pinned, with a dynamic contact angle decreasing from advancing () to finite receding () contact angle; 2) an “unlocked” regime, where the contour line recedes with a constant contact angle closed to . In both regimes, the shape of the drop remains quasistatic, during the suction process, i.e. a spherical cap for small drops and a flat “gravity pancake” for large ones. Received 19 January 2000     

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.     

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where “surface fields” may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given.     

Wetting phase transitions and critical phenomena in condensed matter

Equilibrium wetting phase transitions and critical phenomena are discussed from a phenomenological point of view. The ubiquitous character of the wetting phase transition is illustrated through its occurrence in a variety of condensed matter systems, ranging from classical fluids to superconductors and Bose-Einstein condensates. The intriguing behaviour of the three-phase contact line and its line tension, at wetting, is an example of a fundamental problem in this field on which much progress has been made.     

Switching of banana liquid crystal mesophases under field

Taking advantage of the great number of bent-core or “banana" compounds synthesized and studied in the laboratory, we describe their behaviour under the application of an external electric field. If the field were a static one, we would work within the frame of an equilibrium phase diagram in a (field E, temperature T) space where some phases would be simple dielectrics and others ferroelectric ones with a macroscopic polarization, either spontaneous or induced by the field. In this paper, we deal with the basic responses of “banana” liquid crystals under the application of a low frequency (1 to 100 Hz) AC field. Firstly square-wave voltages allow us to locate the phase boundary between dielectric (at lower field) and ferroelectric phases (higher field) at a given temperature and field threshold. Then we apply slowly varying AC voltages with shapes like triangle or “triple-plateau” to check out the stability of the induced ferroelectric phase versus field removal. Three behaviours are encountered, the unstable one (short lifetime of the high-field ferroelectric phase) where the macroscopic polarization is destroyed and then rebuilt in the opposite direction during each half period and usually called “antiferroelectric”; the stable one (long lifetime) with a polarization that rotates at constant modulus which is labeled as “ferroelectric” and a new one where the macroscopic polarization is proportional to the applied fied, we named this behaviour as “superparaelectric”. Let us stress that these observations apply to the ferroelectric phases of the (E, T) phase diagram not to the zero field (0,T) phases observed in the usual phase characterization experiments except for an eventual spontaneous ferroelectric phase. Received 18 April 2002 and Received in final form 17 January 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: marcerou@crpp.u-bordeaux.fr RID="b" ID="b"URL: http://www.crpp-bordeaux.cnrs.fr     

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.     

“Elastic” fluctuation-induced effects in smectic wetting films

The Li-Kardar field theory approach is generalized to wetting smectic films and the “elastic” fluctuation-induced interaction is obtained between the external flat bounding surface and distorted IA (isotropic liquid-smectic A) interface acting as an “internal” (bulk) boundary of the wetting smectic film under the assumption that the IA interface is essentially “softer” than the surface smectic layer. This field theory approach allows calculating the fluctuation-induced corrections in Hamiltonians of the so-called “correlated” liquids confined by two surfaces, in the case where one of the bounding surfaces is “rough” and with different types of surface smectic layer anchoring. We obtain that in practice, the account of thermal displacements of the smectic layers in a wetting smectic film reduces to the addition of two contributions to the IA interface Hamiltonian. The first, so-called local contribution describes the long-range thermal “elastic” repulsion of the fluctuating IA interface from the flat bounding surface. The second, so-called nonlocal contribution is connected with the occurrence of an “elastic” fluctuation-induced correction to the stiffness of the IA interface. An analytic expression for this correction is obtained.     

平衡接触角对受热液滴在水平壁面上铺展特性的影响

壁面温度是影响壁面润湿性的重要外部条件. 为解决液滴铺展中三相接触线处应力集中问题, 已有研究多采用预置液膜假设, 但无法探究壁面温度对润湿性的影响. 本文针对受热液滴在固体壁面上的铺展过程, 基于润滑理论建立了演化模型, 通过数值模拟, 从平衡接触角角度分析了温度影响壁面润湿性及铺展过程的内部机理. 研究表明: 随温度梯度增大, 液滴所受Marangoni效应增强, 致使液滴向低温区的铺展速率加快; 铺展过程中, 位于高温区的接触线与液滴主体部分间形成一层薄液膜, 重力与热毛细力先后主导该区域的铺展; 当液-固或气-液界面张力对温度的敏感度高于另两个界面时, 低温区方向的平衡接触角不断增大, 使壁面润湿性恶化, 导致液滴铺展减慢; 而当气-固界面张力对温度的敏感度高于其他两个界面时, 低温区方向上的平衡接触角将减小, 由此改善壁面润湿性, 加快液滴铺展; 在温度影响壁面润湿性和液滴铺展过程中, 平衡接触角起关键作用.     

On the universality of string theory

String theory is accused by some of its critics to be a purely abstract mathematical discipline, having lost the contact to the simple yet deeply rooted questions which physics provided until the beginning of this century. We argue that, in contrary, there are indications that string theory might be linked to a fundamental principle of a quantum computational character. In addition, the nature of this principle can possibly provide some new insight into the question of universality of string theory (string theory as the “theory of everything”).     

Super Universality of the Quantum Hall Effect and the?“Large N Picture” of the ? Angle

It is shown that the “massless chiral edge excitations” are an integral and universal aspect of the low energy dynamics of the ϑ vacuum that has historically gone unnoticed. Within the SU(M+N)/S(U(M)×U(N)) non-linear sigma model we introduce an effective theory of “edge excitations” that fundamentally explains the quantum Hall effect. In sharp contrast to the common beliefs in the field our results indicate that this macroscopic quantization phenomenon is, in fact, a super universal strong coupling feature of the ϑ angle with the replica limit M=N=0 only playing a role of secondary importance. To demonstrate super universality we revisit the large N expansion of the CP ^N−1 model. We obtain, for the first time, explicit scaling results for the quantum Hall effect including quantum criticality of the quantum Hall plateau transition. Consequently a scaling diagram is obtained describing the cross-over between the weak coupling “instanton phase” and the strong coupling “quantum Hall phase” of the large N theory. Our results are in accordance with the “instanton picture” of the ϑ angle but fundamentally invalidate all the ideas, expectations and conjectures that are based on the historical “large N picture.”     

Thermodynamic crisis of boiling

The procedure of calculation of the dynamics of rapid near-wall vaporization near a metallic heater is considered. A physical model of explosive boiling-up on bubbles of fluctuation origin is used. The model is limited to regimes when the motion of bubbles can be ignored and convective flows do not have enough time to develop. It is assumed that the dry spot under a bubble thermally insulates the heater wall. The heat removal is provided by the vicinity of the wetting line (WL). An analytical calculation has become possible on the basis of the well-known exact solution to the problem of the temperature field near the wetting line. Generalization of this solution has led to two new problems. These are the problem of allowance for the difference of the dynamic wetting angle from the right angle and that of allowance for thermocapillary flows. A numerical comparison of the results of calculation of the dry area with the use of different methods of allowing for the “tightness” effect in the dynamics of bubble generation and growth has been made. The evolution of bubbles from their generation to growth limited by the heat supply has been investigated. It has been found that the transition stage in the development of bubbles from Rayleigh to thermal ones is of considerable importance in the processes of explosive boiling-up. The dynamics of change in the dry area and wetting line length prior to the stage of bubble merging into a vapor film has been calculated. A condition of passage of the heat flux through a maximum is found. The applicability of the idea of thermodynamic crisis to calculations of miniature devices is justified. The problem of constructing a model to calculate the interphase surface shape near the wetting line under a developed thermocapillary flow and considerable reactive forces of the vapor flow is formulated. The model is in good agreement with the results of experiments on pulsed superheating of liquids at a rate higher than 1 K/μs.     

Wetting of He on rough cesium substrates

We discuss the behaviour of ⁴He meniscus on various disordered Cs substrates. We have first studied the dynamics of the contact line on Cs substrates evaporated at low temperature. The activated motion of the line is consistent with a substrate disorder of mesoscopic length scale. We have performed further studies of the contact line behaviour on substrates with roughness of macroscopic length scale. Close to the wetting transition, we find that a film invades the substrate leading to marked changes in the value of the contact angle.     

Effect of contact line curvature on solid-fluid surface tensions without line tension

For sessile droplets partially wetting a solid surface, it has been observed experimentally that the value of the contact angle depends on the contact line curvature and this dependence has been attributed to tension in the contact line. But previous analyses of these observations have neglected adsorption at the solid-liquid interface and its effect on the surface tension of this interface. We show that if this adsorption is taken into account the relation between the contact angle and contact line curvature is completely accounted for without introducing line tension. Further, from the observed relation between the contact angle and contact line curvature, the adsorption at the solid-liquid interface can be determined, as can the surface tensions of the solid-liquid and solid-vapor interfaces.     

Asymmetric wetting hysteresis on chemical defects

Using the Wilhelmy plate technique, the role of chemical defects in hysteretic wetting behavior was investigated. The wetting and dewetting work differ significantly, depending on the defect energy (i.e., high or low energy with respect to the matrix). For one, or an array of high-energy defects, advancing measurements departed from equilibrium theory, while the receding data were in close agreement. Conversely for low-energy defects, only the receding measurements showed significant departure from theory. We propose that distinct wetting mechanisms for high- and low-energy defects explain the phenomenon of asymmetric hysteresis, where the advancing or receding contact angle deviates more strongly from the equilibrium angle.     

1D to 2D transitional structure of plasmonic crystals: fabrication and characterization

A very interesting structure that has not been explored previously is an array of “corrugated/wavy” lines; an intermediate structure between 1D grating and 2D arrays of plasmonic crystal. This novel structure is studied to fully understand the transitional effect from 1D line to 2D arrays. The changes in geometry will subsequently change the effective refractive index of the crystal hence alters the plasmonic coupling conditions. The azimuthal effect of this structure is also explored to control the SPP magnitude and propagation direction. Interference lithography (IL) technique is used to fabricate this structure. Some geometrical parameters can be controlled in order to optimize the coupling condition for SPP propagation. This will lead us to understand the fundamental geometrical contributions to the field enhancement. Comprehensive mathematical simulations that model these effects to the SPP coupling condition has been undertaken to understand the plasmonic coupling efficiency and the azimuthal angle dependence.     

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.     

Effect of Bohm potential on a charged gas

Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation (QKE): in the present work, propagation of waves in charged quantum gases is investigated starting from this QKE. Dispersion relations are derived for fully and weakly degenerate fermions and bosons (for the latter above critical temperature) and the differences discussed. Use of a kinetic equation permits investigation of “Landau-type” damping: it is found that the presence of damping in fermion gases is dependent upon the degree of degeneracy, whereas it is always present in boson gases. In fully degenerate fermions a phenomenon appears that is akin to the “zero sound” propagation.