A meniscus where three phases coexist at equilibrium: Microscopic derivation of the Herring relations

The geometrical characteristics of a meniscus between two phases are studied. In particular, the behavior of the contact angles as a function of the temperature is derived for SOS-type models. A microscopic derivation of the Herring relations is given within a continuuous Gaussian model.     

Effects of symmetric and asymmetric contact angles and division of menisci during separation

Meniscus and viscous forces are sources of adhesive force when two surfaces are separated with a micro-meniscus present at the interface. The adhesive force can be one of the main reliability issues when the contacting surfaces are ultra-smooth and the normal load is small, as is common for micro/nano devices. In this paper, both meniscus and viscous forces of menisci with symmetric and asymmetric contact angles are modelled. Equations for both meniscus and viscous forces in division of menisci are analytically formulated. The role of these two forces is evaluated during the separation process. The effects of the contact angles, division of menisci, as well as liquid thicknesses, surface tension and viscosity of the liquid, and separation distance and time during separation are presented. It is found that contact angles significantly affect the break point and meniscus force, and the magnitude of meniscus force can be largely reduced by choosing proper asymmetric contact angles. ‘Force scaling’ effects are found to be true for both meniscus and viscous forces when one larger meniscus is divided into large numbers of identical micro-menisci. Meniscus force increases with the number of divisions whereas viscous force decreases by an order of inverse the number of division (1/N). Optimal configurations for low adhesion are identified. This study presents a comprehensive analysis of meniscus and viscous forces during separation of menisci under different physical configurations. It provides a fundamental understanding of the physics of the process and knowledge for control of adhesion due to liquid menisci.     

Langevin dynamics of an interface near a wall

We study dynamical contact angles and precursor films using Langevin dynamics for SOS type models, near a wall which favors spreading. We first solve exactly the Gaussian model and discuss various asymptotic regimes. This is only appropriate to partial wetting. We then consider more general models. Using local equilibrium and scaling arguments, we derive the shape of the dynamical profile and the speed of the precursor film which exists when the spreading coefficient is strictly positive. Long-range potentials lead to a layered structure of the precursor film. We also consider the case of a meniscus in a capillary.     

Capillary Interactions between a Probe Tip and a Nanoparticle

To understand capillary interactions between probe tips and nanoparticles under ambient conditions, a theoretical model of capillary forces between them is developed based on the geometric relations. It is found that the contribution of surface tension force to the total capillary force attains to similar order of magnitude as the capillary pressure force in many cases. It is also shown that the tip shape and the radial distance of the meniscus have great influence on the capillary force. The capillary force decreases with the increasing separation distances, and the variance of the contact angles may change the magnitudes of capillary forces several times at large radial distances. The applicability of the symmetric meniscus approximation is discussed.     

Theoretical Study on the Capillary Force between an Atomic Force Microscope Tip and a Nanoparticle

Considering that capillary force is one of the most important forces between nanoparticles and atomic force microscope （AFM） tips in ambient atmosphere, we develop an analytic approach on the capillary force between an AFM tip and a nanoparticle. The results show that the capillary forces are considerably affected by the geometry of the AFM tip, the humidity of the environment, the vertical distance between the AFM tip and the nanoparticle, as well as the contact angles of the meniscus with an AFM tip and a nanoparticle. It is found that the sharper the AFM tip, the smaller the capillary force. The analyses and results are expected to be helpful for the quantitative imaging and manipulating of nanoparticles by AFMs.     

微平面接触分离中弯月面力的计算

微平面间黏着力对微机电系统(MEMS)非常重要,常是决定其能量损耗乃至寿命长短的最主要因素.MEMS中的黏着力主要来源之一就是介于两互相接触平面间的弯月面力.弯月面力主要取决于相互接触的两平面间形成的弯月面形状.本文通过分析两微小平面在分离过程中弯月面形状的变化,得到在不同表面亲水/疏水性能、初始液面高度、分离距离等条件下的弯月面形状,计算得出在不同初始条件下断裂高度和弯月面力的数值以及随之变化的规律,为MEMS的性能分析和寿命计算提供依据。     

Coalescence of spreading droplets on a wettable substrate

We investigate experimentally and theoretically the coalescence dynamics of two spreading droplets on a highly wettable substrate. Upon contact, surface tension drives a rapid motion perpendicular to the line of centers that joins the drops and lowers the total surface area. We find that the width of the growing meniscus bridge between the two droplets exhibits power-law behavior, growing at early times as t1/2. Moreover, the growth rate is highly sensitive to both the radii and heights of the droplets at contact, scaling as ho3/2/Ro. This size dependence differs significantly from the behavior of freely suspended droplets, in which the coalescence growth rate depends only weakly on the droplet size. We demonstrate that the scaling behavior is consistent with a model in which the growth of the meniscus bridge is governed by the viscously hindered flux from the droplets.     

The capillary interaction between two vertical cylinders

Particles floating at the surface of a liquid generally deform the liquid surface. Minimizing the energetic cost of these deformations results in an inter-particle force which is usually attractive and causes floating particles to aggregate and form surface clusters. Here we present a numerical method for determining the three-dimensional meniscus around a pair of vertical circular cylinders. This involves the numerical solution of the fully nonlinear Laplace-Young equation using a mesh-free finite difference method. Inter-particle force-separation curves for pairs of vertical cylinders are then calculated for different radii and contact angles. These results are compared with previously published asymptotic and experimental results. For large inter-particle separations and conditions such that the meniscus slope remains small everywhere, good agreement is found between all three approaches (numerical, asymptotic and experimental). This is as expected since the asymptotic results were derived using the linearized Laplace-Young equation. For steeper menisci and smaller inter-particle separations, however, the numerical simulation resolves discrepancies between existing asymptotic and experimental results, demonstrating that this discrepancy was due to the nonlinearity of the Laplace-Young equation.     

Equivalence between the Edwards-Anderson and Luttinger models of a spin glass

The random “bond” model of a spin glass, as proposed by Edwards and Anderson, is demonstrated to be a special case of the random “Site” model advanced by Luttinger. An explicit relationship between the seemingly different order parameters employed in the two models is established, and for the pure spin glass phase (i.e. no ferromagnetic transition), the two order parameters are shown to be identical.     

Quadratic contact process: phase separation with interface-orientation-dependent equistability

The quadratic contact process is implemented on a square lattice as a model with random adsorption and correlated desorption requiring empty pairs of diagonal neighbors. The model exhibits a discontinuous phase transition between an active state and an absorbing state, but equistability between these states depends on the orientation of the separating interface. Correspondingly, for a generalized class of models, we find phase coexistence over a finite region of their two-dimensional parameter space. This is in stark contrast to behavior in equilibrium systems.     

微重力下变内角毛细驱动流研究

本文研究了在满足Concus-Finn条件时,微重力环境下内角沿容器轴线变化时的毛细驱动流问题,建立了变内角的毛细流动控制方程,获得了变内角流动的近似解析解,并与FLOW-3D软件的数值模拟结果进行了对比验证. 计算结果表明,随着时间的增大,近似解析解与数值解的相对误差越来越小,在6 s以后,相对误差不超过5%. 论文研究了不同结构参数对内角毛细流动的影响规律,得出液体前缘位置和液面高度均随内角、接触角、内角斜率和内角幂指数的增大而减小的结论. 在不同时刻,液体的液面高度随着时间的增大而增大,但在初始时刻存在一个常高度,该高度不随时间的变化而变化. 在空间流体管理时,可以根据本文的工作进行容器设计和选择适合的溶液. 关键词： 变内角 毛细驱动流 近似解析解 前缘位置     

Geometry-dependent electrostatics near contact lines

Long-ranged electrostatic interactions in electrolytes modify contact angles on charged substrates in a scale and geometry-dependent manner. For angles measured at scales smaller than the typical Debye screening length, the wetting geometry near the contact line must be explicitly considered. Using variational and asymptotic methods, we derive new transcendental equations for the contact angle as functions of the electrostatic potential only at the three phase contact line. Analytic expressions are found in certain limits and compared with predictions for contact angles measured with lower resolution. An estimate for electrostatic contributions to line tension is also given.     

Numerical simulation of an evaporative meniscus on a moving substrate

A hydrodynamic model based on lubrication theory has been developed to describe an evaporative meniscus in a complete wetting configuration, when evaporation takes place in ambient air. We focus on combined effects of evaporation and the substrate motion on the effective contact angle. Numerical simulations show two distinct regimes when varying the substrate velocity on several orders of magnitude. At a small velocity, the effective contact angle is governed by evaporation and is independent of the substrate velocity, while the substrate motion is dominant at a high velocity. In the latter case, a Landau-Levich regime is obtained for the receding contact line, and a Cox-Voinov regime for the advancing contact line. Finally, we use our numerical results to test the simplified model developed by Pham et al. [5,6].     

The spatial focusing of a leaky time reversal chaotic cavity

Elastic waves propagating inside a solid chaotic cavity create a diffusive random field that contains both longitudinal and shear waves. In the current paper, we are interested in the field radiated in a fluid in contact with such cavity. The goal of this paper is to predict the spatial focusing properties that can be obtained in the fluid using a time-reversal piezoelectric transducer in contact with the cavity. We present a statistical approach that supposes a fully diffused wavefield inside the cavity with an equipartition of energy between longitudinal and shear waves. We show that the critical angles of transmission in the solid-fluid interface generate a cut-off of the spatial frequencies and then a degradation in the spatial focusing. This limitation can be overcome using a rough surface. A set of experiments conducted in the MHz range confirm the theoretical model.     

Image encryption based on gyrator transform and two-step phase-shifting interferometry

A novel optical image encryption method is proposed, based on gyrator transform and phase-shifting interferometry. The input two-dimensional image to be encrypted is gyrator transformed two times, and two random phase masks are placed at the input plane and the output plane of the first gyrator transform. Two-step phase-shifting interferometry is used to record the digital holograms of the input image encrypted by use of double-random phase encoding technique in gyrator transform domain. The rotation angles of gyrator transform, the random phase mask in the gyrator plane and the arbitrary phase shift used for recording form the keys for decryption of the input image. Numerical simulations are presented to verify its validity and efficiency.     

Helical signature motif in the fibre diffraction patterns of random-walk chains

Helical geometry is one of the most dominant structural features in polypeptides, nucleic acids, carbohydrates and long-chain polymers in general. Structures of a large number of helical biomolecules and important non-biological polymers have been determined by fibre diffraction and helical diffraction theory. This paper reports on a study of fibre diffraction patterns calculated for two different on-lattice random-walk models of polymers, with no built-in helical features. It is noted that such on-lattice random walks are natural models for polymers with fixed monomer geometries and inter-monomer angles. The presence of layer-line intensities is observed, characteristic of fibre diffraction patterns from helices with an integral number of units per turn. It is shown that under certain circumstances, fibre diffraction patterns of helical objects may be difficult to distinguish from cylindrically-averaged fibre diffraction patterns of random walks on lattices with fixed angles. A simple correspondence is demonstrated between the parameters of a helix and a random-walk chain with equivalent fibre diffraction patterns. These results call for a critical examination of the way the helical diffraction theory is typically used: certain structures that have been modelled as helical might, under some circumstances, be more naturally described as random-walk chains with no preferred conformation even on the shortest length-scale and in the context of a fibre.     

Order-chaos-order transitions in electrosprays: the electrified dripping faucet

Electrosprays have diverse applications including protein analysis, electrospinning, and nanoencapsulation for drug delivery. We show that a variety of electrospray regimes exhibit fundamental analogy with the nonlinear dynamics of a dripping faucet. The applied voltage in electrosprays results in additional period doublings and temporal order-chaos-order transitions. Attractors in the return maps show logarithmic self-similarity in time, suggesting self-similar capillary waves on the meniscus. The bifurcations in ejection time can be explained by phase variations between capillary waves and pinch-off conditions and by ejection mode changes due to contact angle variations.     

Measurement of the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame by means of a laser-based interferometer technique

With a view to measuring the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame, a thin laser beam is sent into the flame perpendicular to the flow direction. The laser beam generally undergoes fluctuations of direction, phase, and amplitude. Only the random deflections of the laser beam may be taken into account. After having traversed the flame, the perturbed laser beam enters into an interferometric system. Materials and experimental procedure are described. In the unperturbed interference pattern, the zones only sensitive to fluctuations of the angle-of-arrival of the laser beam are detected. From the random displacements of the central bright fringe, the structure coefficient of refractive index fluctuations in the flame is measured. To prove that the method of measurement is satisfactory, the result obtained is applied for computing the power spectral density of the angle-of-arrival of the laser beam from the formula of correlations of the laser beam deflection angles which we have demonstrated in previous works. This computed power spectral density is compared to that measured from the effective position of the detector. A good agreement is observed between the two results.     

The Influence of Boundary Conditions on Solid-on-Solid Models

We investigate various 1D solid-on-solid (SOS) models using the transfer matrix method. The main results of the paper concern SOS interfaces near an attracting wall (line) when the end points of the interface are fixed away from the wall (line). We obtain typical interface shapes in the macroscopic scale. If attraction of the wall is strong enough, then a part of the interface is pinned to the wall (line) and the remaining parts of the interface form angles with the wall (line)—the contact angles. Explicit expressions for the contact angles are derived. We show also that for a certain range of parameters the models exhibit reentrant wetting and drying. As a result the free energy of the SOS model as a function of temperature can have up to three points of nonanalyticity. The fluctuations of the SOS interface are investigated in detail. Quite unusual fluctuations are observed at the contact points—the points where unpinned and pinned parts of the interface meet.