Capillary forces between two solid spheres linked by a concave liquid bridge: Regions of existence and forces mapping

This article focuses on the capillary interactions arising when two spherical particles are connected by a concave liquid bridge. This scenario is found in many situations where particles are partially wetted by a liquid, like liquid films stabilized with nanoparticles. We analyze different parameters governing the liquid bridge: interparticle separation, wetting angle and liquid volume. The results are compiled in a liquid volume‐wetting angle diagram in which the regions of existence (stability) or inexistence (instability) of the bridge are outlined and the possible maximum and minimal particle distances for which the liquid bridge may be found. Calculations of the capillary forces discriminate those conditions for which such force is repulsive or attractive. The results are plotted in form of maps that allow an easy understanding of the stability of a liquid bridge and the conditions at which it may be produced for the two particle model. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Effects of blade rake angle and gap on particle mixing in a cylindrical mixer

Performance optimization of a mixer is an issue of great significance in many industrial technologies dealing with particulate materials. By means of Discrete Element Method (DEM), this work examines how the mixing performance of a cylindrical mixer is affected by the two design parameters: blade rake angle and blade gap at the vessel bottom, extending our previous work on particulate mixing. The flow and mixing performance are quantified using the following: velocity fields in vertical cylindrical sections, Lacey’s mixing index, inter-particle forces in vertical cylindrical sections through the particle bed and the applied torque on the blade. Simulation results show that the mixing rate is the fastest for a blade of 90° rake angle, but inter-particle forces are large. Conversely, the inter-particle forces are small for a blade of 135° rake angle, but the mixing rate is slow. The simulation results also indicate that the force applied on particles, velocity field and mixing are interrelated in that order.     

Maximum Force Technique for the Measurement of the Surface Tension of a Small Droplet by AFM

An atomic force microscope (AFM) is used to measure the meniscus force on a vertical quartz rod as the rod is pulled through an air/liquid interface. A fluid bridge forms between the liquid and the base of the rod as the rod is withdrawn from the liquid. The force reaches a maximum as the bridge necks down and finally detaches from the rod. The maximum force on the rod is independent of the material of the rod and can be used to calculate the surface tension of the liquid. Alternately, if the surface tension of the liquid is known, the maximum force of the meniscus can be used to calibrate the spring constant of the AFM cantilever. The contact angle of the liquid on the rod was calculated as the rod was inserted into the liquid droplet. Contact angle hysteresis was observed. Results are presented of the measurement of the meniscus force of water, 10^?3 M cetyl trimethyl ammonium bromide (CTAB) and tetradecane as the rod is withdrawn from the liquid.     

Maximum Force Technique for the Measurement of the Surface Tension of a Small Droplet by AFM

An atomic force microscope (AFM) is used to measure the meniscus force on a vertical quartz rod as the rod is pulled through an air/liquid interface. A fluid bridge forms between the liquid and the base of the rod as the rod is withdrawn from the liquid. The force reaches a maximum as the bridge necks down and finally detaches from the rod. The maximum force on the rod is independent of the material of the rod and can be used to calculate the surface tension of the liquid. Alternately, if the surface tension of the liquid is known, the maximum force of the meniscus can be used to calibrate the spring constant of the AFM cantilever. The contact angle of the liquid on the rod was calculated as the rod was inserted into the liquid droplet. Contact angle hysteresis was observed. Results are presented of the measurement of the meniscus force of water, 10^-3 M cetyl trimethyl ammonium bromide (CTAB) and tetradecane as the rod is withdrawn from the liquid.     

Prediction of effective area and liquid hold-up in structured packings by CFD

Interfacial effective area and liquid hold-up in structured packing geometries are investigated using the volume of fluid method. Three-dimensional numerical simulations of gas–liquid flow on inclined plane plate and in a structured packing are performed. The VOF method is used to capture the gas–liquid interface motion. After a first validation case on the wetting phenomena prediction on an inclined plane plate, the effective interfacial area, the liquid hold-up and the degree of wetting of packing are studied as function of liquid flow rate and wall surface characteristic (adherence contact angle). Results show that the liquid flow-rate and the contact angle play a significant role. It is found that the interfacial effective area and the degree of wetting of packing increase as the liquid flow rate increases and as the contact angle decreases. Moreover, under the influence of the contact angle, different liquid film shapes are observed. The simulations results are compared to experimental data available in literature. This work shows that the CFD is a powerful tool to investigate performance characteristics of structured packings. Moreover, this work shows how CFD can be used as an effective tool to provide information on fluid flow behavior and determination of interfacial area, liquid hold-up and minimum flow-rate to ensure complete wetting. These parameters could be further used in process simulation at larger scale for the development and the design of efficient packings.     

Liquid/Fiber and Solidified-Liquid/Fiber Contact Angles Compared

Data are presented showing that the contact angle formed by a liquid resin droplet placed on a single fiber is comparable with a receding contact angle. This was ascertained by comparing Wilhelmy wetting force measurements with liquid droplet profile analysis. Subsequently, the latter analysis was carried out on cured (solidified) epoxy droplets placed on Kevlar fibers. Dimensional changes observed after curing showed that the contact angles of the solid droplets were smaller than that for liquid resin: however, the presence of residual stresses because of adhesion to the fiber may make droplet profile analysis inaccurate for obtaining an equilibrium receding contact angle for the solid droplets.     

Wetting properties of human hair by means of dynamic contact angle measurement

The interaction between human hair and water occurs continuously in atmospheric air, and even more so, during application of shampoo and conditioner. For this reason the wettability of hair, and how hair care products affect the wetting properties, is of interest to hair care science. In this study, the Wilhelmy balance method is used to measure dynamic contact angle of both conditioner‐treated hairs and those left untreated to study the interaction of hair with water. The method uses a microbalance to measure the force exerted on a single fiber when it is immersed into the wetting liquid of interest. This measured force is related to the wetting force of the liquid on the fiber, and the dynamic contact angle can be calculated. The contact angles of chemically damaged, mechanically damaged, virgin (undamaged) as well as conditioner‐treated hairs and those left untreated are measured and compared. These samples were measured dry, and then also allowed to soak in water before being measured to determine whether a wet environment affects the wetting properties of the hair surface. Additionally, wettability of hairs from subjects of different ethnicities are measured and compared. Further, the mechanisms driving a significant directionality dependence are studied and discussed. The results are also used to explain tribological properties found in previous studies. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102:5255–5265, 2006     

The effect of polymer surface on the wetting and adhesion of liquid systems

Young's equation describes the wetting phenomenon in terms of the contact angle between a liquid and a solid surface. However, the contact angle is not the only parameter that defines liquid–solid interactions, an additional parameter related to the adhesion between the liquid drop and the solid surface is also of importance in cases where liquid sliding is involved. It is postulated that wetting which is related to the contact angle, and interfacial adhesion, which is related to the sliding angle, are interdependent phenomena and have to be considered simultaneously. A variety of models that relate the sliding angle to the forces developed along the contact periphery between a liquid drop and a solid surface have been proposed in the literature. Here, a modified model is proposed that quantifies the drop-sliding phenomenon, based also on the interfacial adhesion that develops across the contact area of the liquid/solid interface. Consequently, an interfacial adhesion strength parameter can be defined depending on the mass of the drop, the contact angle and the sliding angle. To verify the proposed approach the adhesion strength parameter has been calculated, based on experimental results, for a number of polymer surfaces and has been correlated with their composition and structure. The interaction strength parameter can be calculated for any smooth surface from measurements of the contact and the sliding angles.     

Effects of surface flaws on the wettability of solids

Wetting hysteresis, or the variability of contact angle, is recognized to be caused by several phenomena. In particular, we consider it to be due to heterogeneity of the solid surface in contact with the liquid. Results describing the deformation of an initially straight triple line in the proximity of an isolated, small, energetic inhomogeneity are summarized. The theory is extended to describe the behaviour of a wetting front near a circular, high-energy (i.e. corresponding to zero intrinsic contact angle) flaw of dimensions comparable to those of the triple line distortion. A simple model is proposed to explain the breakaway of the isthmus of liquid connecting the flaw to the bulk liquid. Separation time is found to be proportional to ^-5, where 0 is the intrinsic contact angle of the solid/ liquid system. The behaviour of a triple line on a solid possessing a randomly distributed population of identical, small, circular flaws is considered. Contact angle hysteresis can thus be explained, as can the noise often observed in a (dynamic) Wilhelmy plate experiment. A simple statistical model is proposed in which random force fluctuations related to a moving triple line are shown to correspond to the Poisson process of probability theory.     

A new method for the characterisation of the wettability of powders

The wetting characteristics of fine powders play an important role in a variety of processes. The most important way of characterising the wettability of a fluid/fluid/solid system is to measure the contact angle. This paper describes a relatively simple method for the determination of the contact angle on powdery materials. The technique involves the measurement of the dynamic contact angle which is formed when a liquid drop is placed on a horizontal porous surface. On the basis of the measured dynamic contact angle as a function of time an “apparent” static contact angle has been defined, which gives a measure of the wettability of porous solid systems by analogy with the wetting of non-porous solids. Determinations with glass beads and NaCl-powders as the test materials indicate that the measured value depends on the particle size of the powder, the porosity and the temperature. It was concluded that the capillary penetration of the liquid droplet into the porous media itself influences the wetting characteristics.     

黏性颗粒团聚机理及流化特性研究进展

黏性力的存在导致黏性颗粒在流化过程中易发生团聚,干扰正常的流态化。近年来,黏性颗粒流的研究重心逐渐转移到本征的团聚机理和流化特性。本工作综述了4种主要黏性力的力学模型、团聚判据及流态化实验与模拟研究进展,从力、运动及动力学的角度阐述了黏性力作用机制和黏性颗粒流化特性。分析表明,在颗粒尺度上,4种黏性力发展程度差异较大,黏性力动力学模型和团聚过程机理将成为未来研究的主要方向。在反应器尺度上,耦合黏性力模型的离散单元法模拟将继续作为重要的研究方法,其中,机理模型和计算能力是后续模拟中需要突破的重点。     

Capillary and van der Waals force between microparticles with different sizes in humid air

It is well known that surface effect forces, such as van der Waals force and capillary force, are the major contributions to adhesion when microsized particles are in contact in humid environment. But it is very complex to calculate the adhesion force between two smooth unequal particles. In conventional approaches, the effective particle radius approximation and the constant half-filling angle assumptions are often used for computing the van der Waals forces between two microparticles. However, the approximation and the assumption are actually difficult to accurately model the forces between unequal particle sizes when the surfaces are with different properties. In this paper, we present a theoretical study of the van der Waals force and capillary force between two microparticles with different radii and the surface properties linked by a liquid bridge. The proposed model provides the adhesion force predictions in good agreement with the previous formula and existing experiment data. Considering the solid particles are partially wetted by the liquid bridge, the van der Waals force is calculated by divided the particle surface into a wetted part and a dry portion in our stimulation. Since the wetted surface portion of the particle is determined by the half-filling angle, the relationship between two half-filling angles of the unequal size particles is developed from the geometrical consideration, which is relate to the size ratio of the particles, the contact angle, and the separation distance. Then, the van der Waals force is determined using the surface element integration. Moreover, the influences of humidity, particles size, contact angle, and separation distance toward the adhesion forces are discussed using the proposed method. Simulations indicate that a higher relative humidity leads to bigger liquid bridges, suggesting a higher capillary force, but at the same time, the van der Waals force decreases due to the decrease in surfaces energy. As for the influence of contact angle, results show that a higher contact angle, that is, a more hydrophobic surface, reduces the capillary force but increases the van der Waals force (absolute value). The simulations also show that the both the capillary force and the van der Waals force (absolute value) increase as the particle size increases. When the particles are separated from each other, the capillary force and van der Waals force decreases gradually. These results are helpful to understand and utilize the adhesion interaction between particles with unequal sizes at the ambient condition.     

Adhesion and Wetting Hysteresis of a Metal (Mercury) on an Oxide Glass in Air and Nitrogen

In general, oxygen can considerably change the wetting behavior of oxides by molten metals. This work is a basic illustration of the oxidation effect on the wetting behavior of glass by a liquid metal. Taking mercury as a model of a metal, the importance of the metal oxidation in the glass/metal interaction has been observed by measuring wetting contact angles of mercury on glass and the ability of calibrated mercury drops to slide down, under gravitation, on an inclined glass plate in air or in nitrogen. It is believed that the highest force of detachment by sliding of the mercury drop in air results from the metal oxidation which can be interpreted by a higher contact angle hysteresis when the metal is exposed to air.     

Adhesion and Wetting Hysteresis of a Metal (Mercury) on an Oxide Glass in Air and Nitrogen

In general, oxygen can considerably change the wetting behavior of oxides by molten metals. This work is a basic illustration of the oxidation effect on the wetting behavior of glass by a liquid metal. Taking mercury as a model of a metal, the importance of the metal oxidation in the glass/metal interaction has been observed by measuring wetting contact angles of mercury on glass and the ability of calibrated mercury drops to slide down, under gravitation, on an inclined glass plate in air or in nitrogen. It is believed that the highest force of detachment by sliding of the mercury drop in air results from the metal oxidation which can be interpreted by a higher contact angle hysteresis when the metal is exposed to air.     

Wetting hysteresis: effects due to shadowing

Wetting hysteresis due to isolated surface heterogeneities is now fairly well understood but when the solid presents a population of defects, complex cooperative effects between neighbours may exist. One such effect is that of 'shadowing', in which a proportion of the flaws near the triple line, and which would otherwise contribute to hysteresis, are masked by already existing deformations to the wetting front caused by neighbouring heterogeneities. This renders them inactive and, as a result, the hysteretic wetting force is only expected to be a linear function of density for sparse populations. Theoretical predictions are compared with experimental results obtained with model heterogeneous surfaces consisting of overhead projector transparencies bestrewn with circular ink spots - the defects. Agreement is found to be satisfactory when intrinsic angles on both the homogeneous solid and the flaws are finite, whereas the concordance is less satisfactory when the contact angle of the liquid on the homogeneous solid is zero.     

Wetting of a vertical plate by a liquid flowing through a vertical nozzle

A model has been developed describing the wetting of a vertical plate by a liquid, starting from the exact hydrodynamic equations. By incorporating an approximately chosen wetting force term into the Navier-Stokes equations and using laminar boundary layer theory, the velocity field, the width and the actual contact angle characterizing the flow of the liquid were determined.The results predicted by the model were compared with those experimentally obtained for two limiting cases, and good agreement was demonstrated using the aqueous glycerol mixtures. The model was unsatisfactory for the water film since the boundary layer rapidly became turbulent and it was also observed that poor agreement was obtained with the mineral oil.     

Reactive wetting behavior and mechanism of AlN ceramic by CuNi-Xwt%Ti active filler metal

In order to propel the application of the developed CuNi-Xwt%Ti active filler metal in AlN brazing and get the universal reactive wetting mechanism between liquid metal and solid ceramic, the reactive wetting behavior and mechanism of AlN ceramic by CuNi-Xwt%Ti active filler metal were investigated. The results indicate that, with the increasing Ti content, surface tension for liquid CuNi-Xwt%Ti filler metal increases at low-temperature interval, but very similar at high-temperature interval, which influence the wetting behavior on AlN ceramic obviously. CuNi/AlN is the typical non-reactive wetting system, the wetting process including rapid wetting stage and stable stage. The wettability is depended on surface tension of the liquid CuNi filler metal completely. However, the wetting process of CuNi-8wt.%Ti/AlN and CuNi-16 wt%Ti/AlN reactive wetting system is composed by three stages, which are rapid wetting stage decided by surface tension, slow wetting stage caused by interfacial reaction and stable stage. For CuNi-8wt.%Ti/AlN and CuNi-16 wt%Ti/AlN reactive wetting system, although the surface tension of liquid filler metal is the only factor to influence the instant wetting angle θ₀ at rapid wetting stage, the reduced free energy caused by interfacial reaction at slow wetting stage plays the decisive role in influencing the final wettability.     

Inter-particle interactions of alumina powders in UV-curable suspensions for DLP stereolithography and its effect on rheology,solid loading,and self-leveling behavior

For the UV-curable alumina suspensions used in digital light processing (DLP) stereolithography, optimizing the dispersant type is important for achieving low viscosity, high solid loading, and remarkable self-leveling behavior. However, the inter-particle interactions in UV-curable alumina suspensions dispersed using different dispersants are overlooked. Herein, the effect of inter-particle interactions on rheology, solid loading, and self-leveling behavior of UV-curable alumina suspensions was systematically investigated. Three different commercial dispersants were used: oleic acid (OA), alkane-acrylic phosphate ester (PM1590), and copolymer dispersant (BYK111). After dispersing, BYK111 endowed alumina powders with thicker adsorption polymer layer to provide stronger steric repulsion force and facilitated better wetting of alumina powers in the photocurable resin, resulting in a reduced network structure degree, which decreased the viscosity (1.04 Pa s at 30 s^?1); homogeneous packing of alumina powders, which enhanced the maximum solid loading (55 vol%); and inhibition of particle flocculation, which facilitated the spontaneous spreading of suspension.     

Spreading,wetting, and contact angles

The thermodynamic energies associated with conventional wetting, spreading, adhesion, cohesion, and disjoining pressure, as defined in classical equations, are re-examined for their significance in a force field. They are then converted into dimensionless form such that the equilibrium properties of both wetting and spreading all fall on the same line when the dimcnsionless spreading coefficient is plotted as a function of the dimensionless work of adhesion. The effects of a force field such as gravity are examined and it is further shown that spreading is always thickness-dependent, whether in a force field or in a gravity-free field. Non-equilibrium processes such as autophobicity are shown on the same dimensionless plot and indicate clearly that the speed with which the process approaches equilibrium depends on the difference between the initial and equilibrium spreading coefficients. All these processes are expressed in terms of a dimensionless group P_n, the reduced wetting energy, which, when lying between the values of + 1 and -1, equals the cosine of the contact angle, . The implication of this approach to non-equilibrium processes is discussed.