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.     

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.     

Modelling of Binder-Induced Agglomeration

From the analysis of pendular liquid bridge forces between spherical particles, a model has been developed to predict bridge rupture energies. Whilst this model has been shown to predict the correct trends in certain stages of agglomeration, it is limited by the assumptions of zero contact angle, toroidal bridge geometry, spherical particles and quasi-static rupture. The work described here is aimed at extending the model to more generally applicable conditions using direct measurement of bridge rupture energies between particles down to 3 μm in diameter under different physiochemical conditions. Initial results show that the spreading coefficient of the binder to the particle has a marked effect on the dynamic behaviour of the bridge itself and its subsequent geometry at equilibrium, i.e. for non-zero contact angles theoretical equations tend to over-predict the force of adhesion, whilst for zero contact angles the force of adhesion agrees with that predicted using the Laplace equations for constant curvature. On the other hand, the corrected expression for maximum separation distance shows good agreement with experimental results.     

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.     

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.     

脉动热管的接触角滞后和毛细滞后阻力

脉动热管通常采用毛细管制造,液塞在运动过程中前进接触角和后退接触角随着管径、管长、充液量、传热量和工质的选择会有很大的不同,存在着毛细滞后效应的影响。本文对毛细管中单个液塞在运动过程中两个接触角和毛细滞后阻力进行了分析。结果表明,接触角滞后对于上述参数变化比较敏感,接触角滞后对于运行是不利的.可以通过毛细管的选取、工质的选择和充液率的改变等来消除毛细滞后的影响。得到的结果对于进一步完善脉动热管的物理模型有重要参考价值。     

Molecular-Dynamics Simulations of Droplets on a Solid Surface

By using a semi-empirical Lennard-Jones embedded-atom-method potential, we study the influence of many-body forces and atomic size mismatch on the wetting behavior of nano droplets on a solid surface. With molecular dynamics simulations, we find that the contact angle decreases with increasing many-body forces. The increase of atomic size mismatch between solid and liquid results in the decrease of contact angles. Our calculation also shows that the interface structure is strongly affected by the interaction between liquid and solid as well as the atomic size mismatch. For weak solid-liquid interaction, the interface layer of the droplet nearest to the solid exhibits a typical simple liquid structure regardless of the size mismatch. For strong solid-liquid interaction, evident ordering in the interface layer is observed for well matched cases.     

Lateral vibration of a water drop and its motion on a vibrating surface

The resonant modes of sessile water drops on a hydrophobic substrate subjected to a small-amplitude lateral vibration are investigated using computational fluid dynamic (CFD) modeling. As the substrate is vibrated laterally, its momentum diffuses within the Stokes layer of the drop. Above the Stokes layer, the competition between the inertial and Laplace forces causes the formation of capillary waves on the surface of the drop. In the first part of this paper, the resonant states of water drops are illustrated by investigating the velocity profile and the hydrostatic force using a 3d simulation of the Navier-Stokes equation. The simulation also allows an estimation of the contact angle variation on both sides of the drop. In the second part of the paper, we investigate the effect of vibration on a water drop in contact with a vertical plate. Here, as the plate vibrates parallel to gravity, the contact line oscillates. Each oscillation is, however, rectified by hysteresis, thus inducing a ratcheting motion to the water droplet vertically downward. Maximum rectification occurs at the resonant states of the drop. A comparison between the frequency-dependent motion of these drops and the variation of contact angles on their both sides is made. The paper ends with a discussion on the movements of the drops on a horizontal hydrophobic surface subjected to an asymmetric vibration.     

Ellipsoidal particles at fluid interfaces

For partially wetting, ellipsoidal colloids trapped at a fluid interface, their effective, interface-mediated interactions of capillary and fluctuation-induced type are analyzed. For contact angles different from 90( degrees ) , static interface deformations arise which lead to anisotropic capillary forces that are substantial already for micrometer-sized particles. The capillary problem is solved using an efficient perturbative treatment which allows a fast determination of the capillary interaction for all distances between and orientations of two particles. Besides static capillary forces, fluctuation-induced forces caused by thermally excited capillary waves arise at fluid interfaces. For the specific choice of a spatially fixed three-phase contact line, the asymptotic behavior of the fluctuation-induced force is determined analytically for both the close-distance and the long-distance regime and compared to numerical solutions.     

Sliding velocity dependence of adhesion in a nanometer-sized contact

The influence of sliding velocity on the adhesion force in a nanometer-sized contact was investigated with a novel atomic force microscope experimental setup that allows measuring adhesion forces while the probe is sliding at continuous and constant velocities. For hydrophobic surfaces, the adhesion forces (mainly van?der?Waals forces) remain constant, whereas for hydrophilic surfaces, adhesion forces (mainly capillary forces) decrease linearly with a logarithmic increase of the sliding velocity. The experimental data are well explained by a model based on a thermally activated growth process of a capillary meniscus.     

Influence of surface energy and relative humidity on AFM nanomechanical contact stiffness

The effects of surface functionality and relative humidity (RH) on nanomechanical contact stiffness were investigated using atomic force acoustic microscopy (AFAM), a contact scanned-probe microscopy (SPM) technique. Self-assembled monolayers (SAMs) with controlled surface energy were studied systematically in a controlled-humidity chamber. AFAM amplitude images of a micropatterned, graded-surface-energy SAM sample revealed that image contrast depended on both ambient humidity and surface energy. Quantitative AFAM point measurements indicated that the contact stiffness remained roughly constant for the hydrophobic SAM but increased monotonically for the hydrophilic SAM. To correct for this unphysical behavior, a viscoelastic damping term representing capillary forces between the tip and the SAM was added to the data analysis model. The contact stiffness calculated with this revised model remained constant with RH, while the damping term increased strongly with RH for the hydrophilic SAM. The observed behavior is consistent with previous studies of surface energy and RH behavior using AFM pull-off forces. Our results show that surface and environmental conditions can influence accurate measurements of nanomechanical properties with SPM methods such as AFAM.     

Thermodynamic analysis of liquid bridge for fixed volume in atomic force microscope

In ambient condition,capillary forces are the major contributors to the adhesive forces between the tip of an atomic force microscope(AFM) and the sample.In general,capillary forces are thought to be related to water film thickness,contact time and relative humidity and so on.In this paper,an original analysis regarding the liquid bridge,based on the surface and interface thermodynamic theory,is proposed.The cases covered in the study include the capillary forces and temperature of liquid bridge for quickly drawn liquid bridge,and for nonvolatile liquid bridge.The study results show that variation in temperature may occur in the liquid bridge when it is stretched.     

Predicting the Performance of Granulation Binders Through Micro‐Mechanistic Observations

The selection of an appropriate polymeric binder to be used to agglomerate drug with excipients is a critical issue for the development of high shear wet granulation processes for pharmaceutical tablet systems. The aim of the study reported here is to determine the potential for successful granulation through measurement of the interactions of two polymer binder solutions, hydroxypropyl methylcellulose (HPMC) and polyvinyl‐pyrrolidone (PVP), with individual paracetamol drug crystals. A novel micro‐force balance (MFB) has been used to measure different parameters of the crystal‐to‐binder interaction, including the forces exerted by axially strained liquid bridges formed between either two paracetamol crystals or between a reservoir of binder solution and a single paracetamol crystal, the paracetamol‐to‐binder wettability, the post rupture volume distribution and the residue deposited on each crystal. Video images of the separation sequences were obtained simultaneously for analysis of bridge geometry, contact angles, volume distribution and binder residues. It was found that the formation of liquid bridges and their ability to bond particles together depends on the amount of binder left on a crystal after contacting a reservoir of binder (for example, large binder drop). Crystals in contact with HPMC were able to retain more liquid from a binder reservoir than those contacted with PVP solutions. This behaviour is seen to be more important to the final granule strength than the liquid binding force holding particles together in the wet agglomerate.     

Rupture energy of a pendular liquid bridge

We propose a simple expression for the rupture energy of a pendular liquid bridge between two spheres, taking into account capillary and viscous (lubrication) forces. In the case of capillary forces only, the results are in accordance with curve fitting expressions proposed by Simons et al. [2] and Willett et al. [5]. We performed accurate measurements of the force exerted by liquid bridges between two spheres. Experimental results are found to be close to theoretical values. A reasonable agreement is also found in the presence of viscous forces. Finally, for small bridge volumes, the rupture criterion given by Lian et al. [10] is modified, taking into account additional viscous effects. Received 18 September 2000 and Received in final form 10 June 2001     

Very-long-range nature of capillary interactions in liquid films

Micron-sized objects confined in thin liquid films interact through forces mediated by the deformed liquid-air interface. These capillary interactions provide a powerful driving mechanism for the self-assembly of ordered structures such as photonic materials or protein crystals. We demonstrate how optical micro-manipulation allows the direct measurement of capillary interactions between mesoscopic objects. The force falls off as an inverse power law in particles separation. We derive and validate an explicit expression for this exponent whose magnitude is mainly governed by particle size. For micron-sized objects we found an exponent close to, but smaller than 1, making capillary interactions a unique example of strong and very long ranged forces in the mesoscopic world.     

Experimental study of the motion of liquid droplets in a capillary under vibration

Results of an experimental study of the motion of small droplets in a capillary are discussed. The translational velocity of small droplets is studied as a function of the level and frequency of vibration acting together with a static force on the droplet—capillary system. The results are presented in the form of a set of curves, which reveal the nonlinear mechanical features of the system under consideration. The experiments confirm the previously developed theoretical model [7] based on the hysteresis dependence of the surface tension forces on the velocity of the meniscus motion.     

Capillary Adhesion of Microbeams： Finite Deformation Analysis

Capillary force may cause adhesion of devices at micro- and nano-scales. Considering the fact that large deformation is often involved in adhesion of microbeams, we analysed the capillary adhesion of two beams using finite deformation elasticity theory. The critical adhesion condition can be obtained from the present method as a function of the bending stiffness, Young＇s contact angle, the spacing of the two beams as well as the surface tensions of the solid and liquid phases. The solution for the capillary adhesion of a beam with a rigid substrate is also given. The results from the finite deformation analysis are compared with that of infinitesimal deformation method in order to show the necessity of accounting for the nonlinear effect associated with large deflection. The method adopted in this study can also be used to solve other adhesion problems associated with van der Waals force or electrostatic force.     

微重力条件下与容器连通的毛细管中的毛细流动研究

利用落塔的短时微重力条件, 实验研究了与容器连通的毛细管中的流体在微重力条件下的毛细流动过程, 并通过理论分析建立了相应的毛细管中弯月液面高度随时间变化的微分方程. 结果表明, 对于不同的接触角和不同的容器/毛细管参数, 由建立的理论公式得到的数值解结果都与实验结果在定量上较为一致. 此外, 实验中发现, 改变乙醇和去离子水混合液的比例可以明显地改变接触角参数, 但对毛细流动的影响很小, 建立的理论公式也对这一现象给出了合理的解释. 该研究对于预测和分析微流道及空间微重力条件下的毛细流动行为具有明显的应用价值.     

考虑毛细滞后效应的未饱和含湿多孔介质传热和传质理论

毛细滞后是未饱和多孔介质中很重要的特性之一。在许多情况下，毛细滞后现象对介质中传热和传质过程有着显著的影响。本文引入最小梯度概念，用以描述多孔体中毛细水运动滞后的定量行为，进而建立了考虑毛细滞后效应的未饱和含温多孔介质传热和传质的系统理论，为进一步定量研究毛细滞后对传热传质的影响打下了理论基础。     

A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

A multicomponent multiphase(MCMP) pseudopotential lattice Boltzmann(LB) model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio.The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000:1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young's equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie's law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.