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.     

Capillary Forces between Submillimeter Spheres and Flat Surfaces at Constant Liquid Volumes

We investigate the capillary forces between submillimeter spheres and flat surfaces at constant liquid volumes theoretically and experimentally. An iterative method is used to estimate the capillary force with contact angles as the boundary conditions and the constant volume as a constraint. The theoretical analysis shows that the maximum capillary force between them decreases with the increase of the liquid bridge volume at small contact angles. The experimental results show that the force is smaller than the theoretical values at the initial separation distances. It is also observed that the force first increases and then decreases with an increasing separation distance in some cases. These phenomena of capillary forces hysteresis are explained according to the wetting hysteresis.     

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.     

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.     

Capillary force on a nanoscale tip in dip-pen nanolithography

Monte Carlo simulation has been used to characterize the capillary force due to the condensation of a liquid meniscus between a tip with a nanoscale asperity and a flat surface. To consider both hydrophobic and hydrophilic molecules coating the tip as a model of dip-pen nanolithography, tips with various wettabilities are studied. The capillary force due to the meniscus is calculated for various saturations (humidities). We have implemented a thermodynamic integration technique that can project the force into energetic and entropic contributions. In most cases, the force is mainly energetic in origin. At the snap-off separation where the meniscus disappears, the tip feels a significant entropic force at high saturation. Our calculation shows nonmonotonic behavior of the pull-off force as a function of saturation, which is in qualitative accord with experiments.     

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.     

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.     

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。     

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.     

旋转环形浅液池内双组分溶液耦合热-溶质毛细对流渐近解

为了了解水平温度梯度作用下旋转环形浅液池内耦合热-溶质毛细对流基本特征, 采用匹配渐近展开法对旋转环形浅液池内耦合热-溶质毛细对流过程进行了求解, 获得了中心区域的速度、温度和浓度分布,分析了旋转、Soret效应、浮力、溶质扩散 系数和液池的几何尺寸对流动结构的影响.将所得到的渐近解和文献中的已有结果进行对比,证明了所求结果的正确性;在浅液池内,耦合热-溶质毛细力对流体流动起主导作用, 旋转和浮力对流动的影响较小,溶质扩散系数和几何尺寸有较明显影响;当各种耦合的 驱动力作用方向相同时,流动增强;否则, 流动减弱. 关键词： 旋转 环形浅液池 耦合热-溶质毛细对流 渐近解     

On the instability against the surface charge of a liquid meniscus at the end of a capillary

The subject of consideration is instability of the flat meniscus of a viscous liquid at the end of a capillary in the gravitational field and an electrostatic field when the symmetry axis of the capillary is arbitrarily oriented relative to the direction of free-fall acceleration. It is shown that, if the electrostatic field strength is high, the development of meniscus instability does not depend on the orientation of the capillary. The instability growth rate versus wavenumber dependence for annular waves of different types on the meniscus surface is found to be nonmonotonic.     

How narrow can a meniscus be?

A water meniscus naturally forms in air between an atomic force microscope (AFM) tip and a substrate. This nanoscale meniscus produces a capillary force on the AFM, and also serves as a molecular transport channel in dip-pen nanolithography (DPN). A stable meniscus is a necessary condition for DPN and for the validity of the Kelvin equation commonly applied to AFM experiments. Lattice gas Monte Carlo simulations show that, due to thermal fluctuation, a stable meniscus has a lower limit in width. We find a minimum width of 5 molecular diameters (1.9 nm) when the tip becomes atomically sharp (terminated by a single atom).     

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     

Analytic solutions to Maxwell–London equations and levitation force for a general magnetic source in the presence of a long type-II superconducting cylinder

The interaction between a general magnetic source and a long type-II superconducting cylinder in the Meissner or mixed state is studied within the London theory. We first study the Meissner state and solve the Maxwell–London equations when the source is a magnetic monopole located at an arbitrary position. Then the field and supercurrent for a more complicated magnetic charge distribution can be obtained by superposition. A magnetic point dipole with arbitrary direction is studied in detail. It turns out that the levitation force on the dipole contains in general an angular as well as a radial component. By integration we obtain the field and supercurrent when the source is a two-dimensional monopole (a magnetically charged long thread along the axial direction), from which the results for a two-dimensional point dipole easily follow. In the latter case the levitation force points in the radial direction regardless of the orientation of the dipole. The case for a current carrying long straight wire parallel to the cylindrical axis is solved separately. The limit of ideal Meissner state is discussed in most cases. The case of mixed state is discussed briefly. It turns out that vortex lines along the axial direction and vortex rings concentric with the cylinder have no effect outside the cylinder and the levitation forces remain the same as in the case of the Meissner state.     

Surface adhesion properties of graphene and graphene oxide studied by colloid-probe atomic force microscopy

Surface adhesion properties are important to various applications of graphene-based materials. Atomic force microscopy is powerful to study the adhesion properties of samples by measuring the forces on the colloidal sphere tip as it approaches and retracts from the surface. In this paper we have measured the adhesion force between the colloid probe and the surface of graphene (graphene oxide) nanosheet. The results revealed that the adhesion force on graphene and graphene oxide surface were 66.3 and 170.6 nN, respectively. It was found the adhesion force was mainly determined by the water meniscus, which was related to the surface contact angle of samples.     

Microfoam formation in a capillary

The ultrasound-induced formation of bubble clusters may be of interest as a therapeutic means. If the clusters behave as one entity, i.e., one mega-bubble, its ultrasonic manipulation towards a boundary is straightforward and quick. If the clusters can be forced to accumulate to a microfoam, entire vessels might be blocked on purpose using an ultrasound contrast agent and a sound source.In this paper, we analyse how ultrasound contrast agent clusters are formed in a capillary and what happens to the clusters if sonication is continued, using continuous driving frequencies in the range 1-10 MHz. Furthermore, we show high-speed camera footage of microbubble clustering phenomena.We observed the following stages of microfoam formation within a dense population of microbubbles before ultrasound arrival. After the sonication started, contrast microbubbles collided, forming small clusters, owing to secondary radiation forces. These clusters coalesced within the space of a quarter of the ultrasonic wavelength, owing to primary radiation forces. The resulting microfoams translated in the direction of the ultrasound field, hitting the capillary wall, also owing to primary radiation forces.We have demonstrated that as soon as the bubble clusters are formed and as long as they are in the sound field, they behave as one entity. At our acoustic settings, it takes seconds to force the bubble clusters to positions approximately a quarter wavelength apart. It also just takes seconds to drive the clusters towards the capillary wall.Subjecting an ultrasound contrast agent of given concentration to a continuous low-amplitude signal makes it cluster to a microfoam of known position and known size, allowing for sonic manipulation.     

Volume-Charged Cones on a Liquid Interface in an Electric Field

In this study, we explore a novel type of slender conical liquid meniscus arisen in high electric field, which carries surface charge and net bulk charge of opposite sign. Stability of such dissipative structure is ensured by the balance between capillary and electrostatic forces and competition between the surface and bulk electric currents. The bulk charge is governed by the applied voltage being generated by the electric field of the cone due to dissociation/associations reactions at its apex. The effect of the physical parameters of the liquid on the microcone structure is elucidated. It is shown that the cone angle cannot exceed a critical value, which is a function of dielectric permittivity of the liquid. The electric current through the cone is found to be proportional to the square of the applied voltage. The obtained results can be applied for analysis of atomization processes of various liquids.     

Collapse dynamics of smectic-A bubbles

The collapse dynamics of smectic-A bubbles are analyzed experimentally and theoretically. Each bubble is expanded from a flat film stretched at the end of a hollow cylinder and deflated through a pressure release by means of a capillary tube. Its total collapse time can be varied between 0.1s and 20s by suitably choosing the length and the internal diameter of the capillary. This experiment allowed us to show that the collapse takes place in two steps: an initial one, which lasts a fraction of a second, where the meniscus destabilizes and fills up with focal conics, followed by a much longer period during which the bubble collapses and exchanges material with the meniscus. By measuring simultaneously the Laplace pressure and the internal pressure inside the bubble, we were able to fully characterize the shear-thinning behavior of the smectic phase within the meniscus. We emphasize that this method is generic and could be applied as well to other systems such as soap bubbles, on condition that inertial effects are negligible.     

Fabrication of high-quality colloidal crystals by a capillary-enhanced method

High-quality colloidal crystals have been prepared through a novel capillary-enhanced process, which includes both the characteristics of a sedimentation method and a capillary method. The multiple capillary forces driving the formation of colloidal crystals are composed of a primary capillary force and a secondary capillary force controlled by the ambient humidity. When the particles on the surface of the substrate transform into a gel-like layer in a high-humidity condition during the final step of the evaporative process, the secondary capillary force will be effective and fine tune the relative position between the neighboring particles in the microarray to decrease the amount of defects efficiently. Moreover, the close-packed structure can also be fabricated in a large area. Perfect colloidal crystals can easily be prepared in a short processing time by simple operation steps with the assistance of enhanced secondary capillary forces. PACS 42.70.Qs; 68.03.Cd; 68.65.Ac     

Atomistic wear in a single asperity sliding contact

Abrasive wear of sharp silicon tips sliding distances of up to 750 m on a polymeric surface is studied using atomic force microscopy. The data cannot be explained by conventional macroscopic wear models. We present a new model in which the barrier for breaking an atomic bond is lowered by the frictional stress acting on the contact. Quantitative agreement is obtained between the model and wear data for all load forces and sliding distances studied.