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.     

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.     

Large Slip Length over a Nanopatterned Surface

A thermodynamic method is employed to analyse the slip length of hydrophobic nanopatterned surface. The maximal slip lengths with respect to the hydrophobicity of the nanopatterned surface are computed. It is found that the slip length reaches more than 50 μm if the nanopatterned surfaces have a contact angle larger than 160°. Such results are expected to find extensive applications in micro-channels and helpful to understand recent experimental observations of the slippage of nanopatterned surfaces.     

A Model for the Contact Angle of Liquid Droplets on Rough Surfaces

Up to now, measured results of the contact angle on rough surfaces have been explained usually based on the Wenzel equation （1936） and the Cassie-Baxter equation （1944）. However, these equations do not take into account considerations of liquid wetting behaviors on rough surfaces, and this leads to poor understanding of the mechanisms of contact between liquid droplets and rough surfaces （e.g. contact angle hysteresis）. We propose a new model for the contact angle of liquid droplets. By means of the present model, we can well understand the evperimental data which could not be well explained by the Wenzel equation and the Cassie-Baxter equation.     

Non-Contact to Contact Transition： Direct Measurements of Interaction Forces between a Solid Probe and a Planar Air-Water Interface

The interaction force between a solid probe and a planar air-water interface is measured by using an atomic force microscope. It is demonstrated that during the approach of the probe to the air-water interface, the force curves decline all the time due to the van der Waals attraction and induces a stable profile of water surface raised. When the tip approaches very close to the water surface, force curves jump suddenly, reflecting the complex behaviour of the unstable water surface. With a theoretical analysis we conclude that before the tip touches water surface, two water profiles appear, one stable and the other unstable. Then, with further approaching, the tip touches water surface and the non-contact to contact transition occurs.     

Analogies between a Meniscus and a Cantilever

Systematic and quantitative analyses of exact analogies between a meniscus and an elastica are performed. It is shown that the two governing equations take the same style after coordinate translation and scale transformation. The morphologies of the liquid bridge and the cantilever are calculated in terms of elliptic integrations, which can be reduced to the same shape,after converting the boundary conditions. The present analyses can make us grasp the nature of this physical phenomenon deeply and show some inspiration for designing the analogy experiments. Moreover, the calculated results are helpful to engineering applications, such as design and fabrication of MEMS, and micro-manipulations in micro/nano- technology.     

A Thin Liquid Film and Its Effects in an Atomic Force Microscopy Measurement

Recently, it has been observed that a liquid film spreading on a sample surface will significantly distort atomic force microscopy （AFM） measurements. In order to elaborate on the effect, we establish an equation governing the deformation of liquid film under its interaction with the AFM tip and substrate. A key issue is the critical liquid bump height yoc, at which the liquid film jumps to contact the AFM tip. It is found that there are three distinct regimes in the variation of yoc with film thickness H, depending on Hamaker constants of tip, sample and liquid. Noticeably, there is a characteristic thickness H^＊ physically defining what a thin film is; namely, once the film thickness H is the same order as H^＊, the effect of film thickness should be taken into account. The value of H^＊ is dependent on Hamaker constants and liquid surface tension as well as tip radius.     

Wetting and scanning force microscopy on rough polymer surfaces: Wenzel’s roughness factor and the thermodynamic contact angle

The influence of the surface roughness of polypropylene on the contact angle hysteresis is investigated by means of ethylene glycol drops in order to estimate the true Young’s equilibrium contact angle. A new relationship between the contact angle hysteresis and Wenzel’s contact angle is derived. In addition, the determination of Wenzel’s roughness factor by means of scanning force microscopy opens an alternative way to obtaining Young’s equilibrium contact angle without any surface manipulation. The experimental results presented verify this new approach. Received: 2 September 2002 / Accepted: 2 September 2002 / Published online: 5 March 2003 RID="*" ID="*"Corresponding author. Fax: +49-3328/352-452, E-mail: helmut.kamusewitz@gkss.de     

Directional Motion of Droplets in a Conical Tube or on a Conical Fibre

Manipulating the directional movement of liquid droplets is of significance for design and fabrication of some microfluidic devices, An energy-based method is adopted to analyse the directional movement of a droplet deposited in a conical tube or on a conical fibre. We perform an experiment to investigate the directional motion of a droplet in an open conical tube. Our theoretical analysis and experimental observations both demonstrate that surface tension can drive the droplet to move in the conical tube. The critical condition of the liquid moving in the conical tube is presented. We also analyse a droplet on a conical hydrophilic fibre, which can move from the thinner to the thicker end.     

Modelling of the solid–liquid interface during laser processing using an inverse methodology

This study presents a methodology for estimating the melt depth during laser processing of solid materials. The determination of the melt depth is treated as an inverse heat conduction problem, which includes the solid and liquid phases. The conjugate gradient method is applied to treat the inverse problem using the available temperature measurements. Without the inverse methodology the melt depth is very difficult to obtain with precision. The proposed method can also be applied during microthermal machining to determine the location of the solid–liquid interface and the temperature distributions of the two phases by using scanning thermal microscopy.     

Relationship between Spreading Rate and Wetting Behaviour of Oil on Surface of Surfactant Solution

We report a systematic investigation of the spreading of a polydimethylsiloxane oil layer on fiat surfaces of solution containing anionic surfactant of sodium dodecylsulfate. The experiment reveals that different wetting behaviours of the oil follow different spreading rates. In the case of complete wetting, it obeys a 0.75 power law, while in the pseudopartial wetting it follows a non-power law. The results can well be explained by a new simple theory of spreading. The theory further predicts that for a complete wetting state there exists another spreading rate.     

Experimental Study on Physical Mechanism of Drag Reduction of Hydrophobic Materials in Laminar Flow

We experimentally study the physical mechanism of the drag reduction of hydrophobic materials in the macroscopic scale. The experiment includes the drag and velocity measurements of laminar boundary layer flow over flat plates, and the observation of air bubbles on the surfaces. The plate surfaces have different wetting and roughness properties. In the drag measurements, the plates with bubbles on the surfaces lead to drag reduction, but not for those without bubbles. Velocity measurement confirms that the flow is laminar and gives apparent fluid slip on the plate wall with bubbles. In observation, air bubbles in macroscopic size emerge and enlarge on hydrophobic surfaces but not on hydrophilic surfaces. Therefore, the drag reduction of hydrophobic materials is explained by the generation of air bubbles of macroscopic size that cause the apparent velocity slip.     

Dewetting processes in a cylindrical geometry

Dewetting of liquid films of water-glycerol solutions of different viscosities has been studied experimentally in PVC cylindrical tubes. In contrast with plane surfaces, the dewetting capillary number Ca_vd increases with the film thickness h₀ over a large part of the experimental range and follows a same global trend independent of viscosity as a function of h₀. This increase is only partly explained by variations of the capillary driving force predicted in a recent theoretical work for a cylindrical geometry. An additional explanation is suggested, based on different spatial distributions of the viscous dissipation in the dewetting bump in the planar and cylindrical geometries. This mechanism is investigated for films of different thicknesses in a numerical model assuming a polynomial variation of the liquid thickness with distance in the bump region.     

Formation and mobility of droplets on composite layered substrates

A mesoscale fluid film placed on a solid support may break up and form droplets. In addition, droplets may exhibit spontaneous translation by modifying the wetting properties of the substrate, resulting in asymmetry in the contact angles. We examine mechanisms for droplet formation and motion on uniform and terraced landscapes, i.e., composite substrates. The fluid film stability, droplet formation and velocity are studied theoretically in the isothermal case using a lubrication approach in one spatial dimension. The droplet properties are found to involve contributions from both the terraced layer thickness and molecular interactions via the disjoining potential.     

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.     

Demonstration of Four Fundamental Operations of Liquid Droplets for Digital Microfluidic Systems Based on an Electrowetting-on-Dielectric Actuator

An electrowetting-on-dielectric actuator is developed, in which the liquid is sandwiched between top and bottom plates. For the bottom plate, silicon wafer is used as the substrate, the heavily phosphorus-doped polysilicon film is deposited by low pressure chemical vapour deposition as the microelectrode array, and thermally grown SiO2 film as the dielectric layer. The top p/ate is a glass plate covered with transparent and conductive indium tin oxide as the ground electrode. In addition, a Teflon AF1600 film is spun on the surface of both the plates as the hydrophobic layer. The experimental results show that when the gap height between two plates is 133μm, a prototype of the device is capable of creating, transporting, merging and dividing droplets of deionized water in an air environment with a 70V at lOHz voltage pulse. This is also established by simulations using the computational fluidic software of CFD-ACE＋.     

Direct Observation of the Molten State of Nanometer-sized Particles With an Atomic Force Microscope: A Feasibility Study

An atomic force microscope (AFM) was used to directly examine the physical state of nanometer-sized particles. The critical diameter of indium particles, where evidence of melting at room temperature was observed, was 7.8 ± 1.2nm. This conclusion is based on a method relying on the manipulation of particles in ambient air and at constant temperature. This method involves a simple set-up that permits a combination of both manipulation and imaging of individual particles. To determine whether a particle is molten, three criteria are used: the merging of particles to form bigger spherical particles, a tip-induced shape change, and the formation of nanofibers. All three criteria have been checked using other particle materials. An attempt at 56°C revealed oxidation of the indium particles as the major problem for melting investigation. Manipulations under high-purity nitrogen atmosphere support the validity of the findings. The use of the AFM to determine whether a nanoparticle is molten is, however, complicated by the oxidation issue.     

A kinetic approach to the calculation of surface tension of a spherical drop

In literature, surface tension has been investigated mainly from a Thermodynamics standpoint, more rarely with kinetic methods. In the present work, surface tension of drops is studied in the framework of kinetic theory, starting from the Sutherland approximation to Van Der Waals interaction between molecules. Surface tension is calculated as a function of drop radius: it is found that it approaches swiftly an asymptotic value, for radii of several times the distance of minimum approach D of the Sutherland potential. This theoretical asymptotic value is compared to experimental values of surface tension in plane surfaces of a few liquids, and is found in reasonable agreement.     

Towards controlled coupling between a high-Q whispering-gallery mode and a single nanoparticle

We discuss our recent experiments that aim at the realization of coupling between a nano-emitter that is placed at the extremity of a sharp glass-fiber tip and a high-Q whispering-gallery mode. We quantify the influence of the tip using different probes and modes of a microsphere with different quality factors and mode extensions. Our measurements show that a micron-sized tip results in a substantial perturbation of the modes. On the contrary, by using a tip of diameter about 100 nm it should be possible to couple a nanoparticle to the most-confined modes of a microsphere without spoiling quality factors even as high as 10⁸. Received: 10 August 2001 / Revised version: 17 October 2001 / Published online: 23 November 2001