Contact curvature

In general there are two factors capable of bringing about the reduction in chemical potential of the adsorbate, which is responsible for capillary condensation the proximity of the solid surface on the one hand (adsorption effect) and the curvature of the liquid meniscus on the other (Kelvin effect). From considerations advanced in Chapter 1 the adsorption effect should be limited to a distance of a few molecular diameters from the surface of the solid. Only at distances in excess of this would the film acquire the completely liquid-like properties which would enable its angle of contact with the bulk liquid to become zero thinner films would differ in structure from the bulk liquid and should therefore display a finite angle of contact with it. 

Butterfly Valves These valves (Fig. 10-155) occupy less space in the line than any other valves. Relatively tight sealing without excessive operating torque and seat wear is accomphshed by a variety of methods, such as resilient seats, piston rings on the disk, and inclining the stem to limit contact between the portions of disk closest to the stem and the body seat to a few degrees of curvature. 

Slip-ring motors need a regular and meticulous check of brushes, brush holder unit and slip-rings for cleanliness, accurate contacts, brush curvature, wear and tear of slip-rings and arcing (Figure 10.5). The following procedure may be followed ... 

Contact mechanics deals with the deformation of solids in contact. Consider two elastic bodies, shown schematically in Fig. 3, of radii of curvature R[ and Rt, Young s moduli E and E2, and Poisson s ratios and V2. Define... 

When the surfaces are in contact due to the action of the attractive interfacial forces, a finite tensile load is required to separate the bodies from adhesive contact. This tensile load is called the pull-off force (P ). According to the JKR theory, the pull-off force is related to the thermodynamic work of adhesion (W) and the radius of curvature (/ ). 

Israelachvili and coworkers [64,69], Tirrell and coworkers [61-63,70], and other researchers employed the SFA to measure molecular level adhesion and deformation of self-assembled monolayers and polymers. The pull-off force (FJ, and the contact radius (a versus P) are measured. The contact radius, the local radius of curvature, and the distance between the surfaces are measured using the optical interferometer in the SFA. The primary advantage of using the SFA is its ability to study the interfacial adhesion between thin films of relatively high... 

In an attempt to determine the applicability of JKR and DMT theories, Lee [91] measured the no-load contact radius of crosslinked silicone rubber spheres in contact with a glass slide as a function of their radii of curvature (R) and elastic moduli (K). In these experiments, Lee found that a thin layer of silicone gel transferred onto the glass slide. From a plot of versus R, using Eq. 13 of the JKR theory, Lee determined that the work of adhesion was about 70 7 mJ/m". a value in clo.se agreement with that determined by Johnson and coworkers 6 using Eqs. 11 and 16. 

A similar analysis can be done for the curved surface of an essentially spherical particle that contains asperities. Let us assume that all the asperities are the same size. Initially, no more than three asperities on the particle can contact the presumably smooth surface. As the asperities compress under the applied load, more asperities, that are situated further away from the substrate due to the curvature of the particle s surface, come into contact. These are the first to separate from the substrate upon application of a detachment force. In essence, detachment occurs by breaking the contacts between the asperities and the contacting surface, one at a time. 

The force p needed to compress a single asperity and the displacement 8 of its tip relative to the undeformed region of the substrate was calculated using JKR theory and determined to be related to the radius of curvature of the asperity and the contact radius a by... 

To make contact with the SEA experiment one has to realize that the confining surfaces are only locally parallel. Because of the macroscopic curvature of the substrate surfaces, Tzz becomes a local quantity which varies with the vertical distance Sz = Sz x,y) between the substrate surfaces (see Fig. 2). Since the sphere-plane arrangement (see Sec. II Al) is immersed in bulk fluid at pressure Pbuik the total force exerted on the sphere by the film in... 

Ophthalmic—steepening of corneal curvature, intolerance to contact lenses... 

For solid contacts in vapor atmosphere, liquid would condense from the vapor into cracks and pores formed between the contacting surfaces. As a result, a small liquid bridge appears around the contact spot and a meniscus with the curvature of (l/rj-i- l/r2) forms at the solid-liquid-vapor interface, as illustrated in Fig. 4 for a microscopic sphere in contact with a solid plane. 

In 1996, Liu et al. [129] analyzed the wear mechanism based on the rolling kinematics of abrasive particles between the pad and wafer. They summarized that the kinetics of polishing are (1) material removal rate is dependent on the real contact area between the slurry particle and the wafer surface. The real contact area is related to the applied pressure, the curvature, and Young s modulus of the slurry... 

The model is found to be most appropriate for contact between low-elastic-moduli materials with large radii when the work of adhesion is high. In comparison, the following model assumes that the surface forces extend over a finite range and act in the region just outside the contact. It is found to be more appropriate for systems with small radii of curvature, low work of adhesion, and high modulus [12]. 

In many cases the potential P(z) is small compared with the surface energy of the liquid and the droplet shape is very close to a spherical cap. If the height e and the radius of curvature R at the top of the droplets can be measured, an effective contact angle can be defined through the expression ... 

Ideally one would like to visualize the molecular-scale details at the edge of a droplet to obtain direct information about the molecular nature of wetting. This is not always possible, particularly when these details have dimensions below 300 A, the resolution limit of SPFM. However, the height and curvature of a droplet can usually be measured accurately. These parameters can then be used to obtain an effective contact angle, as defined in Eq. (10). We present here a few examples of this type of study. 

In the theoretical section above, the nonlinear polarization induced by the fundamental wave incident on a planar interface for a system made of two centrosymmetrical materials in contact was described. However, if one considers small spheres of a centrosymmetrical material embedded in another centrosymmetrical material, like bubbles of a liquid in another liquid, the nonlinear polarization at the interface of a single sphere is a spherical sheet instead of the planar one obtained at planar surfaces. When the radius of curvature is much smaller than the wavelength of light, the electric field amplitude of the fundamental electromagnetic wave can be taken as constant over the whole sphere (see Fig. 7). Hence, one can always find for any infinitely small surface element of the surface... 

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