Spherical interface

FIG. 2 Schematic representation of different microhole geometries, (a) Recessed microdisk interface, spherical-linear, linear-spherical diffusion, (b) quasi-inlaid microdisk interface, spherical-spherical diffusion, (c) Long microhole with quasi-inlaid interface, spherical-linear diffusion. (Reprinted with permission from Ref. 13. Copyright 1999 Elsevier Science S.A.)... 

Water-ions induced nanoslructuration Adsorption of ions at the interface Spherical-cap-shaped bumps Few tens of nanometers Depend of the amount of gas dissolved in the water, ions in solution and temperature [12, 180, 181]... 

We still refer to Figure 9.11. This time the area of the internal interface (spherical sector DC ) is expressed as follows ... 

Surface tension arises at a fluid to fluid interface as a result of the unequal attraction between molecules of the same fluid and the adjacent fluid. For example, the molecules of water in a water droplet surrounded by air have a larger attraction to each other than to the adjacent air molecules. The imbalance of forces creates an inward pull which causes the droplet to become spherical, as the droplet minimises its surface area. A surface tension exists at the interface of the water and air, and a pressure differential exists between the water phase and the air. The pressure on the water side is greater due to the net inward forces... 

The basic phenomenon involved is that particles of ore are carried upward and held in the froth by virtue of their being attached to an air bubble, as illustrated in the inset to Fig. XIII-4. Consider, for example, the gravity-free situation indicated in Fig. XIII-5 for the case of a spherical particle. The particle may be entirely in phase A or entirely in phase B. Alternatively, it may be located in the interface, in which case both 7sa nnd 7sb contribute to the total surface free energy of the system. Also, however, some liquid-liquid interface has been eliminated. It may be shown (see Problem XIII-12) that if there is a finite contact angle, 0sab> the stable position of the particle is at the interface, as shown in Fig. XIII-5Z>. Actual measured detachment forces are in the range of 5 to 20 dyn [60]. 

Fig. 3. Two-dimensional schematic illustrating the distribution of Hquid between the Plateau borders and the films separating three adjacent gas bubbles. The radius of curvature r of the interface at the Plateau border depends on the Hquid content and the competition between surface tension and interfacial forces, (a) Flat films and highly curved borders occur for dry foams with strong interfacial forces, (b) Nearly spherical bubbles occur for wet foams where...

In chemicals like salol the molecules are elongated (non-spherical) and a lot of energy is needed to rotate the randomly arranged liquid molecules into the specific orientations that they take up in the crystalline solid. Then q is large, is small, and the interface is very sluggish. There is plenty of time for latent heat to flow away from the interface, and its temperature is hardly affected. The solidification of salol is therefore interface controlled the process is governed almost entirely by the kinetics of molecular diffusion at the interface. 

In metals the situation is quite the opposite. The spherical atoms move easily from liquid to solid and the interface moves quickly in response to very small undercoolings. Latent heat is generated rapidly and the interface is warmed up almost to T, . The solidification of metals therefore tends to be heat-flow controlled rather than interface controlled. 

If we know the contact angle we can work out r quite easily. We assume that the nucleus is a spherical cap of radius r and use standard mathematical formulae for the area of the solid-liquid interface, the area of the catalyst-solid interface and the volume of the nucleus. For 0 0 90° these are ... 

In finite boundary conditions the solute molecule is surrounded by a finite layer of explicit solvent. The missing bulk solvent is modeled by some form of boundary potential at the vacuum/solvent interface. A host of such potentials have been proposed, from the simple spherical half-harmonic potential, which models a hydrophobic container [22], to stochastic boundary conditions [23], which surround the finite system with shells of particles obeying simplified dynamics, and finally to the Beglov and Roux spherical solvent boundary potential [24], which approximates the exact potential of mean force due to the bulk solvent by a superposition of physically motivated tenns. 

Two basic principles govern the arrangement of protein subunits within the shells of spherical viruses. The first is specificity subunits must recognize each other with precision to form an exact interface of noncovalent interactions because virus particles assemble spontaneously from their individual components. The second principle is genetic economy the shell is built up from many copies of a few kinds of subunits. These principles together imply symmetry specific, repeated bonding patterns of identical building blocks lead to a symmetric final structure. 

In the JKR experiments, a macroscopic spherical cap of a soft, elastic material is in contact with a planar surface. In these experiments, the contact radius is measured as a function of the applied load (a versus P) using an optical microscope, and the interfacial adhesion (W) is determined using Eqs. 11 and 16. In their original work, Johnson et al. [6] measured a versus P between a rubber-rubber interface, and the interface between crosslinked silicone rubber sphere and poly(methyl methacrylate) flat. The apparatus used for these measurements was fairly simple. The contact radius was measured using a simple optical microscope. This type of measurement is particularly suitable for soft elastic materials. 

Fig. 4. (a) Motion of minor chains that have poked through from one side of the interface, (b) Growth of the minor chain spherical envelopes that have emerged from side of the interface. 

The model has been successfully used to describe wetting behavior of the microemulsion at the oil-water interface [12,18-20], to investigate a few ordered phases such as lamellar, double diamond, simple cubic, hexagonal, or crystals of spherical micelles [21,22], and to study the mixtures containing surfactant in confined geometry [23]. 

Solomatov et al. [131] derived an equation for strength at the polymer - spherical particle interface ... 

Where the particle of B contains m molecules, AGB is the bulk free energy change per molecule, a is the shape factor (4irr2 for a spherical interface) and y is the strain energy per unit area of interface. For a spherical nucleus, where vm is the volume of product per molecule ,... 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

Morphology of the anionically synthesized triblock copolymers of polyfp-methyl-styrene) and PDMS and their derivatives obtained by the selective chlorination of the hard segments were investigated by TEM 146). Samples with low PDMS content (12%) showed spherical domains of PDMS in a poly(p-methylstyrene) matrix. Samples with nearly equimolar composition showed a continuous lamellar morphology. In both cases the domain structure was very fine, indicating sharp interfaces. Domain sizes were estimated to be of the order of 50-300 A. 

The liquid alone pattern showed no entrained bubbles or gas-liquid interface in the field of view. The capillary bubbly flow, in the upper part of Fig. 5.14a, is characterized by the appearance of distinct non-spherical bubbles, generally smaller in the streamwise direction than at the base of the triangular channel. This flow pattern was also observed by Triplett et al. (1999a) in the 1.097 mm diameter circular tube, and by Zhao and Bi (2001a) in the triangular channel of hydraulic diameter of 0.866 mm. This flow, referred to by Zhao and Bi (2001a) as capillary bubbly... 

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