Curved surfaces, pressure

The thermographic activity on the pressure vessel was carried out considering a part of it because of the axial symmetry. Three different partially overlapping area were inspected since it was optically impossible to scan the curved surface of the pressure vessel by a single sweep. The selected areas are shown in fig.7 and the correspondent positions of the thermographic scan unit are also illustrated. The tests were performed with a load frequency of 2, 5 and 10 Hz. 

Fig. IV-21. Surface pressure versus area for monolayers of immiscible components a monolayer of pure cadmium arachidate (curve 1) and monolayers of mixed merocyanine dye, MC2, and cadmium arachidate of molar ratio r = 1 10 (curve 2) 1 5 (curve 3), 1 2 (curve 4), and pure MC2 (curve 5). The subphase is 2.5 x 0 M CdC, pH = 5.5 at 20°C. Curve 3a (O) was calculated from curves 1 and 5 using Eq. IV-44. (From Ref. [116].)...

The Kelvin equation (Eq. HI-18), which gives the increase in vapor pressure for a curved surface and hence of small liquid drops, should also apply to crystals. Thus... 

For some types of wetting more than just the contact angle is involved in the basic mechanism of the action. This is true in the laying of dust and the wetting of a fabric since in these situations the liquid is required to penetrate between dust particles or between the fibers of the fabric. TTie phenomenon is related to that of capillary rise, where the driving force is the pressure difference across the curved surface of the meniscus. The relevant equation is then Eq. X-36,... 

Ultimately, the surface energy is used to produce a cohesive body during sintering. As such, surface energy, which is also referred to as surface tension, y, is obviously very important in ceramic powder processing. Surface tension causes liquids to fonn spherical drops, and allows solids to preferentially adsorb atoms to lower tire free energy of tire system. Also, surface tension creates pressure differences and chemical potential differences across curved surfaces tlrat cause matter to move. 

The Laplace equation, which defines tire pressure difference, AP, across a curved surface of radius, r. 

The equilibrium vapour pressure, P, over a curved surface is defined by tlie Kelvin equation... 

Equations (5,61) and (5.62) can be used to derive a pressure potential equation applicable to thin-layer flow between curved surfaces using the following procedure. In a thin-layer flow, the following velocity boundary conditions are prescribed ... 

The force exerted on a submerged planar surface of area A is given by F = p A where p is the pressure at the geometrical centroid of the surface. The center of pressure, the point of application of the net force, is always lower than the centroid. For details see, for example. Shames, where may also be found discussion of forces on curved surfaces, buoyancy, and stability of floating bodies. 

The pitot tube is used to measure the difference between the impact and static pressures in a fluid. It normally consists of two concentric tubes arranged parallel to the direction of flow the impact pressure is measured on the open end of the inner tube. The end of the outer concentric tube is sealed and a series of orifices on the curved surface give an accurate indication of the static pressure. The position of these orifices must be carefully chosen because there are two disturbances which may cause an incorrect reading of the static pressure. These are due to ... 

FIG. 23 Surface pressure vs. area/molecule isotherms at 300 K from molecular dynamics simulations of Karaborni et al. (Refs. 362-365). All are for hydrocarbon chains with carboxylate-like head groups, (a) (filled squares) A 20-carbon chain, (b) (filled circles) A 16-carbon chain with a square simulation box the curve is shifted 5 A to the right, (c) (open squares) A 16-carbon chain with a nonsquare box with dimensions in the ratio xly = (3/4) to fit a hexagonal lattice the curve is shifted 5 A to the right. (Reproduced with permission from Ref. 365. Copyright 1993 American Chemical Society.)... 

Salts of fatty acids are classic objects of LB technique. Being placed at the air/water interface, these molecules arrange themselves in such a way that its hydrophilic part (COOH) penetrates water due to its electrostatic interactions with water molecnles, which can be considered electric dipoles. The hydrophobic part (aliphatic chain) orients itself to air, because it cannot penetrate water for entropy reasons. Therefore, if a few molecnles of snch type were placed at the water surface, they would form a two-dimensional system at the air/water interface. A compression isotherm of the stearic acid monolayer is presented in Figure 1. This curve shows the dependence of surface pressure upon area per molecnle, obtained at constant temperature. Usually, this dependence is called a rr-A isotherm. 

Capillary phenomena are due to the curvature of liquid surfaces. To maintain a curved surface, a force is needed. In Eq. (8), this force is related to the second term in the integral. The so-called Laplace pressure due to the force to maintain the curved surface can be expressed as, Pl = 2-yIr, where r is the curvature radius. The combination of the capillary effects and disjoining pressure can make a liquid film climb a wall. 

At the curved surface of the sphere, a force is acting that is directed toward the center of the sphere and tends to reduce its surface area. Hence, the gas pressure in the nucleus will be higher than the pressure Pq in the surrounding medium. An infinitely small displacement dr of tfie surface in the direction of the sphere s center is attended by a surface-area decrease dS = Snrdr) and a volume decrease dV (= dr). The work of compression of the nucleus is given by (Pnuci It... 

FIG. 28 Normalized steady-state diffusion-limited current vs. UME-interface separation for the reduction of oxygen at an UME approaching an air-water interface with 1-octadecanol monolayer coverage (O)- From top to bottom, the curves correspond to an uncompressed monolayer and surface pressures of 5, 10, 20, 30, 40, and 50 mN m . The solid lines represent the theoretical behavior for reversible transfer in an aerated atmosphere, with zero-order rate constants for oxygen transfer from air to water, h / Q mol cm s of 6.7, 3.7, 3.3, 2.5, 1.8, 1.7, and 1.3. (Reprinted from Ref. 19. Copyright 1998 American Chemical Society.)... 

The results of this study demonstrated that the rate of oxygen transfer across a clean air-water interface was diffusion-controlled on the time scale of SECM measurements. The rate of this transfer process was, however, significantly reduced with increasing compression of a 1-octadecanol monolayer. Figure 28 illustrates this point, showing approach curves for O2 reduction recorded with the monolayer at different surface pressures. The transfer rate was found to depend on the accessible free area of the interface, as described by the following equation ... 

We studied the surface pressure area isotherms of PS II core complex at different concentrations of NaCl in the subphase (Fig. 2). Addition of NaCl solution greatly enhanced the stability of monolayer of PS II core complex particles at the air-water interface. The n-A curves at subphases of 100 mM and 200 mM NaCl clearly demonstrated that PS II core complexes can be compressed to a relatively high surface pressure (40mN/m), before the monolayer collapses under our experimental conditions. Moreover, the average particle size calculated from tt-A curves using the total amount of protein complex is about 320 nm. This observation agrees well with the particle size directly observed using atomic force microscopy [8], and indicates that nearly all the protein complexes stay at the water surface and form a well-structured monolayer. 

In porous media, liquid-gas phase equilibrium depends upon the nature of the adsorbate and adsorbent, gas pressure and temperature [24]. Overlapping attractive potentials of the pore walls readily overcome the translational energy of the adsorbate, leading to enhanced adsorption of gas molecules at low pressures. In addition, condensation of gas in very small pores may occur at a lower pressure than that normally required on a plane surface, as expressed by the Kelvin equation, which relates the radius of a curved surface to the equilibrium vapor pressure [25],... 

Figure 17 shows the 11/A isotherms of racemic and enantiomeric films of the methyl esters of 7V-stearoyl-serine, -alanine, -tryptophan, and -tyrosine on clean water at 25°C. Although there appears to be little difference between the racemic and enantiomeric forms of the alanine surfactants, the N-stearoyl-tyrosine, -serine, and -tryptophan surfactants show clear enantiomeric discrimination in their WjA curves. This chiral molecular recognition is first evidenced in the lift-off areas of the curves for the racemic versus enantiomeric forms of the films (Table 2). As discussed previously, the lift-off area is the average molecular area at which a surface pressure above 0.1 dyn cm -1 is first registered. The packing order differences in these films, and hence their stereochemical differentiation, are apparently maintained throughout the compression/expansion cycles. 

Mixtures of N-(a-methylbenzyl) stearamides with both stearoyltyrosine and stearoyltryptophan methyl esters show no discrimination in their pressure-area relationships at 35°C, regardless of the surface pressure to which the films are compressed (Fig. 34). The Yl/A curves for homo- and hetero-chiral pairs are exactly coincident. 

Furthermore, we employ the same assumptions to describe a different set of hysteresis experiments a monolayer with surface pressure it at equilibrium is subjected to expansion at a constant speed of v cm /sec. The theoretical curves of surface pressure are plotted against area for various q-values in Figure 4. The curves show that the reduction of surface pressure decreases when the expansion rate is decreased for a given mono-layer, i.e. as q becomes more negative. In Figure 5, curves are plotted for q = -2 with the two different modes initial compression and initial expansion. Because the theoretical curves of the second and subsequent cycles in both modes almost coincide, we can expect that the surface pressure vs. area curves will be independent of how the hysteresis experiment starts after about two initial cycles. 

Such a relation between surface tension and vapour pressure was first established by Lord Kelvin, who demonstrated that the vapour pressure over a curved surface must be different from that over a plane surface of the same liquid. His proof cannot be given here, but the following simple considera-... 

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