Pressure nucleation

Stander [23] concluded that slow movement of the phase boundary is the ratecontrolling step at pressures appreciably different from the equilibrium pressure. At pressures near the equilibrium pressure nucleation seems to play a role. The difference in activation energy for the two mechanisms cannot be regarded as being significant. Furthermore, as the reaction proceeds, nucleation will become less important. Eventually he concluded that nucleation is kinetically unimportant in the decomposition... 

Vertical/horizontal thermo syphon use for clean, relatively low-pressure, nucleate pool boiling 5 to 25% vaporized. Use 45 to 56 kW/m heat flnx for hydrocarbon and petrochemicals, 62 to 75 for aqueous, and 37 to 44 for vacnnm. Rarely used for vacuum or very high-pressure service. U = 1 kW/m K. 

Nitrogen (Fig. 3) has been studied by many investigators, particularly at 1 atm (TjTc 0.61). The high atmospheric superheat data represent mixed boiling at a broad (AT) maximum, whereas the low values are more likely actual nucleate boiling results. At subatmos-pheric pressures nucleate boiling has been found to be poorly developed on thin wires [ ]. 

Figure S. Variations of the specific rate of Figure 6. Variations of the specific rate of growth against oxygen partial pressure nucleation against oxygen partial pressure...

The relation of Tj or better of and AHm (and AVjj) to molecular structure of crystalline polymers has been thoroughly discussed elsewhere ( ) and its display would go beyond the scope of this review. Suffice if to say here, that Tm at atmospheric pressure is measured so easily that its estimation by predictive methods seems an uneconomical thing to do. The estimation of the slope of the Tm vs. P line, ( ) the so-called melting curve of crystalline polymers seems no more difficult than of other substances. However, given the high viscosity of the polymer melt, especially at high pressures, nucleation may be so retarded, to make experimental melting point determination quite uncertain. 

This effect assumes importance only at very small radii, but it has some applications in the treatment of nucleation theory where the excess surface energy of small clusters is involved (see Section IX-2). An intrinsic difficulty with equations such as 111-20 is that the treatment, if not modelistic and hence partly empirical, assumes a continuous medium, yet the effect does not become important until curvature comparable to molecular dimensions is reached. Fisher and Israelachvili [24] measured the force due to the Laplace pressure for a pendular ring of liquid between crossed mica cylinders and concluded that for several organic liquids the effective surface tension remained unchanged... 

The formation of a liquid phase from the vapour at any pressure below saturation cannot occur in the absence of a solid surface which serves to nucleate the process. Within a pore, the adsorbed film acts as a nucleus upon which condensation can take place when the relative pressure reaches the figure given by the Kelvin equation. In the converse process of evaporation, the problem of nucleation does not arise the liquid phase is already present and evaporation can occur spontaneously from the meniscus as soon as the pressure is low enough. It is because the processes of condensation and evaporation do not necessarily take place as exact reverses of each other that hysteresis can arise. 

The variant of the cylindrical model which has played a prominent part in the development of the subject is the ink-bottle , composed of a cylindrical pore closed one end and with a narrow neck at the other (Fig. 3.12(a)). The course of events is different according as the core radius r of the body is greater or less than twice the core radius r of the neck. Nucleation to give a hemispherical meniscus, can occur at the base B at the relative pressure p/p°)i = exp( —2K/r ) but a meniscus originating in the neck is necessarily cylindrical so that its formation would need the pressure (P/P°)n = exp(-K/r ). If now r /r, < 2, (p/p ), is lower than p/p°)n, so that condensation will commence at the base B and will All the whole pore, neck as well as body, at the relative pressure exp( —2K/r ). Evaporation from the full pore will commence from the hemispherical meniscus in the neck at the relative pressure p/p°) = cxp(-2K/r ) and will continue till the core of the body is also empty, since the pressure is already lower than the equilibrium value (p/p°)i) for evaporation from the body. Thus the adsorption branch of the loop leads to values of the core radius of the body, and the desorption branch to values of the core radius of the neck. 

Type V isotherms of water on carbon display a considerable variety of detail, as may be gathered from the representative examples collected in Fig. 5.14. Hysteresis is invariably present, but in some cases there are well defined loops (Fig. 5.14(b). (t ), (capillary-condensed water. Extreme low-pressure hysteresis, as in Fig. 5.14(c) is very probably due to penetration effects of the kind discussed in Chapter 4. 

Increases in the appHed static pressure increase the acoustic intensity necessary for cavitation, but if equal number of cavitation events occur, the coUapse should be more intense. In contrast, as the ambient pressure is reduced, eventuaUy the gas-fiUed crevices of particulate matter which serve as nucleation sites for the formation of cavitation in even "pure" Hquids, wiU be deactivated, and therefore the observed sonochemistry wiU be diminished. 

Initiation and Growth of Cells. The initiation or nucleation of cells is the formation of cells of such size that they are capable of growth under the given conditions of foam expansion. The growth of a hole or cell in a fluid medium at equiUbrium is controlled by the pressure difference (AP) between the inside and the outside of the cell, the surface tension of the fluid phase y, and the radius r of the cell ... 

The mathematical formulation of forced convection heat transfer from fuel rods is well described in the Hterature. Notable are the Dittus-Boelter correlation (26,31) for pressurized water reactors (PWRs) and gases, and the Jens-Lottes correlation (32) for boiling water reactors (BWRs) in nucleate boiling. 

Wet preparation of red iron oxides can involve either a hydrothermal process (see Hydrothermal processing) or a direct precipitation and growth of iron oxide particles on specially prepared nucleating seeds of Fe202- In the hydrothermal process, iron(II) salt is chemically oxidized to iron(III) salt, which is further treated by alkahes to precipitate a hydrated iron(III) oxide gel. The gel can be dehydrated to anhydrous hematite under pressure at a temperature around 150°C. 

The relative effectiveness of nucleating agents in a polymer can be determined by measuring recrystallization exotherms of samples molded at different temperatures (105). The effect of catalyst concentration and filler content has been determined on unsaturated polyesters by using dynamic thermal techniques (124). Effects of formulation change on the heat of mbber vulcanization can be determined by dsc pressurized cells may be needed to reduce volatilization during the cure process (125). 

Under equiUbrium vapor pressure of water, the crystalline tfihydroxides, Al(OH)2 convert to oxide—hydroxides at above 100°C (9,10). Below 280°—300°C, boehmite is the prevailing phase, unless diaspore seed is present. Although spontaneous nucleation of diaspore requires temperatures in excess of 300 °C and 20 MPa (200 bar) pressure, growth on seed crystals occurs at temperatures as low as 180 °C. For this reason it has been suggested that boehmite is the metastable phase although its formation is kinetically favored at lower temperatures and pressures. The ultimate conversion of the hydroxides to comndum [1302-74-5] AI2O2, the final oxide form, occurs above 360°C and 20 MPa. 

Crystal Morphology. Size, shape, color, and impurities are dependent on the conditions of synthesis (14—17). Lower temperatures favor dark colored, less pure crystals higher temperatures promote paler, purer crystals. Low pressures (5 GPa) and temperatures favor the development of cube faces, whereas higher pressures and temperatures produce octahedral faces. Nucleation and growth rates increase rapidly as the process pressure is raised above the diamond—graphite equiUbrium pressure. 

In a typical use of this method, a mixture of hydrogen and methane is fed into a reaction chamber at a pressure of about 1.33 kPa (10 torr). The substrate upon which diamond forms is at about 950°C and Hes about 1 cm away from a tungsten wine at 2200°C. Small diamond crystals, 1 mm or so in si2e, nucleate and grow profusely on the substrate at a rate around 0.01 mm /h to form a dark, rough polycrystalline layer with exposed octahedral or cubic faces, depending on the substrate temperature. 

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