State saturation

If a very high field is appHed the magnetisation can reach its saturated state ia which all the magnetic dipoles are aligned ia the direction of the field. If the magnetic field is switched off, the remanent magnetisation M is left. If the M (or B) is then reduced to sero, a special field strength, the coercivity, is required. 

Aluminum triformate [7360-53-4] commercially available as a white crystalline powder, appears amorphous under the microscope. Its solubiHty in cold water is very low, rising to nearly 25% in boiling water (pH 3.2). It remains in solution in a highly saturated state. Infared analysis of soHd aluminum... 

Although all the techniques are effective, in industrial appHcations there is rarely time to achieve an equiHbrium reduced saturation state (see Filtration), so variables that affect only the kinetics of dewatering and not the equiHbrium and residual moisture are also very important. The most important kinetic variables in displacing the Hquid from the soHd are increases in pressure differentials and viscosity reduction. 

The turboexpander should tolerate the proeess gas stream at a saturated state and eondensation through the expander wheel. 

The bipolar power transistor is a current driven device. To guarantee a switchlike operation, it must operate close or within its saturated state. For this to occur, the on base current must satisfy (also refer to Figure 3-29). 

The seeond seheme, shown in Figure 3-34, is ealled proportional base drive and always drives the transistor at or just below the transistor s saturation state. The eolleetor-emitter voltage is higher than with fixed base drive, but the transistor ean now switeh in about 100 to 200 nS. This is five to ten times faster than with fixed base drive. In praetiee, though, the fixed base drive seheme is used in the majority of low- to medium-power, low-eost applieations. Proportional base drive is used for the higher-power applieations. 

On the primary side of the power supply, the transistor output of the optoiso-lator will be a simple eommoii-emitter amplifier. The MOC8102 has a typieal eurreiit transfer ratio of 100 pereeiit with a +/- 25 pereeiit toleraiiee. When the TL431 is full-on, 6mA will be drawn from the transistor within the MOC8102. The transistor should be in a saturated state at that time, so its eolleetor resistor (Rl) must be... 

To control this loss one typically attempts to minimize the voltage drop across the power switch during its on-time. To do this, the designer must operate the switch in a saturated state. These conditions are given in Equations 4.2a and b. This is identified by overdriving the base or gate such that the collector or drain current is controlled by the external elements and not by the power switch itself. 

For PM control from combustion sources, the tlue gas enters a coagulation area (e.g., ductwork, a chamber, or a cyclone) to reduce the number of ultrafine particles, and then a gas conditioner to cool the gas to a suitable temperature and saturation state. This is generally accomplished by means of a waste heat recovery heat exchanger to reduce the temperature of the flue gas or by spraying water directly into the hot flue gas stream. 

Clausius (1850), in considering Regnault s data for the latent heat of steam, introduced a new specific heat, applicable to either phase of a saturated complex of two phases, viz., the amount of heat absorbed in raising the temperature of unit mass of a saturated phase by 1°, the pressure being at the same time varied so as to preserve the substance in a saturated state. In the case of a vapour, this is called the specific heat of saturated vapour (a). 

Table 11.1 Characteristics of phases (saturated state T = fOO °C) (Vargaftic et al. 1996)...

G. J. Hirasaki 2003, (Diffusion-relaxation distribution functions of sedimentary rocks in different saturation states), Magn. Reson. Imaging 21, 305-310. 

DDIF spectra were obtained on the sample at the several saturation states [65], DDIF spectra for full saturation and co-current imbibition with water saturation of 35.5 and 57.9% (Figure 3.7.6) were found to be of similar shape with a dominant peak at large pores and a shoulder extending to smaller pore sizes. This result... 

Fig. 3.7.6 DDIF spectra and SPRITE MRI images of Berea obtained in different saturation states. (A) The DDIF spectra during cocurrent imbibition at different water saturation (Sw) levels. Note the similar shape of DDIF spectra at different Sw. (B) The DDIF spectra during counter-current imbibition acquired at different water saturation levels. Note the change in the DDIF spectral shape for the different saturation levels. (C, D) A pair of images show 2D longitudinal slices from 3D...

In solutions saturated (i.e., excess solid present) at some pH, the plot of log Co versus pH for an ionizable molecule is extraordinarily simple in form it is a combination of straight segments, joined at points of discontinuity indicating the boundary between the saturated state and the state of complete dissolution. The pH of these junction points is dependent on the dose used in the calculation, and the maximum value of log Co is always equal to log. Sb in a saturated solution. [26] Figure 2.2 illustrates this idea using ketoprofen as an example of an acid, verapamil as a base, and piroxicam as an ampholyte. In the three cases, the assumed concentrations in the calculation were set to the respective doses [26], For an acid, log Co (dashed curve in Fig. 2.2a) is a horizontal line (log Co = log So) in the saturated solution (at low pH), and decreases with a slope of —1 in the pH domain where the solute is dissolved completely. For a base (Fig. 2.2b) the plot of log Co versus pH is also a horizontal line at high pH in a saturated solution and is a line with a slope of +1 for pH values less than the pH of the onset of precipitation. 

Regardless of the flux mechanism, it is clear upon examination of permeability expressions that flux is proportional to the concentration differential across the total barrier to mass transport. This flux is maximal in a given system for a permeant when the penetrating agent is present in the applied phase in a saturated state. There are many situations of pharmaceutical interest where this solubility... 

Langdon, C., Takahashi, T., Sweeney, C., Chipman, D., Goddard, J., Marubini, F., Aceves, H., Barnett, H., and Atkinson, M.J., Effect of calcium carbonate saturation state on the calcification rate of an experimental coral reef, Global Biogeochem. Cy., 14, 639-654,2000. 

Figure 6-8 shows how the partial pressure of carbon dioxide in equilibrium with surface water oscillates in phase with the fluctuations in precipitation rate, saturation state, and temperature. The oscillations in alkalinity and bicarbonate concentrations have shifted in phase by about 90° because these quantities decrease when precipitation and evaporation are removing carbon from the system at above-average rates. 

These three numerical experiments show how the waters of an evaporating lagoon respond differently to the different seasonal perturbations that might affect them. Some record of these perturbations might, in principle, be preserved in the carbonate sediments precipitated in the lagoon. All three perturbations—productivity, temperature, and evaporation rate— cause seasonal fluctuations in the saturation state of the water and in the rate of carbonate precipitation. Temperature oscillations have little effect on the carbon isotopes. Although seasonally varying evaporation rates affect 14C, they have little effect on 13C. Productivity fluctuations affect both of the carbon isotopes. 

Like the climate system described in Chapter 7, this diagenetic system consists of a chain of identical reservoirs that are coupled only to adjacent reservoirs. Elements of the sleq array are nonzero close to the diagonal only. Unnecessary work can be avoided and computational speed increased by limiting the calculation to the nonzero elements. The climate system, however, has only one dependent variable, temperature, to be calculated in each reservoir. The band of nonzero elements in the sleq array is only three elements wide, corresponding to the connection between temperatures in the reservoir being calculated and in the two adjacent reservoirs. The diagenetic system here contains two dependent variables, total dissolved carbon and calcium ions, in each reservoir. The species are coupled to one another in each reservoir by carbonate dissolution and its dependence on the saturation state. They also are coupled by diffusion to their own concentrations in adjacent reservoirs. The method of solution that I shall develop in this section can be applied to any number of interacting species in a one-dimensional chain of identical reservoirs. 

Garrels and Thompson s calculation, computed by hand, is the basis for a class of geochemical models that predict species distributions, mineral saturation states, and gas fugacities from chemical analyses. This class of models stems from the distinction between a chemical analysis, which reflects a solution s bulk composition, and the actual distribution of species in a solution. Such equilibrium models have become widely applied, thanks in part to the dissemination of reliable computer programs such as SOLMNEQ (Kharaka and Barnes, 1973) and WATEQ (Truesdell and Jones, 1974). 

In the simplest class of geochemical models, the equilibrium system exists as a closed system at a known temperature. Such equilibrium models predict the distribution of mass among species and minerals, as well as the species activities, the fluid s saturation state with respect to various minerals, and the fugacities of different gases that can exist in the chemical system. In this case, the initial equilibrium system constitutes the entire geochemical model. 

The saturation state of each mineral that can form in a model must be checked once the iteration is complete to identify supersaturated minerals. A mineral 4/, which is not in the basis, forms by the reaction... 

The program produces in its output dataset a block of results that shows the concentration, activity coefficient, and activity calculated for each aqueous species (Table 6.4), the saturation state of each mineral that can be formed from the basis, the fugacity of each such gas, and the system s bulk composition. The extent of the system is 1 kg of solvent water and the solutes dissolved in it the solution mass is 1.0364 kg. 

Error in the input data can also be significant. The saturation state calculated for an aluminosilicate mineral, for example, depends on the analytical concentrations determined for aluminum and silicon. These analyses are difficult to perform accurately. As discussed in the next section, the presence of colloids and suspended particles in solution often affects the analytical results profoundly. 

Finally, common ion effects link many mineral precipitation reactions, so the reactions do not operate independently. In the seawater example, dolomite precipitation consumed magnesium and produced hydrogen ions, significantly altering the saturation states of the other supersaturated minerals. 

The second model is perhaps more attractive than the first because the predicted saturation states seem more reasonable. The assumption of equilibrium with kaoli-nite and hematite can be defended on the basis of known difficulties in analyzing for dissolved aluminum and iron. Nonetheless, on the basis of information available to us, neither model is correct or incorrect they are simply founded on differing assumptions. The most that we can say is that one model may prove more useful for our purposes than the other. 

The dissolution rate, according to the theory, does not depend on the mineral s saturation state. The precipitation rate, on the other hand, varies strongly with saturation, exceeding the dissolution rate only when the mineral is supersaturated. At the point of equilibrium, the dissolution rate matches the rate of precipitation so that the net rate of reaction is zero. There is, therefore, a strong conceptual link between the kinetic and thermodynamic interpretations equilibrium is the state in which the forward and reverse rates of a reaction balance. 

There is no certainty, furthermore, that the reaction or reaction mechanism studied in the laboratory will predominate in nature. Data for reaction in deionized water, for example, might not apply if aqueous species present in nature promote a different reaction mechanism, or if they inhibit the mechanism that operated in the laboratory. Dove and Crerar (1990), for example, showed that quartz dissolves into dilute electrolyte solutions up to 30 times more quickly than it does in pure water. Laboratory experiments, furthermore, are nearly always conducted under conditions in which the fluid is far from equilibrium with the mineral, although reactions in nature proceed over a broad range of saturation states across which the laboratory results may not apply. 

Fig. 16.1. Results of reacting quartz sand at 100°C with deionized water, calculated according to a kinetic rate law. Top diagram shows how the saturation state Q/K of quartz varies with time bottom plot shows change in amount (mmol) of quartz in system (bold line). The slope of the tangent to the curve (fine line) is the instantaneous reaction rate, the negative of the dissolution rate, shown at one day of reaction.

The predicted saturation states of the formation minerals (Fig. 23.5), furthermore, no longer identify a unique formation temperature. Whereas the temperatures suggested by albite, quartz, and potassium feldspar are quite close to the 250 °C formation temperature, those predicted by assuming that the fluid was in equilibrium with muscovite and calcite are too low, respectively, by margins of about 25 °C and 100 °C. To avoid error of this sort, we would need to determine the amount of gas lost from the sample and reintroduce it to the equilibrium system before calculating saturation indices. 

From a plot of the saturation states of the silica polymorphs (Fig. 23.7), the fluid s equilibrium temperature with quartz is about 100 °C. Quartz, however, is commonly supersaturated in geothermal waters below about 150 °C and so can give erroneously high equilibrium temperatures when applied in geothermometry (Fournier, 1977). Chalcedony is in equilibrium with the fluid at about 76 °C, a temperature consistent with that suggested by the aluminosilicate minerals. 

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