Range of applicability

The use of equation (8.40) involves the assumption that there will be good data available for a and 6 for all ionic species over broad ranges of temperature. As a matter of fact, data on ionic heat capacities for temperatures above 200 C have 

The usual procedure for handling systems which do not respond to the P MEAN Approach is to rely on experimentally determined  

The calculations we have performed apply to the conduction regime because of the assumption that 6 is constant in time. The range of this regime has been discussed in detail by Dubois-Violette et al and shown experimentally by Meyerhofer and Sussman. The low-frequency limit varies as below this frequency both 0 and p are 

The conduction regime as described by Figs. 2 to 4 occurs in suitably doped nematic liquid crystals of negative dielectric anisotropy. This can be seen qualitatively by studying the denominator of Eq. [32]. The first (viscous) term must be larger than the second (dielectric) term for the denominator to be positive and instability to occur. This restricts negative values of Ae to the range —2 to 0 for materials 

[32] shows that instability can also take place for Ae 0, as discussed by Dubois-Violette and Penz. In that case, the threshold voltage becomes independent of frequency at high frequency, but this is not a conduction regime because Vth is then only dependent on k and 6. Furthermore, this threshold is higher than that of the dielectric Freedericksz transition for the case of the entire sample deforming uniformly (S = 0, Vth = Tx/kn/Ae), and so will not occur. In fact. 

Williams domains will occur only over the range of Ae from 0 to approximately 0.5. These considerations are in agreement with experimental observations.  

Meyerhofer and A. Sussman, Electrohydrodynamic Instabilities in Nematic Liquid Crystals in Low-Frequency Fields, Appl. Rhys. Lett., 20, p. 337 (1972). 

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The fluid properties of formation water may be looked up on correlation charts, as may most of the properties of oil and gas so far discussed. Many of these correlations are also available as computer programmes. It is always worth checking the range of applicability of the correlations, which are often based on empirical measurements and are grouped into fluid types (e.g. California light gases). 

The model of non-mteracting hannonic oscillators has a broad range of applicability. Besides vibrational motion of molecules, it is appropriate for phonons in hannonic crystals and photons in a cavity (black-body radiation). 

The easily accessible frequency range of sound and ultrasound waves confines the range of applicability of... 

The generally low chemical, mechanical and thennal stability of LB films hinders their use in a wide range of applications. Two approaches have been studied to solve this problem. One is to spread a polymerizable monomer on the subphase and to polymerize it either before or following transfer to the substrate. The second is to employ prefonned polymers containing hydrophilic and hydrophobic groups. 

The critical factor for any method involving an approximation or an extrapolation is its range of application. Liu et al. [15] demonstrated that the approach performed well for mutations involving the creation or deletion of single atoms. The method has also been successfully applied to the prediction of the relative binding affinities of benzene, toluene and o-, p-, and m-xylene to a mutant of T4-lysozyme [16]. In both cases, however, the perturbation to the system was small. To investigate range over which the extrapolation may... 

The investigation of molecular structures and of their properties is one of the most fascinating topics in chemistry. Chemistry has a language of its own for molecular structures which has been developed from the first alchemy experiments to modem times. With the improvement of computational methods for chemical information processing, several descriptors for the handling of molecular information have been developed and used in a wide range of applications. 

Metal salts of A-4-thiazoline-2-thione are used in the rubber industry Zn salts (123, 152), Pb and Mg salts (54). Cd salts (151, 324), Cu salts (325), in photographic processes (146). and in analysis (328). Zn, Ni, Co and Cd salts are used as germicides (329). Despite their wide range of application, little is known about their physical and chemical properties. 

A good LC/MS instrument routinely provides a means for obtaining the identities and amounts of mixture components rapidly and efficiently. It is not unusual to examine micrograms or less of materia). LC/MS is used in a wide range of applications, including environmental, archaeological, medical, forensic, and space sciences, chemistry, biochemistry, and control boards for athletics and horse racing. 

Lithium [7439-93-2] Li, an element with unique physical and chemical piopeities, is useful ia a wide range of applications. The estimated iaciease ia future demand has led to the development of lower cost resources as weU as additional plant openings. Capacity as of this writing (ca 1994) is ia excess of demand. 

More than half of the elements in the Periodic Table react with silicon to form one or more silicides. The refractory metal and noble metal silicides ate used in the electronics industry. Silicon and ferrosilicon alloys have a wide range of applications in the iron and steel industries where they are used as inoculants to give significantly improved mechanical properties. Ferrosilicon alloys are also used as deoxidizers and as an economical source of silicon for steel and iron. 

Backward-Curved Blade Blowers These blowers are used when a higher discharge pressure is needed. It is used over a wide range of applications. Both the forward and backward curved blades do have much higher stresses than the radial bladed blower. 

There are no satisfactory specific guides for selecting mixing equipment because the ranges of application of the various types of equipment overlap and the effects or flow properties on process performance have not been adequately defined. Nevertheless, what is frequently done in selec ting equipment is described in the following paragraphs. 

Polymeric flocculants are available in various chemical compositions and molecular weight ranges, and they may be nonionic in character or may have predominantly cationic or anionic charges. The range of application varies but, in general, nonionics are well suited to acidic suspensions, anionic flocculants work well in neutral or alkaline environments, and cationics are most effective on organic material and colloidal matter. 

FIG. 19-1 Particle -size range as a guide to the range of applications of various solid-solid operations. 

Leading Examples These apphcations are commercial, some on a very large scale. They illustrate the range of application for gas-separation membranes. Unless otherwise specified, all use polymeric membranes. 

Carbon is the cheapest and most effective alloying element for hardening iron. We have already seen in Chapter 1 (Table 1.1) that carbon is added to iron in quantities ranging from 0.04 to 4 wt% to make low, medium and high carbon steels, and cast iron. The mechanical properties are strongly dependent on both the carbon content and on the type of heat treatment. Steels and cast iron can therefore be used in a very wide range of applications (see Table 1.1). 

The range of applications for magnesium anodes includes the internal protection of boilers, feedwater tanks, filter tanks, coolers, pipe heat exchangers and condensers. They are mainly used in conjunction with coatings and where impressed current equipment is too expensive or cannot be installed. 

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