Size relationships

Subsequently, Calvert (R-19, p. 228) has combined mathematical modehng with performance tests on a variety of industrial scrubbers and has obtained a refinement of the power-input/cut-size relationship as shown in Fig. 14-130. He considers these relationships sufficiently reliable to use this data as a tool for selection of scrubber type and performance prediction. The power input for this figure is based solely on gas pressure drop across the device. 

More recently, Johnson and Sutherland have used bridged monoazacrowns as host molecules for bis-ammonium salts. The intramolecular bis-crown diammonium complex formed when the size relationships are appropriate is shown below as structure 8. 

Figure 4-84. Ton-mile derrick height and line-size relationships [11]. ...

It was found that the signs of rotation of the recovered a-phenylbutyric acid corresponded to the known absolute configurations of the deuteriated alcohols if and only if the size relationships CH3 > CD 3 and H>D were valid. In the case of (-t-)-(S)-2-propanol-l,l,l-d3 (4), the optical yield was between 0-4 and 0 5% (Horeau et al., 1965), corresponding to A AG value of about 23 cal mol at 25°C. For the primary alcohols, quite analogous results were obtained (Horeau and Nouaille, 1966). 

Brown and McDonald (1966) provided another type of kinetic evidence for these size relationships by determining secondary kinetic isotope effects in reactions of pyridine-4-pyridines with alkyl iodides. For example, the isotopic rate ratio in the reaction between 4-(methyl-d3)-pyridine and methyl iodide at 25-0 C in nitrobenzene solution was determined to be kjyfk = l-OOl, while that in the corresponding reaction with 2,6-(dimethyl-d6)-pyridine was 1-095. (Brown and McDonald (1966) estimate an uncertainty of 1% in the k jk values.) Furthermore, the isotopic rate ratio in the case of the 2-(methyl-d3)-compound increased from 1 030 to 1-073 as the alkyl group in the alkyl iodide was changed from methyl to isopropyl, i.e. the isotope effect increased with increasing steric requirements of the alkyl iodide. 

Tolls, J., van Dijk, J., Verbruggen, E.J.M., Mermens, J.L.M., Loeprecht, B., and Schiiiirmann, G. Aqueous solubility - molecular size relationships A mechanistic case study using Cio- to Ci9-alkanes, J. Phys. Chem. A, 106(11) 2760-2765, 2002. 

FIGURE 6.10 Experimentally measured diameter of submicron fused silica particles as a function of particles diameter determined from scanning electron microscopy measurements. Dashed line corresponds to 1 1 size relationship. (From Shcheslavskiy, V., Petrov, G. I., Faustov, A., Yakovlev, V. V., and Saltiel, 5. Optics Lett., 31(10) 1486-1488, 2006. Used with permission.)... 

Siemann, E. Tilman, D. Haarstad, J. (1996) Insect species diversity, abundance, and body size relationships. Nature, 380, 704-6. 

Crystal Size Influence on Detonation Velocity. See Detonation Velocity - Crystal Size Relationship... 

Detonation Velocity Crystal Size Relationship. See under Detonation Velocity -Particle Size Distribution Relationship... 

Wadge, A., Hutton, M. Peterson, P. J. 1986. The concentration and particle size relationships of selected trace elements in fly ashes from U.K coal-fired power plants and a refuse incinerator. Science of the Total Environment, 54, 13-27. 

The last simplification is possible because the solute molecule is n times larger than a solvent molecule, and the same size relationship applies to the partial molar volumes. According to Equation (79), the second virial coefficient is given by... 

The l29Xe chemical shift - pore size relationship was extended to the mesopore region with a number of controlled pore glasses with pores in the 75-385 A range. There is a correlation of the pore diameter with the inverse of the chemical shift. For small pores there is markedly different behaviour with the switch occurring near the nanopore - mesopore transition at 10-20A. 

The same type of ionic size relationship is observed in uranates (U4+ = 1.05), where Gd, Tb, Dy, Ho and Er are more abundant than other rare earths. 

Absorption and fluorescence spectra of aromatic hydrocarbons are not greatly affected by change of solvent, except for small solvent shifts. At low temperatures the vibrational structure of the bands sharpens up, and some peculiar solvent effects have been noted. When frozen in solution of normal paraffins coronene shows doubling of some of its vibrational bands, and the separation of the components varies with the number of carbon atoms in the solvent molecule chain. The most probable cause is some size-relationship factor between solvent and solute molecules (7). 

Figure 2.15 (Ripmeester, 2000) correlates the observations of double hydrates and demonstrates the complexity of the structure-size relationship for hydrates containing two types of guest molecules. The combinations of two different types of guests forming sll and sH double hydrates are also listed in Tables 2.6 and 2.7, respectively.

Elversson, J., A. Millqvist-Fureby, G. Alderborn, and U. Elofsson. 2003. Droplet and particle size relationship and shell thickness of inhalable lactose particles during spray dtjnP arm Sci 92 900-910. 

The pressure recovery factor is a constant for any given valve at a given opening. The value of this factor can be established by flow test and is published by the valve manufacturer. If the actual pressure differential across the valve is greater than the choked pressure differential of Eq. (8-115), then Apcboked should be used in Eq. (8-111) to determine the correct valve size. A more complete presentation of sizing relationships is given in ANSI 75.01.01, including provisions for pipe reducers and Reynolds number effects. 

A range of values of reactor sizes is explored. For each value the capital costs of the reactor, the column and the heat exchangers are calculated using the cost and sizing relationships given in Table 2.6. The recycle stream is assumed to be 322 K. 

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