Consistency coefficient for

Conventional stirred-tank polymeric reactors normally use turbine, propeller, blade, or anchor stirrers. Power consumption for a power-law fluid in such reactors can be expressed in a dimensionless form, Ne = Reynolds number based on the consistency coefficient for the power-law fluid. Various forms for the function f(m) in terms of the power-law index have been proposed. Unlike that for Newtonian fluid, the shear rate in the case of power-law fluid depends on the ratio dT/dt and the stirrer speed N. For anchor stirrers, the functionality g developed by Beckner and Smith (1962) is recommended. For aerated non-Newtonian fluids, the study of Hocker and Langer (1962) for turbine stirrers is recommended. For viscoelastic fluids, the works of Reher (1969) and Schummer (1970) should be useful. The mixing time for power-law fluids can also be correlated by the dimensionless relation NO = /(Reeff = Ndfpjpti ) (Tebel et aL 1986). 

Young s modulus (Pa) power-law consistency coefficient (Pa s") power-law consistency coefficient for first normal stress difference (Pa S ) first normal stress difference (Pa) second normal stress difference (Pa) power-law index (-) pressure (Pa) total normal stress (Pa)... 

Another, purely experimental possibility to obtain a better estimate of the friction coefficient for rotational motion in chemical reactions consists of measuring rotational relaxation times of reactants and calculating it according to equation (A3,6,35) as y. =... 

The general fomi of the expansion is dictated by very general synnnetry considerations the specific coefficients for the example of a polymer blend can be derived from the self-consistent field theory. For a... 

Table 8-8 gives some nonelectrolyte transfer free energies, and Table 8-9 lists single ion transfer activity coefficients. Note especially the remarkable values for anions in dipolar aprotic solvents, indicating extensive desolvation in these solvents relative to methanol. This is consistent with the enhanced nucleophilic reactivity of anions in dipolar aprotic solvents. Parker and Blandamer have considered transfer activity coefficients for binary aqueous mixtures. 

The coefficients for uncontracted basis functions—consisting of only a single primitive—are usually 1.0. This is the case for functions 6 through 19 in the 6-31++G(d,p) example we have been examining. 

Here, occ means occupied and virt means virtual. In the restricted Hartree-Fock model, each orbital can be occupied by at most one a spin and one (i spin electron. That is the meaning of the (redundant) Alpha in the output. In the unrestricted Hartree-Fock model, the a spin electrons have a different spatial part to the spin electrons and the output consists of the HF-LCAO coefficients for both the a spin and the spin electrons. 

This unit consists of two pipes or tubes, the smaller centered inside the larger as shown in Figure 10-92. One fluid flows in the annulus between the tubes the other flows inside the smaller tube. The heat transfer surface is considered as the outside surface of the inner pipe. The fluid film coefficient for the fluid inside the inner tube is determined the same as for any straight tube using Figures 10-46-10-52 or by the applicable relations correcting to the O.D. of the inner tube. For the fluid in the annulus, the same relations apply (Equation 10-47), except that the diameter, D, must be the equivalent diameter, D,.. The value of h obtained is applicable directly to the point desired — that is, the outer surface of the inner tube. ... 

Conditioned fabric maintains a relatively consistent dust-load deposit following a number of filtration and cleaning cycles. K may be more than 10 times the value of the resistance coefficient for the original clean fabric. If the depth of the dust layer on the fabric is greater than about inch (which corresponds to a fabric dust loading on the order of 0.1 Ibm/ft ), the pressure drop across the fabric, including the dust in the pores, is usually negligible relative to that across the dust layer alone. 

Thermodynamic consistency tests for binary vapor-liquid equilibria at low pressures have been described by many authors a good discussion is given in the monograph by Van Ness (VI). Extension of these methods to isothermal high-pressure equilibria presents two difficulties first, it is necessary to have experimental data for the density of the liquid mixture along the saturation line, and second, since the ideal gas law is not valid, it is necessary to calculate vapor-phase fugacity coefficients either from volumetric data for... 

Yamase and Goto406 determined first- and second-order rate coefficients for the aluminium chloride-catalysed reaction of halide derivatives of benzoic acid (lO5 = F, 1.73 Cl, 4.49 Br, 4.35 I, 0.81) and phenylacetic acid (105fc2 = F, 12 Cl, 21 Br, 9 I, 6) with benzene. The maxima in the rates for the acid chloride are best accommodated by the assumption that a highly (but not completely) polarised complex takes part in the transition state. Polarisation of such a complex would be aided by electron supply, and consistently, the acetyl halides are about a hundred times as reactive as the benzoyl compounds (see p. 180, also Tables 105 and 108). 

The observed second-order rate coefficients can, in all cases, be treated empirically as consisting of the sum of a second-order rate coefficient (for the uncatalyzed reaction) and the product of a third-order rate coefficient and the catalyst concentration (for the catalyzed reaction), as indicated by eqn. (4). If the catalyst is a base this constitutes base catalysis in a formal sense, at least. Nevertheless,... 

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