Static values

Second, the creep modulus, also known as the apparent modulus or viscous modulus when graphed on log-log paper, is normally a straight line and lends itself to extrapolation for longer periods of time. The apparent modulus should be differentiated from the modulus given in the data sheets, which is an instantaneous or static value derived from the testing machine, per ASTM D 638. 

Thus, the enhancement of heat transfer may be connected to the decrease in the surface tension value at low surfactant concentration. In such a system of coordinates, the effect of the surface tension on excess heat transfer (/z — /zw)/ (/ max — w) may be presented as the linear fit of the value C/Cq. On the other hand, the decrease in heat transfer at higher surfactant concentration may be related to the increased viscosity. Unfortunately, we did not find surfactant viscosity data in the other studies. However, we can assume that the effect of viscosity on heat transfer at surfactant boiling becomes negligible at low concentration of surfactant only. The surface tension of a rapidly extending interface in surfactant solution may be different from the static value, because the surfactant component cannot diffuse to the absorber layer promptly. This may result in an interfacial flow driven by the surface tension gradi-... 

While the above refers mainly to the static limit, new effects come into play when a moving contact line, i.e. spreading, is considered. It has been observed experimentally that the contact angle of a moving contact line 0, the dynamic contact angle, deviates from the corresponding static value 0. As an example, for a completely wettable surface (i.e. 6(, = 0), a relationship of the form... 

At last, the extrapolation procedure employed in that calculation gives the final a(N - c ) value to be 4.503, i.e. 0.07% above the exact static value of a. 

If the crossover points Q (x) are determined from Fig. 45, taking the x-values at half-step height, Q (x) = 1/1 (x) = (0.7 + 0.2)x is obtained in the case of the PS system. This has to be compared with static value Qs (x) = 1.6x, derived from the same polymer solvent system by elastic neutron scattering [103], As long as no corresponding data from other polymer solvent systems are available, the final decision as to whether static and dynamic scaling lengths coincide or not, is still open. 

In a static field both components of the polarization contribute, and the static value es of the dielectric constant must be used in Eq. (6.25). The slow polarization is obtained by subtracting Pf, which gives ... 

Extrapolated static values, see Table 2 of Ref. 43 and references therein. 

In general, the coefficients of variation decrease with smaller values of 02. This is definitely desirable since it indicates that for higher expected profits there is diminishing uncertainty in the model, thus signifying model and solution robustness. It is also observed that for values of 02 approximately greater than or equal to 2, the coefficient of variation remain at a static value of 0.5237, thus indicating overall stability and a minimal degree of uncertainty in the model. 

This is easy to explain because values derived from the elution partial isotherm only pay regard to the amount adsorbed in the mesopores and the outer surface area. By contrast, the static method is not able to distinguish between these contributions and the micropore part of adsorption. Therefore the obtained values are higher but have no physical meaning whereas the elution values give a more realistic picture. The results for the standard carbon are very similar to the static values. This means that there are almost no micropores and the sorption processes take place in the mesopores and the outer surface area. This is confirmed by the huge difference in the thermodesorption peak of both materials. 

In order to provide accurate static values for this purpose, we have recently undertaken a series of calculations of the polarizability and hyperpolarizability of the rare gases. An extensive basis set investigation was performed for Ne, and we shall consider these results in detail. We shall also discuss aspects of the correlation treatment and computational methodology. We begin by considering methods for the calculation of the polarizability and hyperpolarizability. 

The value of the parameters can be determined with only a cursory consideration of design. The area resistance, r, is composed of the membrane resistance and the stream resistance, its square root appearing in the smallest cost expression. The membrane resistance quoted by manufacturers is a static value, measured while the membrane still has its minority carriers and consequently is not yet markedly permselective. In operation the membrane has a resistance nearly twice the values quoted. A value of 25 ohms per sq. cm. per pair, measured for some thin membranes, is used in the following calculations. Because the resistance of the concentrate stream can be made arbitrarily small by an increase of concentration, a value /4 of dilute stream resistance has been used for the fluid resistance in the preparation of Figure 1. 

Let us discuss the experimental data on the curing of phenolic resins, which are shown in Fig. 2.33. In order to make theoretical calculations, the following characteristics of the resin derived from the experimental data were used 114,118 at To = 393K, the "static" value of to corresponding to the limit of very low shear rates, equals 240 s oo = 0.2 MPa Cp = 2 kJ/(kg K) p = lxlOr kg/m3 U = 41.8 kJ/mol. Using these values, the dimensionless shear rate can be expressed as... 

The ratio of the alternating variation of capacitance ACs t) to the static value of capacitance Cso without time dependence is given as [3]... 

For exponential W(r) this serves as an alternative to the contact estimate of Ko at slow diffusion given in Eq. (3.65). The latter tends to zero as /T) > 0 while Ko from (3.67) approaches the lowest but finite static value, lini/j, oKo(/J) / 0. The Stem-Volmer constant increases monotonously with diffusion from this value up to the kinetic rate constant ko = linio Xl Ko(D). As shows Figure 3.10, at the same ko the more efficient the remote transfer is, the greater the tunneling length l. 

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