Terminal zone

Zone 4 is a terminal zone in which the residual velocity decays quickly into large-scale turbulence. Within a few diameters, the maximum velocity subsides to below 0.25 m/s. Though this zone has been studied by several researchers, its characteristics are still not well understood. 

The throw of downward-projected heated jets or upward-projected chilled jets can be derived from Eqs. (7.85) and (7.88) for K equal to some value, e.g., 0.1. Helander and Jakowatz, in their work on heated jets projected downward, have called attention to some of the differences between the actual conditions and those assumed for analysis. One of these is the radial escape of warm air in the terminal zone of a hot stteam projected downward. This escaping warm air then rises and causes a change in ambient conditions for the upper part of the jet. The terminal zone and the edges of the jet are zones of marked instability, with definite surges and fluctuations, so that the jet envelope is very difficult to define or to determine experimentally. In the closure to the paper presented by Knaak, Dr. Helander suggested that from the point of view of practical application, the distance to the beginning of the unstable, tet-minal zone of the jet is about 80% of the jet throw. 

Investigation of the linear viscoelastic properties of SDIBS with branch MWs exceeding the critical entanglement MW of PIB (about -7000 g/mol ) revealed that both the viscosity and the length of the entanglement plateau scaled with B rather than with the length of the branches, a distinctively different behavior than that of star-branched PIBs. However, the magnitude of the plateau modulus and the temperature dependence of the terminal zone shift factors were found to... 

Figure 21.2 The anatomical organisation of the spinal cord, showing the grey and white matter with the laminae terminal zones of the different afferent fibre t5 pes...

The opiate receptors in the spinal cord are predominantly of the mu and delta type and are found in the C-fibre terminal zone (the substantia gelatinosa) in the superficial dorsal horn. Considerable numbers of ORL-1 receptors are also found in this area. Up to 75% of the opiate receptors are found presynaptically on the C-fibre terminals and when activated inhibit neurotransmitter release. The opening of potassium channels will reduce calcium flux in the terminal and so there will be a resultant decrease in... 

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

The large scale molecular motions which take place in the rubber plateau and terminal zones of an uncross-linked linear polymer give rise to stress relaxation and thereby energy dissipation. For narrow molecular weight distribution elastomers non-catastrophic rupture of the material is caused by the disentanglement processes which occur in the terminal zone, e.g., by the reptation process. In practical terms it means that the green strength of the elastomer is poor. 

Odani,H., Nemoto.N., Kurata,M. The viscoelastic properties of undiluted linear polymers of narrow molecular weight distribution in the terminal zone. Bull. Inst. Chem. Res., Kyoto U. 50,117-133 (1972). 

This equation, also as equation (6.49) gives description of the frequency dependency of dynamic modulus at low frequencies (the terminal zone). Both in equation (6.49) and (9.35), the second terms present the contribution from the orientational relaxation branch, while the first ones present the contribution from the conformational relaxation due to the different mechanisms diffusive and reptational. 

One can see that introduction of the reptation mechanism of conformational relaxation, instead of diffusive mechanism, does not affect the values of the terminal quantities, but, one can expect, improves the situation in the region of the minima of the loss modulus G" reptation branch fill the gap between the orientational and the second conformational branches of relaxation times. Thus, the description with help of two relaxation branches is valid in the terminal zone and for higher frequencies close to it. 

Isothermal measurements of the dynamic mechanical behavior as a function of frequency were carried out on the five materials listed in Table I. Numerous isotherms were obtained in order to describe the behavior in the rubbery plateau and in the terminal zone of the viscoelastic response curves. An example of such data is shown in Figure 6 where the storage shear modulus for copolymer 2148 (1/2) is plotted against frequency at 10 different temperatures. 

It has to be mentioned that the effect of dilution is in the terminal zone (long times) greater than in the glass-rubber transition zone (short times), which is specified by log ac. This becomes also clear from Fig. 16.11 the values of log ac in Figs. 16.12-16.14 were taken in the transition zone. It is beyond the scope of this book to go into more detail into this subject. For more details of the time-concentration superposition principle the reader is referred to the monograph by Ferry (General references, 1980, Chap. 17). 

In close analogy to the PCL based nanocomposites, the terminal zone dependence of G and G" for the 2 and 5 weight % samples, show non-terminal behavior with power-law dependencies for G and G" much smaller than the expected 2 and 1 respectively. Furthermore, like the PCL based nanocomposites, there also appears to be a gradual decrease in the power-law dependence of G and G" with increasing silicate loading. 

Recently we have conducted rheological experiments wherein the end-tethered PCL nanocomposites were blended with pure PCL homopolymer. Rheological behavior, particularly the terminal zone slopes, obtained for 5% and 10% (obtained by blending equal weight fractions of PCL homopolymer with a 10 weight % PCL and 20 weight % PCL respectively) were found to be similar to those obtained from the as-prepared nanocomposites. 

When short Mg chains are introduced into a sample of entangled Ml - chains with a voliune fraction < ) of long chains such as (j) Ml > Mg, the blend can be viewed as a concentrated solution of the long chains, or in other words, the Mg component is acting as a solvent at least in the terminal zone of relaxation of the long chains. 

Table 7 gives a summary of qualitative performances and problems encountered for simple shear and uniaxial elongational flows, using the Wagner and the Phan Thien Tanner equations or more simple models as special cases of the former. Additional information may also be found in papers by Tanner [46, 64]. All equations presented hereafter can be cast in the form of a linear Maxwell model in the small strain limit and therefore are suitable for the description of results of the linear viscoelasticity in the terminal zone of polymer melts. 

An attempt has been made to describe the particular stress-optical behaviour observed close to Tg. The idea was to associate the entropic part of the stress with relaxation times corresponding roughly to the rubbery plateau and the terminal zone (see Fig. 12), whereas the non-entropic part is assumed to be related to shorter time relaxation phenomena (glass transition and glassy state). This approach is similar to that proposed by Inoue et al. [34] who considered two contributions to the stress with different associated stress-optical coefficients. 

In the glass-like zone, the values of the creep compliance function seem to be independent of the concentration however, the changes that take place in the values of J t) in the transition zone are larger the lower the concentration. The length of the plateau increases with the concentration, and the plateau and terminal zones merge into a single region at low concentrations. The location of the isotherms on the time scale is shifted to shorter chains as the concentration decreases. 

Cross-linking effects are more important in the plateau and terminal zones. For moderately cross-linked polymers, such as soft vulcanized rubbers, the equilibrium modulus is similar in magnitude to the entanglement network modulus before vulcanization. In some cases, however, the former modulus may be higher by as much as a factor of 2 than the latter one, thus... 

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