Disengagement time

The plateau modulus is determined by the region in which these two relaxation modes cross. The plateau modulus, the low shear viscosity and the tube disengagement time are given in Section 6.4.3 as... 

Figure 6.23 Prediction of stress overshoot for different tube disengagement times. The shear rate used for the calculation was 5 s l...

Hydrolytic and radiolytic degradation of TAP solution in normal paraffinic hydrocarbon (NPH) in the presence of nitric acid was investigated. Physicochemical properties such as density, viscosity, and phase-disengagement time (PDT) were measured for undegraded and degraded solutions (197). The variations in these parameters were not very different from those obtained with degraded TBP. Thus, the hydro-dynamic problems expected during the solvent-extraction process with TAP would be similar to those encountered with TBP/NPH system. The influence of chemical... 

The monomeric friction coefficient sets the time scale of all motions, e.g., the disengagement time ... 

This agrees with the leading tenn in eq 2.21. Thus, we may consider that while g t) follows the type, the primitive chain essentially stays in the initial tube. In other words, for t > the primitive chain is surrounded by tubes which are substantially different from the initial one. For this reason ra is called the disengagement time. It is also the time at which the chain begins to lose the memory of its initial tube. 

The longest relaxation time of (P(l) P(0)) is given by tj. This is called the reptation or disengagement time, since it is the time needed for the primitive chain to disengage from the tube it was confined to at r = 0. 

If the contour length fluctuation is neglected, the disengagement time is estimated as the time necessary for the chain to move the distance L,... 

The superscript (NF) stands for no fluctuation .) On the other hand if there are fluctuations, the chain can disengage from the tube when it moves the distance L — AL because the chain ends are fluctuating rapidly over the distance AL. Hence the disengagement time is estimated as... 

Contour length fluctuation. As was shown in the previous chapter, the contour length fluctuation reduces the disengagement time significantly. From eqns (6.20), (6.101), and (7.54), the disengagement time of a chain with fluctuation is given by... 

Continuous liquid-liquid extraction is carried out in a centrifugal contactor at low rotor speeds to achieve 90% efficiency. Mixing and disengaging times range from 10 to 30 s, respectively. Efficient two-phase mixing is achieved in the annulus between the spinning rotor and fixed housing. 

Figure 4.34. Tube renewal, a The tube at a certain time (light gray) shares a part with the old tube that enclosed the test chain at f = 0 (dark gray), b The tube renewal continues, and finally the tube (light gray) shares no part with the old tube. The time needed to reach the latter state is called the disengagement time (f ).

When the primitive chain slides along the tube with D the disengagement time ti, the time needed for the primitive chain to renew its encasing tube, is given as... 

The disengagement time is proportional to A. A slight increase in N leads to a large increase in 1. The overall dynamics of the chains becomes a lot slower. 

Equation 57a of Chapter 10 can be used to estimate the disengagement time tj of the Doi-Edwards theory. The microstructure is sufficiently close to that of the polybutadiene identified with footnote b in Table 12-III and footnote c in Table 13-1 to use the values of fo and G%) from those sources. The result is 11... 

The equilibrium extraction of Ce(III) and La(III) from sodium chloride solutions by the commercial extractant SME 529, 2-hydroxy-5-nonyl-acetophenone oxime, in n-heptane diluent was found by Urbanski et al. (1992) to be highly dependent on the pH and extractant concentration. SME 529 contains mainly the anti-form (>99%) which is a much better extractant than the syn-isomer. The equilibration time was around 2 minutes and the disengagement time was found to depend on the extractant concentration and pH. Phase disengagement is very slow and lanthanum Itydroxide precipitate appears at the interface at pH values where extraction and precipitation occur simultaneously. Precipitation generally occurs above pH 6.5. The extraction of cerium is more efficient below pH 6.5 compared to lanthanum and thus less ceriiun is precipitated. 

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