Terminal flow region

Finally, as the temperature is increased still further the time necessary for disentanglement becomes shorter, chain diffusion becomes faster than the measurement time of the experiment and we enter the terminal flow region where a polymer melt is much more liquid-like in its properties. The various relaxation processes that are associated with chain conformational changes and disentanglement are still important, however, and polymer melts remain viscoelastic, accounting for phenomena like jet swelling and melt fracture that we discussed earlier. 

Cooperative processes in the glass transition to terminal flow region... 

The question we now wish to address concerns the WLF equation. Why does the temperature dependence of the shift factor have this form for temperatures ranging from the T into the terminal flow region ... 

Doi and Edwards analysed the described disentangling process of the primitive chain in more detail. As in the case of the Rouse-motion, the dynamics of the disentangling process can also be represented as a superposition of independent modes. Again, only one time constant, the disentangling time Td, is included, and it sets the time scale for the complete process. In the Doi-Edwards treatment, ra is identified with the longest relaxation time. Calculations result in an expression for the time dependent shear modulus in the terminal flow region. It has the form... 

The relaxation behavior of amorphous polymers was dominated by two processes, the glass-rubber transition and the terminal flow region, which are both characterized by a temperature dependence given by the WLF equation. For polyethylene, one cannot expect a flow transition because flow is suppressed by the crystallites in the sample. The fact is that for linear polyethylene, i.e., polyethylene with high crystallinity, there is no WLF-controlled process at all. The numerous measurements in the literature provide clear evidence that the two processes observed in linear polyethylene, a and 7, are both based on activated mechanisms obeying the Arrhenius law. The process... 

David W. Taylor Model Basin, Washington, September 1953 Jackson, loc. cit. Valentin, op. cit.. Chap. 2 Soo, op. cit.. Chap. 3 Calderbank, loc. cit., p. CE220 and Levich, op. cit.. Chap. 8). A comprehensive and apparently accurate predictive method has been publisned [Jami-alahamadi et al., Trans ICE, 72, part A, 119-122 (1994)]. Small bubbles (below 0.2 mm in diameter) are essentially rigid spheres and rise at terminal velocities that place them clearly in the laminar-flow region hence their rising velocity may be calculated from Stokes law. As bubble size increases to about 2 mm, the spherical shape is retained, and the Reynolds number is still sufficiently small (<10) that Stokes law should be nearly obeyed. 

In the slug flow region, Griffith and Wallis (1961) suggested the terminal velocity,... 

The region of particle Reynolds number between 10 and 0.5 is known as the Stokes or streamline flow region. When a particle settles by gravity, it reaches a constant settling velocity, known as the terminal velocity. In terms of a force balance, the gravity force on the particle is equal to the sum of the drag force plus the buoyancy force. The terminal velocity for spherical particles in the Stokes region can be easily derived. The velocity is equal to ... 

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