Shear-rate dependent viscosity, spin

Velocity maps were measured with How-compensated spin-echo sequences [Rof l], The expefimental data were analysed in terms of a power law for the shear stress a[2 which solves the constitutive equation (T 2 = f)(dy/d/)" for the shear-rate-dependent viscosity rj and the applied shear strain y. The azimuthal velocity at radius r and rotation speed wr of the inner cylinder can be expressed as... 

Flow processes iaside the spinneret are governed by shear viscosity and shear rate. PET is a non-Newtonian elastic fluid. Spinning filament tension and molecular orientation depend on polymer temperature and viscosity, spinneret capillary diameter and length, spin speed, rate of filament cooling, inertia, and air drag (69,70). These variables combine to attenuate the fiber and orient and sometimes crystallize the molecular chains (71). 

Solve the fiber spinning problem for a non-Newtonian fluid with viscosity that depends upon shear rate. The problem without inertia is... 

We studied the dependence of spin modes on viscosity in the HDDA/persulfate system. Determining the viscosity is complicated by the shear-thinning behavior of silica gel suspensions. Figure 6 shows the apparent viscosity vs. shear rate for different percentages of silica gel in HDDA. The linear stability analysis assumes Newtonian behavior so we need to estimate the viscosity at zero shear, which is something we can not reliably estimate with our viscometer. We used the viscosities at the lowest shear rate we could measure and recognize that we are underestimating the true value. Fortunately, this does not affect the qualitative trends. 

When producing carbon fibers from pitch, a critical processing parameter is the viscosity of the pitch, which is extremely dependent on the spinning temperature. If pitch was a truly Newtonian fluid, the viscosity would be independent of shear rate, attaining its value almost instantaneously. It would be expected that the ratio of the hot filament diameter to the orifice diameter (die swell ratio) would be less than 1.1 and the molten fluid would not climb the stirring rod (the so called Weissenberg effect) [228]. 

Nazem [259] showed that a 100% isotropic pitch reached a steady viscosity in about 50 s, whereas a mesophase pitch prepared from it (97% anisotropic) failed to achieve a steady state even after 400 s. However, intermediate pitches prepared with about 75% anisotropy did attain a reasonably constant viscosity at high shear rates and are termed pseudo-Newtonian, which are suitable for spinning. Brooks and Taylor mesophase and neomesophase have also been shown to behave in a similar manner. Figures 4.28 and 4.29 show the dependence of viscosity on temperature for a number of pitches, emphasizing the difference between isotropic and mesophase pitches. 

Bulk Polymerization. Absolute viscosities of the C7, C9, and Cu diols at temperatures from 24 to 66 C were measured to facilitate the selection of the method and conditions of polymerization. The viscosities of the diols exhibit no dependence on the spin rate (the effective shear rate was from 0.046 to 4.6 sec ) and show an Arrhenius-type dependence on temperature. Correlations between viscosity and the absolute temperature were found using linear regression techniques. They are for C7 diol p (poise) = 13.9... 

---