Orientation shear viscosity

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). 

Substitution of Equation (3.62) into Equation (3.60) gives the relative zero shear viscosity. When the shear rate makes a significant contribution to the interparticle interactions, the mean minimum separation can be estimated from balancing the radial hydrodynamic force, Fhr, with the electrostatic repulsive force, Fe. The maximum radial forces occur along the principle axes of shear, i.e. at an orientation of the line joining the particle centres to the streamlines of 6 = 45°. This is the orientation shown in Figure 3.19. The hydrodynamic force is calculated from the Stokes drag, 6nr 0au, where u is the particle velocity, which is simply... 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

In the second half of this article, we discuss dynamic properties of stiff-chain liquid-crystalline polymers in solution. If the position and orientation of a stiff or semiflexible chain in a solution is specified by its center of mass and end-to-end vector, respectively, the translational and rotational motions of the whole chain can be described in terms of the time-dependent single-particle distribution function f(r, a t), where r and a are the position vector of the center of mass and the unit vector parallel to the end-to-end vector of the chain, respectively, and t is time, (a should be distinguished from the unit tangent vector to the chain contour appearing in the previous sections, except for rodlike polymers.) Since this distribution function cannot describe internal motions of the chain, our discussion below is restricted to such global chain dynamics as translational and rotational diffusion and zero-shear viscosity. 

In fact, the fiber contribution to the shear viscosity of a fiber suspension at steady state is modest, at most. The reason is that, without Brownian motion, the fibers quickly rotate in a shear flow until they come to the flow direction in this orientation they contribute little to the viscosity. Of course, the finite aspect ratio of a fiber causes it to occasionally flip through an angle of n in its Jeffery orbit, during which it dissipates energy and contributes more substantially to the viscosity. The contribution of these rotations to the shear viscosity is proportional to the ensemble- or time-averaged quantity (u u ), where is the component of fiber orientation in the flow direction and Uy is the component in the shear gradient direction. Figure 6-21 shows as a function of vL for rods of aspect... 

Polyester BB1 was run twice in steady mode at 290°C (Figure 10), and shows that the orientational effect of the first run has a drastic effect on steady shear viscosity. In the first run the log viscosity vs. log shear rate had a slope of -0.92 (solid like behaviour, yield stress), but in the second run a pseudo-Newtonian plateau was reached from approx. 1 sec 1. Capillary viscosity values corresponded reasonably well with the second run steady shear data. The slope at high shear rates was close to -0.91 which corresponds nicely to the first-run steady shear run. All this could suggest, that this system is not completely melted, but still has some solid like regions incorporated. At 300°C capillary viscosity data showed an almost pseudo-Newtonian plateau. This corresponds quite well to the fact that fiber spinning as mentioned earlier was difficult and almost impossible below 290°C, but easy at 300°C. At an apparent shear rate of 100 sec 1, a die-swell was found to be approximately 0.95. 

Isotropic solutions exhibit a monotonic increase in shear viscosity with increasing concentration. The viscosity increases to a maximum when the isotropic to anisotropic transition is approached. Upon formation of the anisotropic phase, the viscosity begins to decrease, after which the viscosity increases strongly as the concentration continues to increase (Fig. 6). In the isotropic state, the hydrodynamic volume is large because of the random polymer orientation. This restricts the polymer diffusivity and causes an increase in viscosity. In the anisotropic phase, the aligned polymer leads to a small hydrodynamic volume and a decrease in viscosity as rotational diffusion is much easier with a net orientation. 

Figure 3.66 shows the steady-shear viscosity for a polymer system at three molar masses. Note the plateau in viscosity at low shear rates (or the zero-shear viscosity). Also note how the zero-shear viscosity scales with to the power 3.4. (This is predicted by Rouse theory (Rouse, 1953).) Figure 3.67 shows the viscosity and first normal-stress difference for a high-density polyethylene at 200 C. Note the decrease in steady-shear viscosity with increasing shear rate. This is termed shear-thinning behaviour and is typical of polymer-melt flow, in which it is believed to be due to the polymer chain orientation and non-affine motion of polymer chains. Note also that the normal-stress difference increases with shear rate. This is also common for polymer melts, and is related to an increase in elasticity as the polymer chain motion becomes more restricted normal to flow at higher shearing rates. 

An integration over all orientations of the vector R has been effected in these equations. The first term arises from momentum transport from mass motion and can be neglected in comparison with the second term. The indicated integration of Eq. 42 has been carried out numerically. That of Eq. 43 proved to be too sensitive to variation in the radial distribution function g0(2) to yield reliable results. In order to obtain the shear viscosity r), it is now necessary to evaluate the frictional coefficient f. A solution in series was obtained by Kirkwood25 but its numerical evaluation is too unwieldy for practical calculations. The analysis, however, stiggests the following estimate for the frictional coefficient ... 

Contributing factors include molecular orientation, shearing forces, die length, relaxation, mass temperature, viscosity, and molecular form (constitution). 

In the low shear rate region, the first normal stress difference increases with the fiber content, which may be due to the hydrodynamic effect associated with fiber orientation in the flow direction. The effect of surface treatment was identical to that in the high shear rate region. The shear viscosity and the first normal stress difference as a function of shear rate for maleic anhydride modified PP (5wt.%) added composites (GF/mPP/PP compositese) are plotted in Fig. 2. Although the overall level of the both functions rj and Nj was higher than that in GF/PP composites (Fig. 1), the effect of surface treatment by lwt.% ASC on rj and NiofGF/PP composites is similar to that of GF/mPP / PP. 

C. Lin, J.W. Shan, Ensemble-averaged particle orientation and shear viscosity of single-wall-carbon-nanotube suspensions under shear and electric fields, Phys. Fluids, 2010, 22, 022001. 

The zero shear viscosity scales with Nf" to contrast Af dependence for isotropic polymers [20] So far, we have examined the dynamics of rod-Uke macromolecules in isotropic semi-dilute solution. For anisotropic LCP solutions in which the rods are oriented in a certain direction, the diffusion constant increases, and the viscosity decreases, but their scaling behavior with the molecular weight is expected to be unchanged [2,17], Little experimental work has been reported on this subject. The dynamics of thermotropic liquid crystalline polymer melts may be considered as a special case of the concentrated solution with no solvent. Many experimental results [16-18] showed the strong molecular weight dependence of the melt viscosity as predicted by the Doi-Edwards theory. However, the complex rheological behaviors of TLCPs have not been well theorized. 

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