Viscous flow curves

Figure 9 Temporal viscous flow curves for urethane polymerization.

Fig. 6.17. Map of polycluster mechanical states. Region I elastic and anelastic (shaded area) deformations Region II inhomogeneous plastic deformation Region III homogeneous diffusional-viscous flow. Curves 1-3 show the temperature dependence of the stress at different constant strain rates...

Though the accuracy of description of flow curves of real polymer melts, attained by means of Eq. (10), is not always sufficient, but doubtless the equation of such a structure based on the idea of relaxation mechanism of non-Newtonian polymer flow, correctly reflects the main peculiarities of viscous properties. Therefore while discussing the effect a filler has on the viscosity properties of polymer melts, besides the dependences Y(filler modifies the characteristic time of relaxation. According to [19], a possible form of the X versus

[Pg.86]

A similar thing takes place when we consider flow curves obtained at different temperatures. As seen from Fig. 7, if we take a region of low shear rates, then due to the absence of the temperature dependence Y, the apparent activation energy vanishes. At sufficiently high shear rates, when a polymer dispersion medium flows, the activation energy becomes equal to the activation energy of the viscous flow of a polymer melt and the presence of the filler in this ratio is of little importance. 

At low values of the Reynolds number, less than about 10, a laminar or viscous zone exists and the slope of the power curve on logarithmic coordinates is — 1, which is typical of most viscous flows. This region, which is characterised by slow mixing at both macro-arid micro-levels, is where the majority of the highly viscous (Newtonian as well as non-Newtonian) liquids are processed. 

Figure 10.48 Typical flow curves demonstrating behaviour of viscous liquids [342]...

Figures 5 and h show how the shape of the creep curve is modified by changes in the constants of the model. The values of the constants are given in Table I. Curve I is the same as shown in Figure 4, curve II shows onlv a small amount of viscous creep, and in curve 111, viscous flow is a prominent part of the total creep. The same data were used in Figures 5 and 6, but notice the dramatic, change in the shapes of the curves when a linear time scale is replaced by a logarithmic time scale. In the model, most of the recoverable creep occurs "Within about one decade of the retardation time.

Beyond Tfl, whole molecules are moving and contributing to viscous flow [i.e., equation (44) describes the long-time tail of the stress relaxation curve or the onset of the flow regime]. 

Although PBT fiber also has a plateau region in the stress-strain curve [4], the crystalline chains do not respond to external strain in the first few percent of deformation. They increased in length only when the strain is above 4% (see Figure 11.13). Therefore, initial macroscopic deformation involved viscous flow of the amorphous phase. Furthermore, PBT undergoes strain-induced crystal transformation at moderately low strains of 15-20% [75], The differences in their microscopic crystalline chain deformation explained why PTT has a better elastic recovery than PBT even though both have contracted chains and knees in their stress-strain curves [4, 69],... 

The total deformation in the four-element model consists of an instantaneous elastic deformation, delayed or retarded elastic deformation, and viscous flow. The first two deformations are recoverable upon removal of the load, and the third results in a permanent deformation in the material. Instantaneous elastic deformation is little affected by temperature as compared to retarded elastic deformation and viscous deformation, which are highly temperature-dependent. In Figure 5.62b, the total viscoelastic deformation is given by the curve OABDC. Upon unloading (dashed curve DFFG),... 

The Reynolds number NBe accounts for viscous forces, and the Froude number NFr for the force of gravity when this is important. For a typical impeller-tank arrangement, curves of the sort shown in Fig. 1 result, based on Eq. (2). Briefly, at low values of NRe (viscous flow, A to 5 in the figure) for both baffled and unbaffled tanks, no vortex is produced and the Froude number is unimportant n = 0). In turbulent flow the... 

Atoms are transported by viscous flow by differences in the capillary pressure at nonuniformly curved surfaces. 

For a nematic polymer in a transition region from LC to isotropic state, maximal viscosity is observed at low shear rates j. For a smectic polymer in the same temperature range only a break in the curve is observed on a lgq — 1/T plot. This difference is apparently determined by the same reasons that control the difference in rheological behaviour of low-molecular nematics and smectics 126). A polymeric character of liquid crystals is revealed in higher values of the activation energy (Ef) of viscous flow in a mesophase, e.g., Ef for a smectic polymer is 103 kJ/mole, for a nematic polymer3 80-140kJ/mole. 

In the case of polymer networks there is not possibility of viscous flow irrespective of the increment on the temperature. The network when reach a temperature higher than Tg, the modulus is like that for a rubber with a constant value (see curves 3 and 4) in Fig. 2.5. 

Ford und Ulbrecht [41] performed homogenization measurements with aqueous CMC and PAA solutions in a vessel with a screw stirrer arranged in a central draught tube. The pumping direction of the screw could be changed as well. Initially, the liquid with a lower viscosity rested in a layer on top of the more viscous one (volume ratio cp = 1). The data measured were first represented in the space n0, Reefr, Fig. 22, whereby peff was taken from the flow curve of the homogenized mixture at the shear rate of y 5 s-1, which was effective in the draught tube. 

Most leaks have a viscous flow of gas. That is, the length of the gas s mean free path is such that a gas molecule is more likely to hit a wall before hitting another molecule. On a bell-shaped distribution curve of average leaks found, this size... 

Figure 8-31 Examples of Compression Curves of Shortenings. (1) and (2) soy-palm (3) soy-canola-palm (4) soy only (5) tallow-lard (6) lard (7) palm-vegetable (8), palm-palm kernel, a = elastic non-recoverable deformation b = viscous flow B = breaking force P = plateau force distance between B and P is an indication of brittleness.

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