Polymer Melts and Solutions

FIGURE 14.4 Flow curves for time-dependent fluids under continuously increasing and then decreasing shear. 

at low shear rates (or low stresses), a lower Newtonian region is reached with a so-called zero-shear viscosity, rj.  

FIGURE 14.5 Generalized flow properties of polymer melts and solutions. 

INTRODUCTION TO VISCOUS FLOW AND THE RHEOLOGICAL BEHAVIOR OF POLYMERS 

over several decades of intermediate shear stress, the material is pseudoplasatic, and 

When the flow properties of polymer melts and solutions can be measured over a wide enough range of shearing, the logarithmic flow curves appear as in Fig. 15.5. It is generally observed that  

At very high shear rates, an upper Newtonian region, with viscosity is attained. 

It is worthwhile to consider here what happens to the highly oriented molecules when the shear field is removed. The randomizing effect of thermal energy tends to return them to their low-shear configurations, giving rise to an elastic retraction. 

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Polymer solutions are often characterized by their high viscosities compared to solutions of nonpolymeric solutes at similar mass concentrations. This is due to the mechanical entanglements formed between polymer chains. In fact, where entanglements dominate flow, the (zero-shear) viscosity of polymer melts and solutions varies with the 3.4 power of weight-average molecular weight. 

R. Granek. Stress relaxation in polymer melts and solutions Bridging between the breathing and reptation regimes. Macromolecules 2<5 5370-5371, 1995. 

R. G. Larson, Constitutive Equations for Polymer Melts and Solutions, Butterworths, Boston (1988). 

The thickness of interphases in polymer melts and solutions may be much greater than in low-molecular matrices owing to the greater size of their macromolecules and existence in them of submolecular associates [51],... 

Many papers deal with the crystallization of polymer melts and solutions under the conditions of molecular orientation achieved by the methods described above. Various physical methods have been used in these investigations electron microscopy, X-ray diffraction, birefringence, differential scanning calorimetry, etc. As a result, the properties of these systems have been described in detail and definite conclusions concerning their structure have been drawn (e.g.4 13 19,39,52)). 

Larson RG (1988) Constitutive equations for polymer melts and solutions, Butter-worths, Boston, p 256... 

J. P. W. Baaijens, Evaluation of Constitutive Equations for Polymer Melts and Solutions in Complex Flows, Eindhoven University of Technology, Department of Mechanical Engineering, Eindhoven, The Netherlands (1994). 

We have tried to give a quick glimpse of the interrelationships among some commonly used constitutive equations for polymer melts and solutions. None predicts quantitatively the entire spectrum of the rheological behavior of these materials. Some are better than others, becoming more powerful by utilizing more detailed and realistic molecular models. These, however, are more complex to use in connection with the equation of motion. Table 3.1 summarizes the predictive abilities of some of the foregoing, as well as other constitutive equations. 

Extrudate swelling refers to the phenomenon observed with polymer melts and solutions that, when extruded, emerge with cross-sectional dimensions appreciably larger than those of the flow conduit. The ratio of the final jet diameter to that of the capillary D/Dq, for Newtonian fluids varies only from 1.12 at low shear rates to 0.87 at high rates. Polymer... 

Experimentally, as indicated in Fig. 12.13, we find that D/Dq depends on the shear stress at the wall xw (a flow variable) and the molecular weight distribution (MWD) (a structural variable) (22). The length-to-diameter ratio of the capillary (a geometric variable) also influences D/Dq. The swelling ratio at constant xw decreases exponentially with increasing L/Dq and becomes constant for L/Dq > 30. The reason for this decrease can be explained qualitatively as follows. Extrudate swelling is related to the ability of polymer melts and solutions to undergo delayed elastic strain recovery, as discussed in... 

Polymer melts and solutions, on the other hand, are Theologically more complex fluids and, even under simple radiating flows in the entrance region, would need more stress components to sustain them thus there are larger entrance pressure drops. Additionally, the entrance flow patterns with polymer melts and solutions are typically more complex.6... 

Estimation of Entrance Pressure-Pressure Losses from the Entrance Flow Field17 Consider the entrance flow pattern observed with polymer melts and solutions in Fig. 12.16(a). The flow can be modeled, for small values of a, as follows for 0 < a/2 the fluid is flowing in simple extensional flow and for a/2 < 0 < rc/2 the flow is that between two coaxial cylinders of which the inner is moving with axial velocity V. The flow in the outer region is a combined drag-pressure flow and, since it is circulatory, the net flow rate is equal to 0. The velocity V can be calculated at any upstream location knowing a and the capillary flow rate. Use this model for the entrance flow field to get an estimate for the entrance pressure drop. 

Larson RG, "Constitutive Equations for Polymer Melts and Solutions", Butterworth, London, 1988. 

If)/ is independent of shear history, the material is said to be time independent. Such liquids can exhibit different behavior patterns, however, if, as is frequently the case with polymers, )/ varies with shear rate. A material whose viscosity is independent of shear rate, e.g., water, is a Newtonian fluid. Figure 11-26 illustrates shear-thickening, Newtonian and shear-thinning rj-y relations. Most polymer melts and solutions are shear-thinning. (Low-molecular-weight polymers and dilute solutions often exhibit Newtonian characteristics.) Wet sand is a familiar example of a shear-thickening substance. It feels hard if you run on it, but you can sink down while standing still. 

A variety of laboratory instruments have been used to measure the viscosity of polymer melts and solutions. The most common types are the coaxial cylinder, cone-and-plate, and capillary viscometers. Figure 11 -28 shows a typical flow curve for a thermoplastic melt of a moderate molecular weight polymer, along with representative shear rate ranges for cone-and-plate and capillary rheometers. The last viscometer type, which bears a superficial resemblance to the orifice in an extruder or injection molder, is the most widely used and will be the only type considered in this nonspecialized text. 

In the story of numerical flow simulation, the ability to predict observed and significant viscoelastic flow phenomena of polymer melts and solutions in an abrupt contraction has been unsuccessful for many years, in relation to the incomplete rheological characterization of materials, especially in elongation. The numerical treatments have often been confined to flow of elastic fluids with constant viscosity, described by differential constitutive equations as the Upper Convected Maxwell and Oldroyd-B models. Fortunately, the recent possibility to use real elastic fluids with constant viscosity, the so-called Boger fluids [10], has narrowed the gap between experimental observation and numerical prediction [11]. 

Chemical Process Equipment Staniey M. Waha Constitutive Equation s for Polymer Melts and Solutions Ronald C- Laram... 

Perhaps the most important distinction between classical solids and classical liquids is that the latter quickly shape themselves to the container in which they reside, while the former maintain their shape indefinitely. Many complex fluids are intermediate between solid and liquid in that while they maintain their shape for a time, they eventually flowr They are solids at short times and liquids at long times hence, they are viscoelastic. The characteristic time required for them to change from solid to liquid varies from fractions of a second to days, or even years, depending on the fluid. Examples of complex fluids with long structural or molecular relaxation times include glass-forming liquids, polymer melts and solutions, and micellar solutions. 

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