Characteristics of Polymer Flow

Upon a large shear rate, the polymer flow exhibits nonlinear viscoelasticity. In this case, the Boltzmann superposition principle becomes invalid, and the fluid appears as a non-Newtonian fluid. A typical treatment is to consider the nonlinear resptmse as separate processes at two different time scales the first one is the rapid elastic recovery in association with the shear rate, which can relax part of the stress instantaneously the second one is the slow relaxation of the rest stress in associa-ti(Mi with time. Thus, the nonlinear relaxation modulus can be expressed as 

Such a behavior of stress relaxation is called time-strain separability (Larson 1988). The factor h(y) is called the damping function. The empirical damping functions that are often used in polymer melts include the exponential function 

Here n and a are both positive constants. Doi and Edwards also derived a complicated damping function from the mbe model, which is close to the empirical reciprocal function with a = 0.2 (Larson 1988). 

The molecular dynamics theories need to make a proper combination to describe the rheological behaviors of polymer melt in various regions of shear rates (Bent et al. 2003). Above 1/t the convective constraint release dominates the rheological behaviors of polymers in shear flow, and thus explains the shear-thinning phenomenon. Beyond 1/t, the extensional deformation reaches saturation, and the shear flow becomes stable, entering the second Newtonian-fluid region, as demonstrated in Fig. 7.6. 

Shear flow can be roughly separated into the inclined extensional flow brought by the transverse velocity gradient, and the rotating flow, as illustrated in Fig. 7.8. The extensional flow leads to the major deformation of polymer coils, while the rotating flow makes tumbling of polymer coils upon flow. The latter realizes the 

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Inaccessible PV has been observed in all types of porous media for both polyacrylamides and biopolymers and is considered to be a general characteristic of polymer flow in porous media. The magnitude of the inaccessible PV can range from 1 % to 2% to as much as 25% to 30%, depending on the polymer and porous medium. Table 5.5 presents representative data on inaccessible PV for a xan-than and polyacrylamide in porous materials. A slight decrease in inaccessible PV with concentration is indicated by the polyacrylamide data, Several models have been offered to explain why inaccessible PV occurs,55 but none has gained universal acceptance. 

In polymer science we typically do not measure viscosity directly, but rather look at relative viscosity measures by determining the flow rate of one material relative to that of a second material. Viscosity is one of the most widely used methods for the characterization of polymer molecular weight because it provides the easiest and most rapid means of obtaining molecular weight-related data that requires minimal instrumentation. A most obvious characteristic of polymer solutions is their high viscosity, even when the amount of added polymer is small. This is because polymers reside in several flow planes (Figure 3.19b), acting to resist the flow of one plane relative to the flow of another plane. 

The Tg of elastomers must be below the use temperature. The high degree of cold flow which is characteristic of polymers at temperatures above the Tg is reduced by the incorporation of a few crosslinks to produce a network polymer with a low crosslink density. 

In 102,103) we have also studied rheological characteristics of the flow of molten polymers and compositions under conditions of acoustic treatment. Experiments indicate that the flow-rate of polymers through channels can be increased significantly with the help of acoustic treatment of molten polymers. Figures 21 gives the relative increase in the flow rate of high-density polyethylene versus amplitude of acoustic treatment. 

Increase in the flow of materials under acoustic treatment is conditioned by different factors. Investigation into rheological and molecular-mass characteristics of polymers having been subjected to acoustic treatment has revealed that, in the case of a low-intensity treatment, the effect is of a reversible (thixotropic) character. However, at high intensities of acoustic treatment, rheological characteristics of the material are not restored completely after the vibration effect is terminated and the... 

When a crack propagates in polystyrene at low crack velocities, the craze ruptures close to its median plane by a mechanism having the approximate characteristics of viscous flow. Each fracture surface is then covered by a thin layer of craze. At higher crack velocities, however, failure occurs along the boundaries between the craze and the adjacent bulk polymer by practically brittle fracture (I). The change in fracture... 

Dominguez, J.G., Willhite, G.P., 1977. Retention and flow characteristics of polymer solutions in... 

The quantitative layout of the eavity region and gating system requires primarily rheological expertise-in other words, knowledge of the flow characteristics of polymer melts. 

First of all, let s start with the problem of polymer flow. This also happens to be an important practical issue, because, during shaping and processing, polymers must undergo fluid flow (the "plastic" state). Long chains (which are not cross-linked) may slide and flow like any other liquid—when in solution or in a state that allows motion (above Tg, in the case of an amorphous polymer, or above T for a crystalline polymer). Compared to simple liquids, polymers are very different and have extremely high viscosity and a special flow characteristic, which is termed "non-Newtonian." It is therefore appro-... 

The mixing of reactants on a microlevel is substantially influenced by the physical characteristics of liquid flows, in particular, by the density and viscosity (Figure 2.12). Increasing the viscosity and decreasing the density of the reactants fed into a tubular turbulent device, can result in the situation where the reaction mixture homogenisation will be limited by molecular diffusion, which is common in the case of polymer solutions. The analysis of Equations 2.26-2.28 makes it possible to propose the criterion for breaking the automodel mode of reaction mixture flow, i.e., reduction in the efficiency of tubular turbulent diffuser-confusor devices with an increase of the medium viscosity [29] ... 

Like SEC, the primary object of thermal FFF is to fractionate polymer components in a flow column so that they emerge at different times characteristic of polymer molecular mass. The time-based detection of the emergent polymer sample can then be translated into the molecular-mass characteristics of the polymer distribution. 

The shear viscosity in polymer melts and solutions has been investigated for more than a half century. The blending process of polymers is generally performed in the molten state, particularly in shear flow. It is thus necessary to understand the flow (or better rheological) characteristics of polymer melts [66-70]. In both reactive and non-reactive blends, the shear viscosity of each polymer, and thus viscosity ratio, and bulk viscosity of polymer blend system needs to be understood. 

Section 3 describes how the flow characteristics of polymer solutions can be estimated from fundamental rheological properties. Using established structure-property relationships, it is possible to calculate the... 

Non-Newtonian characteristics are introduced by expressing the wall shear in the capillary tube as an equivalent shear derived from a rheological model such as the power-law model (Equation 1) or the Carreau Model A (Equation 2). Derivations of polymer flow models based upon power-law and Carreau Model A are found in references 6 and 7. Equation 7... 

The requirements for the presentation of the general flow characteristics of polymer solutions were best met by high molecular mass (3.5 10 ) hydrolyzed (40%) polymer. Concentration of the polymer was 100 ppm, viscosity of the solution under laboratory conditions (24 C) was 3.05 mPas. Taking into consideration the rock s permeability (59 10 and 62 10" ym ) and the equivalent diameter of the random coils (2600A), the polymer-rock system may be regarded as compatible. In the course of the experiments, comparison is made between the flow phenomena observed in the porous cores considered to be water wet and oil wet, respectively. When the permeability was determined by "connate water" (2% sodium chloride solution), the injection sequence of the fluids was as follows 1) polymer solution, 2) connate water, and 3) distilled... 

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