Rheology elastic behavior

Detailed treatments of the rheology of various dispersed systems are available (71—73), as are reviews of the viscous and elastic behavior of dispersions (74,75), of the flow properties of concentrated suspensions (75—82), and of viscoelastic properties (83—85). References are also available that deal with blood red ceU suspensions (69,70,86). 

From a technical standpoint, it is also important to note that colloids display a wide range of rheological behavior. Charged dispersions (even at very low volume fractions) and sterically stabilized colloids show elastic behavior like solids. When the interparticle interactions are not important, they behave like ordinary liquids (i.e., they flow easily when subjected to even small shear forces) this is known as viscous behavior. Very often, the behavior falls somewhere between these two extremes the dispersion is then said to be viscoelastic. Therefore, it becomes important to understand how the interaction forces and fluid mechanics of the dispersions affect the flow behavior of dispersions. 

Thus far we have given exclusive attention to the flow of purely viscous fluids. In practice the chemical engineer often encounters non-Newtonian fluids exhibiting elastic as well as viscous behavior. Such viscoelastic fluids can be extremely complex in their rheological response. The le vel of mathematical complexity associated with these types of fluids is much more sophisticated than that presented here. Within the limits of space allocated for this article, it is not feasible to attempt a summary of this very extensive field. The reader must seek information elsewhere. Here we shall content ourselves with fluids that do not exhibit elastic behavior. 

Real materials are neither truly Hookean nor truly Newtonian, though some exhibit Hookean or Newtonian behavior under certain conditions (Barnes et al., 1989). Real materials may exhibit nonlinearity, which is a lack of direct proportionality between stress and strain, or between stress and strain rate. Real materials may exhibit either predominantly elastic behavior or predominantly viscous behavior, or a measurable combination of the two, depending on the stress or strain and the duration of its application (Barnes et al., 1989). Such materials are termed viscoelastic. Barnes et al. (1989) pointed out that it is better to classify rheological behavior than to classify materials, a given material can then be included in more than one rheological class depending on experimental conditions. 

As with cylinder- and lamellae-forming block copolymers, the rheological behavior of block copolymers that form spherical domains depends on whether or not the domains possess macrocrystalline order. If the domains are disordered, then the low-frequency moduli show terminal behavior typical of ordinary viscoelastic liquids that is, G and G" fall off steeply as the frequency becomes small (Watanabe and Kotaka 1983, 1984 Kotaka and Watanabe 1987). When the spherical domains are ordered, however, elastic behavior is observed at low frequency that is, G approaches a constant at low frequency, and a yield stress is observed in steady shearing. 

In general, a material can be characterized based on the two types of rheological behavior, that is, viscous and elastic. A solid body is characterized by its elastic behavior when the deformation is fully recovered... 

Rheological studies of PET nanocomposites are not ample, but show very interesting features. In the low frequency range, the nanocomposites display a more elastic behavior than that of PET. It appears that there are some physical network structures formed due to filler interactions, collapsed by shear force, and after all the interactions have collapsed, the melt state becomes isotropic and homogeneous. Linear viscoelastic properties of polycaprolactone and Nylon-6 [51] with MMT display a pseudo-solidlike behavior in the low frequency range of... 

Indeed, to exploit effectively the viscoelasticity of fluids for chaotic flow instability, and thus mixing, sharper and smaller geometries should be employed. Stress singularities developed at such comers have been the source of elastic instabilities in many macroscale experiments [3], while rounded comers tend to suppress elastic behavior. From a practical standpoint, it is necessary to understand the rheological nature of such flow in order to optimize the use of viscoelastic effects... 

Major effects of vulcanization [2-4] on use-related properties are illustrated by the idealization of Fig. 2. It should be noted that static modulus increases with vulcanization to a greater extent than does the dynamic modulus. (Here, static modulus is more correctly the equilibrium modulus, approximated by a low strain, slow-strain-rate modulus. Dynamic modulus is generaUy measured with the imposition of a sinusoidal, small strain at a frequency of 1-100 Hz.) The dynamic modulus is a composite of viscous and elastic behavior, whereas static modulus is largely a measure of only the elastic component of rheological behavior. 

A characteristic feature of a gel is its elastic behavior the gel deforms by an imposed force and it relaxes to its original state after releasing the force. Elastin, a crosslinked polypeptide network takes care of the elasticity of human and animal connective tissues, such as skin, ligaments, and arterial walls. For a more extensive discussion on the rheological properties of gels, the reader is referred to Chapter 17. 

The classification of materials given here is based on the rheological properties discussed in the foregoing section. Elastic behavior is independent of the duration of the deformation but with viscous systems time-independent and time-dependent behavior may be distinguished. 

In many practical systems, polymers are added to solutions to conttol their flow characteristics. The attractive feature of polymeric additives is that even in rather low concenttations they can dramatically affect the rheology of a fluid, imparting to a solution properties intermediate between those of elastic solids and those of viscous fluids. The elastic behavior is dominant in solids. It is described by Hooke s law (a = Ey, Eq. 19, see above). Viscous behavior is dominant in simple liquids. It is described by Newton s law (Eq. 43), which states that the applied stress a is proportional to the rate of strain dyidt, with a proportionality constant ii, the viscosity. 

An experimental study was made [48] that compared the heat-transfer behavior of a polyethylene having marked elastic behavior to one whose rheological data showed only slight elasticity (i.e., much lower normal stress values). Some typical temperature profile curves for the polymer are shown in Figs. 4-51-4-56. 

Flowing systems are also typical examples in which this Unear behavior is broken. This is the case of rheology, the study of viscosity of complex fluids, that is, of fluids with internal structure that exhibit a combination of viscous and elastic behavior under strain (Beris Edwards, 1994 Doi Edwards, 1998). Examples of such fluids are polymer solutions and melts, oil and toothpaste, among many others. 

In the rheology of condensed phases, the elastic modulus G is often used as the sole characteristic of elastic behavior. In isotropic media mechanics, it has been established that for solid-like bodies, the modulus G 2/5 of the Young s modulus [10]. 

Let us first focus on the elastic behavior case (i.e., restrict ourselves to the initial linear portion of the rheological curve). In so doing, we define the root of our solution, that is, set the dependence between the stress and the strain in the elementary volume, that is, in our case Hooke s law yields x = Gy = Gp /H per unit area. In order to find the stress in the entire ring, that is, within any horizontal cross section of the selected volume element, we need to multiply x by 2)tpdp, that is,... 

Up to this point the linear dependence between M and 4) has been assumed. This dependence corresponds to linear elastic behavior, that is, M = const (f). This means that in the construction of the deformation curve other rheological factors may start to play a role. These factors include the viscous flow and failure. When conducting measurements in... 

Figure 8 shows low shear rate rheological results for an ethylene homopolymer and an ethylene/1-hexene copolymer with catalyst 15/MAO [81]. Ethylene homopolymers by this catalyst exhibit the rheological behavior of linear chain polymers. In contrast, the copolymer displays a higher molecular weight and broader MWD than the corresponding ethylene homopolymers and, as shown in Fig. 8, in the copolymer melt the elastic behavior dominates even at the lowest frequencies. Behavior like this suggests the presence of widely different relaxation times, as in a crosslinked network structure (but the polymer was completely... 

Viscoelasticity refers to rheological behavior that is a combination of viscous (liquid-like) and elastic (solid-like) behavior. Ideal elastic behavior is called Hookean, where the stress is directly proportional to the strain. A Hookean solid deforms as long as stress is applied. Once stress is removed, it fuUy recovers its original shape. This behavior can be modeled by a spring that stores energy under deformation and then releases it Ideal viscous behavior is called Newtonian , where the stress is directly proportional to the rate of strain. 

The dimensionless blend time, NO, is a constant for a helical ribbon operating in the laminar regime (see, e.g., Hoogendoom and den Hartog, 1967 Johnson, 1967 Rieger et al., 1986). This means that the blend time is independent of Reynolds number and the fluid viscosity, so that even if the fluid is shear-thinning the blend time will not be affected by the rheological behavior. This is not true for visco-elastic behavior. 

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