Pseudo plastic behavior

In order to understand the nature and mechanisms of foam flow in the reservoir, some investigators have examined the generation of foam in glass bead packs (12). Porous micromodels have also been used to represent actual porous rock in which the flow behavior of bubble-films or lamellae have been observed (13,14). Furthermore, since foaming agents often exhibit pseudo-plastic behavior in a flow situation, the flow of non-Newtonian fluid in porous media has been examined from a mathematical standpoint. However, representation of such flow in mathematical models has been reported to be still inadequate (15). Theoretical approaches, with the goal of computing the mobility of foam in a porous medium modelled by a bead or sand pack, have been attempted as well (16,17). 

Solyom and Ekwall (20) have studied rheology of the various pure liquid crystalline phases in the sodium caprylate-decanol-water system at 20 °C, for which a detailed phase diagram is available. Their experiments using a cone-and-plate viscometer show that, in general, apparent viscosity decreases with increasing shear rate (pseudo-plastic behavior). Values of apparent viscosity were a few poise for the lamellar phase (platelike micelles alternating with thin water layers), 10-20 poise for the reverse hexagonal phase (parallel cylindrical micelles with polar... 

The term viscosity, as used above, is not accurate. Dense media at higher solid concentrations exhibit characteristics of non-Newtonian liquids, namely, Bingham plastic or pseudo-plastic behavior, as shown in Fig. 14. ... 

The reduction of viscosity with increasing shear rate is called pseudo-plastic behavior see Fig. 6.11, curve c. The shear stress-shear rate relationship of non-Newtonian fluids is non-linear. Therefore, non-Newtonian fluids are also referred to as non-linear fluids. 

It should be noted that fundamentally it is not entirely correct to take an expression derived for a Newtonian fluid and insert a power law viscosity form into it. However, if this simplification is not made, the analysis becomes much more complex and analytical solutions much more difficult to obtain, if not impossible. Results of the analytical solutions have been compared to results of numerical computations for a two-dimensional flow of a power law fluid. In most cases, the results are within 10 to 20% [2]. It should be noted that the results are exact when the power law index is unity, i. e., for Newtonian fluids. However, if the optimum depth and helix angle for a pseudo-plastic fluid are calculated using expressions valid for Newtonian fluids only, very large errors can result, particularly when the power law index is about one-half or less. It is therefore very important to take the pseudo-plastic behavior into account, because the large majority of polymers are strongly non-Newtonian. 

For optimization of just the helix angle or the channel depth, the results from the Newtonian flow rate equation with correction factors for pseudo-plastic behavior, Eq. 8.54, are more accurate than the results from the modified Newtonian analysis, Eq. 8.36. It should again be noted that simultaneous optimization only makes sense for relatively large positive pressure gradients. When the pressure gradient is negative, the output increases monotonicaiiy with channel depth. In this case, there is no optimum channei depth. 

Fig. 15.3 Flow curve of systems with characteristic different behaviors (a) Newtonian behavior, (b) shear thinning behavior, (c) shear thickening behavior, (d) pseudo-plastic behavior...

Elevated temperature applications require materials that can maintain good mechanical properties such as strength and hardness. Ceramics have good mechanical properties at high temperature and, thus, appear to be good candidates for elevated temperature applications. However, due to their brittle nature, monolithic ceramics are unsuitable for many applications where reliability is a critical issue. In the last few years, a new class of ceramic materials has been developed and studied. It is understood that two brittle materials can show non-brittle behavior if they are properly mixed. Fiber-reinforced ceramic matrix composites (CMCs) exhibit pseudo-plastic behavior at room temperature, as well as in an elevated temperature environment. Since the fiber and the matrix are made of ceramic material, creep behavior and hazardous emissions are reduced considerably. 

The difficulty with implementing fracture mechanics mechanisms to address the problems of crack openings in carbon cathode blocks arises because the mechanical behavior of carbon cathode blocks is not fully elastic. Even at room temperature, carbon cathode blocks demonstrate elastoplastic or pseudo-plastic behavior (Figs. 1.10, 1.12, and 1.13) [69]. 

This law gives a decreasing viscous resistance with increasing shear rate and it therefore describes shear thinning or pseudo-plastic behavior. It is often convenient to use dimensionless variables in order to compare experimental data with the predictions of the Giesekus model. This can be achieved by dividing the steady-state shear viscosity by the zero shear viscosity and by multipl3dng the shear rate with the relaxation time ... 

Flow curves - Melt rheological properties of PES were evaluated on a capillary instrument attached to a Shimadzu Universal Materials Testing Machine model AG-IOTA. Viscosity curves measured at 315, 330 and 350°C and for shear rates ranging from 10 to 10000 1/s are presented in Figure 1. A typical pseudo-plastic behavior can be seen. That is, the melt viscosities of PES decrease with the increase of apparent shear rates. 

It has been broadly reported that the solubility of pectin is attributed to the valency of the salt forming cations. Monovalent cationic salts of pectin are highly soluble in water whereas di- ortri-valent cationic salts of pectin are weakly soluble in water. Dilute solutions of pectin show Newtonian behavior but at moderate concentrations they exhibit Non-Newtonian behavior. Further, pectin tends to show a pseudo plastic behavior, which could be related to its concentration in a solution [49]. The viscosity of the pectin on the other hand, is influenced by the molecular weight, degree of esterification, concentration of the preparation and the pH. 

In order to obtain complete thermal similarity, the screw rotation rate has to be decreased drastically, relative to the adiabatic case, with increasing screw diameter. As a result, the scale factor for the throughput is only 1.5 for Newtonian fluids (and decreases even fruilier for fluids with pseudo-plastic behavior). This scaling-up factor q) for the throughput is defined from ... 

Fig. 1. Behavior of non-Newtonian substances 0) true plastic (sometimes called a Bingham body (2) pseudo plastic (3) dllatant (4) thixotropic and (5) rheopectic...

There are two general types of constitutive equations for fluids Newtonian and non-Newtonian. For Newtonian fluids, the relation between the stress tensor, t, and the rate of deformation tensor or the shear stress is linear. For non-Newtonian fluids the relation between the stress tensor and the rate of deformation tensor is nonlinear. The various Newtonian and non-Newtonian rheologies of fluids are shown in Figure 12.2. There are four types of behavior (1) Newtonian, (2) pseudo-plastic, (3) Bingham plastic, and (4) dilatent. The reasons for these different rheological behaviors will also be discussed in subsequent sections of this chapter. But first it is necessary to relate the stress tensor to the rate of deformation tensor. 

At h h polymer concentrations, polymer molecules entangle, producing pseudo-plastic rheological behavior. This occurs at a polymer concentration, cf = comparable to that in the polymer... 

All the polymers that have been suggested as mobility control agents are pseudoplastic, i.e., they are shear-thinning. The extent of pseudo-plasticity is different for polyacrylamides, polysaccharides, and hydroxy ethyl cellulose. Viscosities of these polymers are plotted against shear rate in Figure 12. One model that describes the shear-thinning behavior observed is the Ost-wald-de Waele relationship ... 

An alternative classification for shear thinning and thickening is pseudo-plasticity and diiatancy however, these flow categories are rather limited to the so-called power law fluids. The flow behavior of a power law fluid may be described by the e. pression... 

Deviations from Newtonian flow can occur when shear stress does not increase in direct proportion to shear rate. Such deviation may be in the direction of thickening (called dilatent flow) and in the direction of thinning (called pseudo plastic). Related to non-Newtonian flow is the behavior of thixotropic liquids when subjected to shear, as explained above. Flow behavior can be represented by the following equation ... 

Flow behavior index for pseudo-plastic non-Newtonian liquid (—) Number of orifices in a given multiorifice nozzle (—)... 

In order to conduct the substructure pseudo-dynamic test, the prototype structure is modelled in two parts. One is the actual specimen which is experimentally tested so that the elasto-plastic behavior of the critical part of the structure is realistically represented. The behavior of the other part, which is expected not to critically affect the total response of the structure, is numerically calculated using a conventional nonlinear computational approach. The substracture pseudo-dynamic test is developed on a basis of pseudo-dynamic testing, which is an experimental technique for simulating the seismic response of the tested structure or component. 

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