Pseudo plastic behavior fluids

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). 

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. 

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 ... 

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. 

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... 

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