Power law model fluid

Cloud, J.E. and Clark, P.E. "Stimulation Fluid Rheology III. Alternatives to the Power Law Fluid Model for Crosslinked Fluids," SPE paper 9332, 1980 SPE Annual Technical Conference and Exhibition, Dallas, September 21 24. 

Newtonian fluids can be correlated by this method that is, the same correlation applies to both Newtonian and non-Newtonian fluids when the Newtonian Reynolds number is replaced by either Eq. (7-40) for the power law fluid model or Eq. (7-41) for the Bingham plastic fluid model. As a first approximation, therefore, we may assume that the same result would apply to friction loss in valves and fittings as described by the 2-K or 3-K models [Eq. 7-38)]. 

This relationship, as we will see in Section 3.3, is called the Power Law fluid model, and is used extensively in modeling flows in polymer processing. 

Fig. E5.1 Parameter reflecting thermal degradation of unplasticized PVC, Geon 101 EP-F24, as indicated by the time dependence of the consistency index m of the Power Law fluid model. [Reprinted by permission from E. A. Collins, B. F. Goodrich Chemical Co., Avon Lake, Ohio. Paper presented at the 1965 Society of Plastics Engineers Annual National Technical Conference, March 1966.]...

In this case, the system does not show a yield value rather, it shows a limiting viscosity ri 6) at low shear rates (that is referred to as residual or zero shear viscosity). The flow curve can be fitted to a power law fluid model (Ostwald de Waele)... 

As the power law model [Equation (20.3)] fits the experimental results for many non-Newtonian systems over two or three decades of shear rate, this model is more versatile than the Bingham model, although care should be taken when applying this model outside the range of data used to define it. In addition, the power law fluid model fails at high shear rates, whereby the viscosity must ultimately reach a constant value - that is, the value of n should approach unity. 

The polymer solutions or base gels and suspensions exhibited pseudoplastic non-Newtonian behavior, and they were characterized by the following Ostwald-de Waele or power law fluid model. 

Estimate the hindered settling velocity of a 30% (by volume) defloccu- (a) lated suspension of 50 /rm (equivalent spherical diameter) china clay particles in a polymer solution following the power-law fluid model... 

The rheological behaviour of the polymer solution is well approximated by the power-law fluid model with n = 0.5 and m = 1.6Pa s". 

Figure 5.55 Thermal degradation of unplasticized PVC, Ceon 101 EP-F24, as indicated by the time dependence of the consistency index m of the power law fluid model [1]. See text for details.

In turbulent flow, the Fanning friction factor ff for the slurry described by a power-law fluid model depends on both the generalized Reynolds number Re and the flow behaviour index n. 

Now, non-Newtonian behavior is almost Invariably observed in various lubrication processes, such fluids violate the Newtonian postulate which assumes a linear relationship between shear stress and rate of shear. Various theories have been postulated in recent years to describe the flow behavlous of non-Newtonian fluids. One of the models is that of the "power law" fluid model, in which the shear stress varies as some power of shear rate. The so-called "power law" constitutive equation is widely used because not only some fluids yeild this constitutive relation in certain condition, but also its simplisity. The power law exponent n is the rheological index. For n=l, the fluid is Newtonian, for nl, it is a dilatant fluid. 

For the above pseudo-plastic flow, one may apply a power law fluid model, a Bingham model [9] or a Casson model [10]. These models are represented by the following equations respectively. 

The various early approaches to the mathematical modelling of non-Newtonian rheology in porous media are reviewed by Savins (1969). One of these is via a capillary bundle view of the porous medium combined with a simple (usually power law) fluid model. From the discussion in Section 6.2, one might not expect this approach to be very fruitful. However, it has been used by a number of workers—in fact, virtually all studies of xanthan flow in porous media present a version (see below)—and results have been sufficiently simple and promising to deserve some further attention. The main objective in these studies is to relate the in-situ rheology of the polymer to... 

The most effective model for non-Newtonian flow is the Ostwald-de Waele two-parameter, power-law fluid model [13]. The popularity of this model is easily traced to its Iractability in mathematical manipulations. In the power-law model, the apparent viscosity y = j. l CM Idy = r/y of a polymer fluid subject to a simple steady shear flow is given by... 

Applying the power-law fluid model (Equation 7.12) gives... 

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