Ostwald-de Waele

A useful two-parameter model is the power-law model, or Ostwald-de Waele law to identify its first proponents. The relation between shear stress and shear rare is given by ... 

A highly concentrated suspension of flocculated kaolin in water behaves as a pseudo-homogeneous fluid with shear-thinning characteristics which can be represented approximately by the Ostwald-de Waele power law, with an index of 0.15. It is found that, if air is injected into the suspension when in laminar flow, the pressure gradient may be reduced even though the flowrate of suspension is kept constant, Explain how this is possible in slug flow and estimate the possible reduction in pressure gradient for equal volumetric flowrates of suspension and air. 

The study of bubble formation in non-Newtonian fluids has not been reported in literature in spite of the great industrial uses of these fluids. Recently, Subramaniyan and Kumar (S16) have studied bubble formation under constant flow conditions in fluids following the Ostwald-de-Waele rheological model. The model of Kumar and Kuloor (K16, K18, K19) has been extended to take into consideration the drag variation caused by the complexity of the rheological equation. 

These liquids are known as Ostwald-de Waele Fluids. Figure 8 depicts a typical course of such a flow curve. 

Figure 8 Typical course of the flow curve of an Ostwald-de Waele fluid obeying the so-called power law behavior.

These liquids are known as Ostwald-de Waele fluids. Figure 5 depicts a typical course of such a flow curve. Figure 6 shows a dimensionless standardized material function of two pseudoplastic fluids often used in biotechnology. It proves that they behave similarly with respect to viscosity behavior under shear stress. 

In this case, p is an arbitrary constant, chosen as the zero shear rate viscosity. The expression for the non-Newtonian viscosity is a constitutive equation for a generalized Newtonian fluid, like the power law or Ostwald-de-Waele model [6]... 

One of the most common empirical models used to describe the behaviour of pseudoplastic fluids is the the Ostwald-de Waele [374,375] model or, more colloquially, the power law model ... 

The power law, or Ostwald-de Waele, model is the simplest and most widely used rheologic empiricism. The power law states... 

In the description of processes in which Ostwald-de Waele fluids take part, H and are included into the relevance list. can be formulated in a dimensionless manner as well as by other x quantities relevant to the process. In pipe flow it can be replaced by (1/v), whereby v and 1 are the characteristic flow velocity and length, respectively. The Reynolds number then has the following appearance ... 

According to (8.57), the material function of pseudoplastic fluids (IIrheoi = m), whose viscosity obeys the power law of Ostwald-de Waele, can be represented in the pi-space ... 

Several models have been proposed to describe the dependence of viscosity on shear rate. One of the most used in engineering applications is the two-parameter Ostwald-De Waele model given by (45)... 

To the same family of curves belong pseudoplastic materials. These fluids show a decrease in apparent viscosity with an increase in the rate of shear and are typical of the majority of non-Newtonian liquid food products. The way most often used to describe the properties of these materials is an empirical Ostwald-de Waele power law equation ... 

If, in a double logarithmic plot of the viscosity curve, a straight line with a slope nt < 1 is found (see dashed curve (4) in Fig. 1.28, right side), this liquid is termed an Ostwald - de Waele fluid, whose viscosity curves obey the so-called power law ... 

The material functions of pseudoplastic fluids, whose viscosities obey the power law (Ostwald-de Waele fluids), can according to the above be represented dimensionally analyticaly correctly as follows ... 

For determining the sedimentation velocity of spherical particles in pseudoplastic liquids, whose viscosity obeys the power law according to Ostwald - de Waele, see [294]. 

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)... 

Newtonian Ostwalde-de Waele power-law fluid Shvedov-Bingham... 

Power-law dependence of consistence factor on temperature. The experiments described [286] dealt with water solutions of carboxymethylcellulose, whose flow curve is well described by the power-law Ostwalde-de Waele equation. It was shown that the index n is virtually invariable in the temperature interval 15 to 60°C, whereas the medium consistence factor can be approximated by the expression... 

This equation predicts a straight line on a log-log plot of viscosity and shear rate with a slope of [n-1]. A horizontal line or n s 1 indicates a Newtonian fluid. The fluids that obey the Ostwald-de Waele model are called power-law fluids and n is referred to as the power-law index. 

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