Ostwald de-Waele law

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 ... 

This law, also called the Ostwald-de Waele law, is valid only in a definite range (generally, the 10 range) of shear rate. 

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. 

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

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... 

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 ... 

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. 

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. 

The log-log plots of apparent shear stress versus apparent shear rate for STR5L/ EPDM and STR5L/BEPDM blends with various blend compositions are shown in Figs. 15.12 and 15.13, respectively (71). Flow curves of all the blends show reasonably straight hnes, whose intercept K and slope n correspond to the power law equation (the Ostwald-de Waele equation) (72). Table 15.4 shows the power law index and the consistency of flow of STR5L/EPDM and STR5L/BEPDM blends. The values of n n < 1) indicate the pseudoplastic nature of STR5L, EPDM, BEPDM, and their blends. 

In many cases the experimental curves for both dilatant and pseudoplastic fluids can be reasonably well represented by the power law, also called the Ostwald-de Waele equation. ... 

The results obtained during the Couette flow of aqueous solutions of polyethylene oxide and other water-soluble polymers appear especially promising since they showed an appreciable increase in the current noise level with shear rate. The current noise level depended also on the viscosity (molecular weight) of the solution. A slight increase of thermal noise was recorded also. The pseudoplasticity exponent n in the Ostwald-de Waele power law formula and the exponent a in the l/f -frequency distribution of the current noise were interrelated. This relation appeared to be generally valid. 

The literature [5] lists numerous different, material laws. It therefore should be noted at this point that the more coefficients a material law has, the more complicated it is to measure them, and the more difficult it is to incorporate them into equations of momentum and motion. For the calculation of an extruder, such equations yield differential-equation systems with elaborate flow laws that defy analytical resolution. Consequently, the measured flow curve should be approximated with the aid of a relatively uncomplicated material law that still adequately describes the extrusion compound. Several of the approaches used in plastics/rubber/pharma-ceutical technology include [6] power approach after Ostwald/de Waele and formulations according to Carreau, Miistedt, Casson, Herschel/ Bulk-ley, Bingham and Reiner/Philippoff... 

The rheological profile obtained from the viscometer is fitted with Ostwald-de Waele Power law model. This mathematical model has been reported to have lowest standard error. The power law mathematical model is given by ... 

---