Power pseudoplastic fluids

A common choice of functional relationship between shear viscosity and shear rate, that u.sually gives a good prediction for the shear thinning region in pseudoplastic fluids, is the power law model proposed by de Waele (1923) and Ostwald (1925). This model is written as the following equation... 

Power consumption for impellers in pseudoplastic, Bingham plastic, and dilatant nonnewtonian fluids may be calculated by using the correlating lines of Fig. 18-17 if viscosity is obtained from viscosity-shear rate cuiwes as described here. For a pseudoplastic fluid, viscosity decreases as shear rate increases. A Bingham plastic is similar to a pseudoplastic fluid but requires that a minimum shear stress be exceeded for any flow to occur. For a dilatant fluid, viscosity increases as shear rate increases. 

Figure 7.8. Power curve for pseudoplastic fluids agitated by different types of impeller...

An extensive class of non-Newtonian fluids is formed by pseudoplastic fluids whose flow curves obey the so-called power law ... 

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 ... 

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 ... 

Both polymeric and some biological reactors often contain non-Newtonian liquids in which viscosity is a function of shear rate. Basically, three types of non-Newtonian liquids are encountered power-law fluids, which consist of pseudoplastic and dilatant fluids viscoplastic (Bingham plastic) fluids and viscoelastic fluids with time-dependent viscosity. Viscoelastic fluids are encountered in bread dough and fluids containing long-chain polymers such as polyamide and polyacrylonitrite that exhibit coelastic flow behavior. These... 

From this relationship, we see that for Newtonian foods ( = 1) the pressure gradient is proportional to the (ro) power. Therefore, a small increase in the radius of the mbe will result in a major reduction in the magnitude of the pressure gradient. In contrast, for a highly pseudoplastic fluid (e.g., n = 0.2), increasing the pipe radius does not have such a profound effect on the pressure gradient. 

For a Newtonian fluid, the power law index n = 1, and k is the fluid viscosity. Also, for shear-thinning (pseudoplastic) fluids, n < 1. 

Power Law Fluid or Emulsion A fluid or emulsion whose rheological behavior is reasonably well-described by the power law equation. Here shear stress is set proportional to the shear rate raised to an exponent n, where n is the power law index. The fluid is pseudoplastic for n < 1, Newtonian for n = 1, and dilatant for n > 1. 

Under typical processing conditions, polymer melts behave as pseudoplastic fluids. The viscosity of a pesu-doplastic fluid is shear rate dependent and is described by the following power law [Eq. (1)] ... 

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 ... 

Godleski E.S., Smith ).C., Power Requirements and Blend Times in the Agitation of Pseudoplastic Fluids,... 

In general, a polymer solution behaves like a pseudoplastic fluid. The reduction in polymer solution viscosity as a function of shear rate (y) is described by the power-law model (Bird et al., 1960), which is given by... 

One can see that the index n of a power-law fluid substantially affects the velocity profile. With increasing pseudoplasticity the distribution of the velocity becomes more and more homogeneous, approaching a quasisolid distribution with profile V = (V) = const in the limit as n —> 0. On the contrary, dilatancy makes the flow field more and more nonuniform, and as n - oo the velocity profile approaches the triangular shape given by... 

Figure 9.14 shows the power number-Reynolds number correlation for a six-blade turbine impeller in pseudoplastic fluids. The dashed curve is taken from Fig. 9.12 and applies to newtonian fluids, for which = nDlpJix. The solid curve is for pseudoplastic liquids, for which is given by Eqs. (9.25) and... 

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. 

Steady shear measurements were used to determine flow properties and to estimate the degree of structure breakdown with shear (Elliott and Ganz, 1977). The power law equation (Eq. 3) has been used to describe the shear stress-shear rate behavior of salad dressings (Figoni and Shoemaker, 1983 Paredes et al, 1988, 1989). The flow behavior index of five commercial salad dressings at different temperatures and storage times of up to 29 days were all less than one, indicating that they were pseudoplastic fluids. The consistency index (/f) decreased with the increase in product temperature. 

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. ... 

Here K and n are constants whose values are determined by fitting experimental data. For newtonian fluids n = 1 and AT = /x. For pseudoplastic fluids n is less than 1, and for dilatant fluids it is greater than 1. The power law has little theoretical basis its virtues are that it represents a considerable amount of experimental data with reasonable accuracy and that it leads to relatively simple mathematics. Many other equations have been used to represent these stress-strain rate curves. Some of the simpler ones are those of Ellis [3]... 

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