Dilatant fluid 556 INDEX

The values of the consistency index K and the flow behavior index n of a dilatant fluid are 0.415 and 1.23, respectively. Estimate the value of the apparent viscosity of this fluid at a shear rate of 60 s T... 

The simple concept of an average mixer shear rate has been widely used in laboratory and industrial work and in most applications it has been assumed that the shear rate constant, k, is only a function of impeller type. Research is continuing on the possible influence of flow behaviour index and elastic properties, and also on procedures necessary to describe power consumption for dilatant fluids. It should be noted that in all aspects of power prediction and data analysis, power law models (equation 8.12) should only be used with caution. Apparent variability of k, may be due to inappropriate use of power law equations when calculations are made it should be ascertained that the average shear rates of interest (y = k N) lie within the range of the power law viscometric data. 

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. 

Figure 10 shows representative streamline patterns for oblates, prolates, and spheres in Newtonian and shear-thinning fluids similar results (not shown here) are obtained for dilatant fluids. The streamline patterns for sphere match with the literature predictions for example see Clift et al. (1978) for Newtonian fluids and Adachi et al. (1973) for power-law fluids (n< 1). The effect of the flow behavior index on streamline patterns for a sphere is found to be negligible, except the fact that the wake formation is somewhat delayed. For prolate spheroids (E = 5), no wake formation occurs even at Re = 100, whereas for oblates, a visible wake is formed even at Re= 10 for = 0.2. To recap, the flow patterns appear to be much more sensitive to the... 

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. 

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... 

With a power law index, = 1, the fluid behaves Newtonian. If 0 < < 1, the viscosity decreases when shear rates increase. This behavior, which applies to virtually all polymers, is called pseudoplasticity or shear thinning behavior. If > 1, the liquid is called dilatant or shear thickening. This behavior, in which viscosity increases when the shear rate increases, has only been observed in materials with a very high concentration of fillers and has no relevance to reactive extrusion. 

Ostwald-de Waele equation A simplified power law relaflonshlp used to describe non-Newtonian fiulds as T=ay ". Depending on the value of the power index, n, the fluid can be classified as being pseudoplastic (n < 1), Newtonian (n= 1), or dilatant (n> 1). It is named alter German chemist Friedrich Wilhelm Ostwald (1853 1932) and British chemist Armand de Waele (1887-1966). 

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