Fluid consistency index

Here, k is the fluid consistency index and m the flow behavior index. While no data for a gassed system under laminar and transition flow were reported, Pg is expected to depend on impeller dimensions in these regimes. 

In order to identify the behavior of the suspension fluid, the data in Table 10.7 can be plotted to verify resemblance to the typical fluids represented in Figure 10.2. The parameters of characterization can be determined from a logarithmic plot, where n would represent the flow behavior index and the intercept of the line on the y-axis the fluid consistency index. Plotting data from Table 10.7, Figure 10.16 is obtained. 

Estimate the cut point when treating 1 L/s of suspension in a hydrocyclone of 2 in diameter. The concentration of the suspension is 15% by volume, its density is 1250 kg/m , and behaves as non-Newtonian with determined values of the flow behavior index of 1.28 and the fluid consistency index of 2.03 x 10 . The density of the suspended solids is 2800 kg/m . 

K Ratio of horizontal to vertical pressure in silo, fluid consistency index (MT"/U),... 

Comparing Equations 8.34 and 8.35, it is seen that K and n can be obtained from the fluid consistency index K and the power law index n ... 

Fluid Consistency (Pa s)a Flow index Y (s 1) Yield stress (Pa) Flow rates (mL s"1)... 

Hydraulic fracturing fluids are solutions of high-molecular-weight polymers whose rheological behavior is non-Newtonian. To describe the flow behavior of these fluids, it is customary to characterize the fluid by the Power Law parameters of Consistency Index (K) and Behavior Index (n). These parameters are obtained experimentally by subjecting the fluid to a series of different shear rates (y) and measuring the resultant shear stresses (t). The slope and Intercept of a log shear rate vs log shear stress plot yield the Behavior Index (n) and Consistency Index (Kv), respectively. Consistency Indices are corrected for the coaxial cylinder viscometers by ... 

Here, K is sometimes referred to as the consistency index and has units that depend on the value of the power law index, n—for example, N-s"/m. The power law index is itself dimensionless. Typical values of K and n are listed in Table 4.4. In general, the power law index is independent of both temperature and concentration, although fluids tend to become more Newtonian (n approaches 1.0) as temperature increases and concentration decreases. The consistency factor, however, is more sensitive to temperature and concentration. To correct for temperature, the following relationship is often used ... 

The consistency index K (or K ), which characterizes the consistency or thickness of a fluid. It is analogous to the viscosity of a Newtonian fluid and similarly enables quantitative comparison of the consistency of fluids having identical flow-behavior indexes. 

As pointed out in Section I, viscosities are really meaningful if compared only for Newtonian fluids or at specified shear rates for other materials. A similar limitation must be imposed on the consistency indexes K and K values of either are comparable only for fluids with the same flow behavior indexes n or n . 

Decreases in concentration or increases in temperature usually decrease the consistency indexes K and K but leave the flow-behavior indexes n and n relatively unaltered. The latter appear to be determined primarily by the components of the non-Newtonian fluid and increase only slightly with increases in temperatures or decreases in concentration for pseudoplastic materials. 

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 consistency index constant, Kpl, and the consistency index number, ft, were calculated for all corn stover suspensions, using linear regression. The results are presented in Table 1. All of the regression coefficients are above 0.99. The parameters are independent of the method of measuring rheologic data and dependent on the fluid. 

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.]...

If the viscosity curve is plotted in a log-log scale and the transition range between p0 and po= is represented by a straight line with the slope m < 1, see Fig. 18, then one speaks about a Ostwald-de Wade fluid whose viscosity curve obeys the so-called power laid (peff- effective viscosity, K - consistency index, m - flow index) ... 

A wide range of temperatures are encountered during processing and storage of fluid foods, so that the effect of temperature on rheological properties needs to be documented. The effect of temperature on either apparent viscosity at a specified shear rate (Equation 2.42) or the consistency index, K, of the power law model (Equation 2.43) of a fluid can be described often by the Arrhenius relationship. The effect of temperature on apparent viscosity can be described by the Arrhenius relationship ... 

For foods that follow the simple power law model, the flow behavior index is determined as the slope of a double logarithmic plot of log N (abscissa) versus log torque (ordinate). In order to determine the consistency index, magnitudes of torque must be determined in the same container for the test fluid and for a standard fluid whose... 

In Equation (2), n is the flow behavior index (-),K is the consistency index (Pa secn), and the other terms have been defined before. For shear-thinning fluids, the magnitude of nshear-thickening fluids n>l, and for Newtonian fluids n=l. For PFDs that exhibit yield stresses, models that contain either (Jo or a term related to it have been defined. These models include, the Bingham Plastic model (Equation 3), the Herschel-Bulkley model (Equation 4), the Casson model (Equation 5), and the Mizrahi-Berk model (Equation 6). 

In the case of non-Newtonian fluids, one can use either the apparent viscosity,Tla, at a specified shear rate or the consistency index, K, in the power law model in place of T. ... 

COJ of 65 °Brix is a mildly shear-thinning fluid 160) with magnitudes of flow behavior index of the power law model (n) (Equation 2) of about 0.75 that is mildly temperature dependent. In contrast, the consistency index (K) is very sensitive to temperature for example, Vital and Rao (hi) found for a COJ sample magnitudes of 1.51 Pa sec11 at 20 °C and 27.63 Pa secn at -19 °C. Mizrahi and Firstenberg (hi) found that the modified Casson model (Equation 5) described the shear rate-shear stress data better than the Herschel-Bulkley model (Equation 4). 

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