Consistency index

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 ... 

T able 3 Shear viscosity, die swell, flow behavior index, and consistency index of various samples at a shear rate of 61.2 s-1... 

Sample designation Shear viscosity (kPa-s) Die swell (%) Flow behavior index (n) Consistency index (k) (xIO 4 kPa-s)... 

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. 

With these instruments the relationship between DAP/4L and 8 V/D is obtained directly. On a logarithmic plot of DAP/4L versus 8 V/D the slope of the curve at any point is equal to the flow-behavior index n extension of the tangent to the curve at this point to a value of 8V/D of unity gives the corresponding value of the consistency index K. ... 

Determine the values of the consistency index K, the flow behavior index n, and also the apparent viscosity at the shear rate of 50 s . ... 

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... 

Estimate the stirrer power requirement P for a tank fermentor, 1.8 m in diameter, containing a viscous non-Newtonian broth, of which the consistency index A = 124, flow behavior index n = 0.537, density p = 1050 kg m", stirred by a pitched-blade, turbine-type impeller of diameter d = 0.6 m, with a rotational speed AT of 1 s . ... 

Figure 6.34 Comparison between experiments and theoretical predictions of maximum pressure between the rolls during the calendering process of an unplasticized PVC film. A power law index, n, of 0.1505 and a consistency index, m, of 155.2 kPa-s were used in the power law model of the viscosity.

Sample balancing problem. Let us consider the multi-cavity injection molding process shown in Fig. 6.54. To achieve equal part quality, the filling time for all cavities must be balanced. For the case in question, we need to balance the cavities by solving for the runner radius R2. For a balanced runner system, the flow rates into all cavities must match. For a given flow rate Q, length L, and radius R, solve for the pressures at the runner system junctures. Assume an isothermal flow of a non-Newtonian shear thinning polymer. Compute the radius R2 for a part molded of polystyrene with a consistency index (m) of 2.8 x 104 Pa-s" and a power law index (n) of 0.28. Use values of L = 10 cm, R = 3 mm, and Q = 20 cm3/s. 

Predicting pressure profiles in a disc-shaped mold using a shear thinning power law model [1]. We can solve the problem presented in example 5.3 for a shear thinning polymer with power law viscosity model. We will choose the same viscosity used in the previous example as the consistency index, m = 6,400 Pa-sn, in the power law model, with a power law index n = 0.39. With a constant volumetric flow rate, Q, we get the same flow front location in time as in the previous problem, and we can use eqns. (6.239) to (6.241) to predict the required gate pressure and pressure profile throughout the disc. 

A 15 cm diameter, 2 m wide calendering system is used to produce a PVC sheet with a shear thinning power law viscosity with a consistency index, m=17,000 Pa-sn and a power law index, n=0.26. The roll speed, U=6 m/s and the distance between the nips is 5 mm. 

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