Consistency coefficient

C RVISC MEU NOUGHT CONSISTENCY COEFFICIENT C RPLAM PENALTY PARAMETER... 

The rheological properties of a particular suspension may be approximated reasonably well by either a power-law or a Bingham-plastic model over the shear rate range of 10 to 50 s. If the consistency coefficient k is 10 N s, /m-2 and the flow behaviour index n is 0.2 in the power law model, what will be the approximate values of the yield stress and of the plastic viscosity in the Bingham-plastic model ... 

A fluid which exhibits non-Newtonian behaviour is flowing in a pipe of diameter 70 mm and the pressure drop over a 2 m length of pipe is 4 x 104 N/m2. A pitot lube is used to measure the velocity profile over the cross-section. Confirm that the information given below is consistent with the laminar flow of a power-law fluid. Calculate the power-law index n and consistency coefficient K. 

Considink, D. M. 272 Consistency coefficient of fluids 108 Constitutive equations 111 Contact angle and no-slip condition 670 -----boiling 483... 

The two viscous rheological properties are m, the consistency coefficient, and n, the flow index. The apparent viscosity function for the power law model in terms of shear rate is... 

A film of paint, 3 mm thick, is applied to a flat surface that is inclined to the horizontal by an angle 9. If the paint is a Bingham plastic, with a yield stress of 150 dyn/cm2, a limiting viscosity of 65 cP, and an SG of 1.3, how large would the angle 9 have to be before the paint would start to run At this angle, what would the shear rate be if the paint follows the power law model instead, with a flow index of 0.6 and a consistency coefficient of 215 (in cgs units) ... 

The latter form is required to reflect the fact that the direction of the shear stress must reverse when the shear rate is reversed, and to overcome objections such as y , and therefore r, having imaginary values when y is negative. The power n is known as the power law index or flow behaviour index, and K as the consistency coefficient. 

Clearly, shear thinning behaviour corresponds to nshear thickening behaviour to n> 1. The special case, n = 1, is that of Newtonian behaviour and in this case the consistency coefficient K is identical to the viscosity fx. Values of n for shear thinning fluids often extend to 0.5 but less commonly can be as low as 0.3 or even 0.2, while values of n for shear thickening behaviour usually extend to 1.2 or 1.3. 

Several objections can be raised against the power law, for example the consistency coefficient is not a genuine physical property, which is clear from its units, Pa s . In addition, there is a discontinuity in the gradient of... 

A general time-independent non-Newtonian liquid of density 961 kg/m3 flows steadily with an average velocity of 2.0 m/s through a tube 3.048 m long with an inside diameter of 0.0762 m. For these conditions, the pipe flow consistency coefficient K has a value of 1.48 Pa s0,3 and n a value of 0.3. Calculate the values of the apparent viscosity for pipe flow p.ap, the generalized Reynolds number Re and the pressure drop across the tube, neglecting end effects. 

The value of the consistency coefficient k may be obtained by substituting n = 0.67 and the experimental data for any one set of data and, if desired, the constancy of this value may be confirmed by repeating this procedure for each set of the data. 

Conventional stirred-tank polymeric reactors normally use turbine, propeller, blade, or anchor stirrers. Power consumption for a power-law fluid in such reactors can be expressed in a dimensionless form, Ne = Reynolds number based on the consistency coefficient for the power-law fluid. Various forms for the function f(m) in terms of the power-law index have been proposed. Unlike that for Newtonian fluid, the shear rate in the case of power-law fluid depends on the ratio dT/dt and the stirrer speed N. For anchor stirrers, the functionality g developed by Beckner and Smith (1962) is recommended. For aerated non-Newtonian fluids, the study of Hocker and Langer (1962) for turbine stirrers is recommended. For viscoelastic fluids, the works of Reher (1969) and Schummer (1970) should be useful. The mixing time for power-law fluids can also be correlated by the dimensionless relation NO = /(Reeff = Ndfpjpti ) (Tebel et aL 1986). 

Figure 2-10 The Influence of Insoluble Solids on Apparent Viscosity at a Shear Rate of 100 s (Va, lOO) Consistency Coefficient, K, of Pera Concentrated Orange Juice, Data of Vitali and...

The effect of concentration (c) of soluble solids (°Brix) and insoluble solids (Pulp) on either apparent viscosity or the consistency index of the power law model of FCOJ can be described by exponential relationships (Vitali and Rao, 1984a, 1984b). Equations 2.36 and 2.37 are applicable to the consistency coefficient (K) of the power... 

The ratio of mean granule diameters (Dt/Do) can be used to correlate consistency coefficient data of starch dispersions. At low values of cQ, the granules were sufficiently apart and did not affect dispersion viscosity substantially. As cQ increased... 

Figure 4-25 The Relationship between the Granule Diameter Ratio (Di/Dq) and the Consistency Coefficient (K) of Gelatinized 2.6% Tapioca Starch Dispersions (Rao and Tattiyakul, 1998).

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