Power-law liquids

G Hansford, M Litt. Mass transport from a rotating disk into power-law liquids. Chem Eng Sci 23 849, 1968. 

The laminar flow velocity profile in a pipe for a power law liquid in steady state flow is given by the equation... 

A system total head against mean velocity curve for a particular power law liquid in a particular pipe system can be represented by the equation... 

Transitional Flow. Reynolds numbers and friction factors at which the flow changes from laminar to turbulent are indicated by the breaks in the plots of Figures 6.4(a) and (b). For Bingham models, data are shown directly on Figure 6.6. For power-law liquids an equation for the critical Reynolds number is due to Mishra and Triparthi [Trans. IChE 51, T141 (1973)],... 

The melt flow under isothermal conditions, when it is described by the rheological equation for the Newtonian or power law liquid, has been studied in detail63 66). The flow of the non-Newtonian liquid in the channels of non-round cross section for the liquid obeying the Sutterby equation have also been studied 67). In particular, the flow in the channels of rectangular and trigonal cross section was studied. In the analysis of the non-isothermal flow, attention should be paid to the analysis 68) of pseudo-plastic Bingham media. 

The propeller in Prob. 9.1 is replaced with a six-blade turbine 400 mm in diameter, and the fluid to be agitated is a pseudoplastic power-law liquid having an apparent viscosity of 15 P when the velocity gradient is 10 s At what speed should the turbine rotate to deliver 1 kW/m of liquid For this fluid n = 0.75 and p = 950 kg/m. ... 

The relative extensional viscosity of suspensions in a power-law liquid can be expressed as [Goddard, 1978] ... 

It was also reported that this relationship can be applied to Newtonian liquids as well as power law liquids, since the second term of Equation 6.19 in parenthesis is much smaller than unity and therefore allows approximation to a linear relationship. ... 

A relatively close counterpart of Newtonian liquids is the family of the nonlinear power law liquids, which do not possess any viscoelastic, thixotropic, orrheopectic... 

The quasi-one-dimensional theory of capillary breakup of pseudoplastic jets provides an explanation of the phenomenon of sausage-like breakup [29, 107]. In the case of the power law liquids, the continuity and momentum balance equations of straight jets have the form (1.49) and (1.50), whereas, based on (1.62), (1.51) is replaced by a more general one ... 

Vi, is the critical velocity for the transition from laminar to turbulent flow. For a given power-law liquid (i.e. known m and n), density and pipe diameter, D, Vl may be estimated simply by setting the Reynolds munber (equation 3.8b) equal to 2000, i.e. 

Figure 5.2 Drag coefficient for spheres in power-law liquids (see Chhabra [1990] for original sources of data)...

For any given sphere and power-law liquid combination, the value of the Archimedes number can be evaluated using equation (5.12). The sphere Reynolds munber can then be expressed in terms of Ar and n as follows ... 

The drag coefficient for freely falling spherical droplets (or rising gas bubbles) of Newtonian fluids in power-law liquids at low Reynolds munber has been approximately evaluated and, in the absence of smface tension effects, it is given by equation (5.4), i.e. 

Liquid-solid fluidised systems are generally characterised by the regular expansion of the bed which takes place as the liquid velocity increases from the minimum fluidisation velocity to a value approaching the terminal falling velocity of the particles. The general form of relation between velocity and bed voidage is found to be similar for both Newtonian and inelastic power-law liquids. For fluidisation of uniform spheres by Newtonian liquids, equation (5.21), introduced earlier to represent hindered settling data, is equally applicable ... 

Figure 5.15 Correlations for liquid-solid mass transfer in beds fluidised by power-law liquids...

Laminar boundary layer flow of power-law liquids over a plate... 

Consideration is now given to the flow of an incompressible power-law liquid of temperature To over a plane surface maintained at a higher temperature Ts. At any given distance from the leading edge, the temperature of the fluid progressively decreases with distance y from the surface reaching To at the extremity of the thermal boundary layer, y = St. The temperature at a distance y from the surface can be approximated by a polynomial of the form ... 

It is desired to scale-up a mbcing tank for the agitation of a power-law liquid. The same fluid is used in both model and large-scale equipment. Deduce the functional dependence of power consumption per unit volume of fluid on the size of the impeller and the speed of rotation. 

Estimate the time needed to empty a cylindrical vessel (Dj = 101 mm), open to the atmosphere, fllled with a power-law liquid (m = 4Pa-s" andrt = 0.6, density = lOlOkg/m ). A 6mmID capillary tube 1.5 m long is fltted to the base of the vessel as shown in the diagram for... 

For a Newtonian, organic hquid of viscosity O.SmPa s, flowing through the tube at the same mean velocity, the pressure drop is 10 kPa compared with 100 kPa for the power-law liquid. What is the power-law consistency coefiicient, m, of the non-Newtonian liquid ... 

Two liquids of equal densities, the one Newtonian and the other a power-law liquid, flow at equal volumetric rates down two wide inclined surfaces (30° from horizontal) of the same widths. At a shear rate of 0.01 s , the non-Newtonian fluid, with a power-law index of 0.5, has the same apparent viscosity as the Newtonian fluid. What is the ratio of the film thicknesses if the surface velocities of the two liquids are equal ... 

A 19.5% (by volume) kaolin-in-water suspension is flowing under laminar conditions through a horizontal pipe, 42 mm diameter and 200 m long, at a volumetric flow rate of 1.25 m /h. The suspension behaves as a power-law liquid with n = 0.16 and m = 9.6Pa-s", and has a density of 1320 kg/m. Estimate the pressure drop across the pipe. Air at 298 K is now introduced at a upstream point at the rate of 5 m /h (measured at the pressure at the mid-point of the pipe length). What will be the two-phase pressure drop over the pipe according to ... 

A generalized analysis that combines the effects of shear, temperature and pressure on the rheological parameters, may lead to an expression of a so-called effective viscosity, p, for a power-law liquid in a limited operational range. 

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