Fluid nonNewtonian

When the shear-stress viscosity relation of the fluid does not obey the simple newtonian expression of Eq. (5-1), the above equations for free-convection heat transfer do not apply. Extremely viscous polymers and lubricants are examples of fluids with nonnewtonian behavior. Successful analytical and experimental studies have been carried out with such fluids, but the results are very complicated. The interested reader should consult Refs. 48 to 50 for detailed information on this subject. 

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A wide variety of nonnewtonian fluids are encountered industrially. They may exhibit Bingham-plastic, pseudoplastic, or dilatant behavior and may or may not be thixotropic. For design of equipment to handle or process nonnewtonian fluids, the properties must usually be measured experimentally, since no generahzed relationships exist to pi e-dicl the properties or behavior of the fluids. Details of handling nonnewtonian fluids are described completely by Skelland (Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). The generalized shear-stress rate-of-strain relationship for nonnewtonian fluids is given as... 

For nonnewtonian fluids, pressure readings with taps may also be low because of fluid-elasticity effects. This error can be largely eliminated by using flush-mounted diaphragms. 

Measurements by Harris and MagnaU [Trans. Jn.st. Chem. Eng. (London), 50, 61-68 (1972)] with a venturi (p = 0.62) and orifices wiSi radius taps (P = 0.60-0.75) indicate that the discharge coefficient for nonnewtonian fluids, in the range Nr (generalized Reynolds number) 3500 to 100,000, is approximately the same as for newtonian fluids at the same Reynolds number. 

Power consumption for impellers in pseudoplastic, Bingham plastic, and dilatant nonnewtonian fluids may be calculated by using the correlating lines of Fig. 18-17 if viscosity is obtained from viscosity-shear rate cuiwes as described here. For a pseudoplastic fluid, viscosity decreases as shear rate increases. A Bingham plastic is similar to a pseudoplastic fluid but requires that a minimum shear stress be exceeded for any flow to occur. For a dilatant fluid, viscosity increases as shear rate increases. 

Pseudoplasticity. Low-concentration solutions of water viscosifiers are usually nonnewtonian fluids(54) and therefore fail to follow the pressure and flow behavior predicted by newtonian models of flow. To... 

With nonnewtonian fluids the pressure measured at the wall with non-flush-mounted pressure gauges may be in error (see subsection Static Pressure ). 

Free convection through vertical plane layers of nonnewtonian fluids is discussed in Ref. 38, but the results are too complicated to present here. 

A wide variety of nonnewtonian fluids are encountered industrially. They may exhibit Bingham-plastic, pseudoplastic, or dilatant behavior... 

Metzner and Friend [Ind. Eng. Chem., 51, 879 (1959)] present relationships for turbulent heat transfer with nonnewtonian fluids. Relationships for heat transfer by natural convection and through laminar boundary layers are available in Skellands book (op. cit.). 

If the liquid laminae of a foam system can be converted to impermeable solid membranes, the film viscosity can be regarded as having become infinite, and the resulting solid foam will be permanent. Likewise, if the laminae are composed of a gingham plastic or a thixotrope, the foam will be permanently stable for bubbles whose buoyancy does not permit exceeding the yield stress. For other nonnewtonian fluids, however, and for all newtonian ones, no matter how viscous, the viscosity can only delay but never prevent foam disappearance. The popular theory, held since the days of Plateau, that foam life is proportional to surface viscosity and inversely proportional to interfacial tension, is not correct, according to Bikerman (op. cit., p. 161), who points out that it is contradicted by experiment. 

This may be contrasted to, e.g., the isotropic pressnre developed in a fluid under pressure, with only nonnewtonian fluids able to develop and sustain a nonisotropic distribution of normal stress. In addition, the radial normal stress acting at the wall develops a wall shear stress that opposes gravity and helps support the weight of the powder. As originally developed by Janssen [Zeits. D. Vereins Deutsch Ing., 39(35), 1045 (1895)], from a balance of forces on a differential slice, the axial stress as a function of depth z is given by... 

Apparent viscosity APP app = Th but as determined for a nonNewtonian fluid, usually by a method suitable only for Newtonian fluids. 

Cho, Young I. Department of Mechanical Engineering and Mechanics, Drexel University (chap. 1, Basic Concepts of Heat Transfer, chap. 10, Nonnewtonian Fluids), e-mail ycho coe.drexel.edu... 

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