Polymers, nonnewtonian fluids

Here t, 4, and 4 2 are three important material functions of a nonnewtonian fluid in steady shear flow. Experimentally, the apparent viscosity is the best known material function. There are numerous viscometers that can be used to measure the viscosity for almost all nonnewtonian fluids. Manipulating the measuring conditions allows the viscosity to be measured over the entire shear rate range. Instruments to measure the first normal stress coefficients are commercially available and provide accurate results for polymer melts and concentrated polymer solutions. The available experimental results on polymer melts show that , is positive and that it approaches zero as y approaches zero. Studies related to the second normal stress coefficient 4 reveal that it is much smaller than 4V and, furthermore, 4 2 is negative. For 2.5 percent polyacrylamide in a 50/50 mixture of water and glycerin, -4 2/4 i is reported to be in the range of 0.0001 to 0.1 [7]. 

The physical properties of nonnewtonian fluids necessary for the study of forced convection heat transfer are the thermal conductivity, density, specific heat, viscosity, and elasticity. In general these properties must be measured as a function of temperature and, in some instances, of shear rate. In the special case of aqueous polymer solutions it is recommended that all properties except the viscous and elastic properties be taken to be the same as those of water. 

Lee et al. [16] measured thermal conductivities of various nonnewtonian fluids at four different temperatures using a conventional thermal conductivity cell. These results, shown in Table 10.2, support the common practice of assuming that the thermal conductivity of aqueous polymer solution is equal to that of pure water of a corresponding temperature if the concentration of the polymer is less than 10,000 wppm (that is, 1 percent by weight). 

Earlier investigators studying the drag-reducing phenomenon in viscoelastic fluids often used Re and Reeff. The former is generally valid only for dilute polymer solutions, in which case the solution viscosity is quite close to that of the solvent. The use of Reeff seems inappropriate in the study of the drag coefficient because it does not represent any physical property of nonnewtonian fluids, although it produces a unique reference line for experimental friction data in laminar pipe flow ... 

An exception to the generally observed drag reduction in turbulent channel flow of aqueous polymer solutions occurs in the case of aqueous solutions of polyacrylic acid (Carbopol, from B.F. Goodrich Co.). Rheological measurements taken on an oscillatory viscometer clearly demonstrate that such solutions are viscoelastic. This is also supported by the laminar flow behavior shown in Fig. 10.20. Nevertheless, the pressure drop and heat transfer behavior of neutralized aqueous Carbopol solutions in turbulent pipe flow reveals little reduction in either of these quantities. Rather, these solutions behave like clay slurries and they have been often identified as purely viscous nonnewtonian fluids. The measured dimensionless friction factors for the turbulent channel flow of aqueous Carbopol solutions are in agreement with the values found for clay slurries and may be correlated by Eq. 10.65 or 10.66. The turbulent flow heat transfer behavior of Carbopol solutions is also found to be in good agreement with the results found for clay slurries and may be calculated from Eq. 10.67 or 10.68. 

For turbulent flow the friction factors for nonnewtonian fluids are generally less than those for newtonian fluids. Some polymer solutions have surprisingly low friction factors. 

Rheology. Polymers are often added to change solvent or process flow properties. The addition of polymers almost always causes nonnewtonian flow behavior in the resulting fluid. 

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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