Viscosity drag reduction

The average Nusselt number, Nu, is presented in Fig. 4.10a,b versus the shear Reynolds number, RCsh- This dependence is qualitatively similar to water behavior for all surfactant solutions used. At a given value of Reynolds number, RCsh, the Nusselt number, Nu, increases with an increase in the shear viscosity. As discussed in Chap. 3, the use of shear viscosity for the determination of drag reduction is not a good choice. The heat transfer results also illustrate the need for a more appropriate physical parameter. In particular. Fig. 4.10a shows different behavior of the Nusselt number for water and surfactants. Figure 4.10b shows the dependence of the Nusselt number on the Peclet number. The Nusselt numbers of all solutions are in agreement with heat transfer enhancement presented in Fig. 4.8. The data in Fig. 4.10b show... 

Kim, O.K., Little, R.C., and Ting, R.Y. "The Correlation of Drag-Reduction Effects with Polymer Intrinsic Viscosity," J. Colloid Interface Sci.. 1974, 47(2). 

The model for turbulent drag reduction developed by Darby and Chang (1984) and later modified by Darby and Pivsa-Art (1991) shows that for smooth tubes the friction factor versus Reynolds number relationship for Newtonian fluids (e.g., the Colebrook or Churchill equation) may also be used for drag-reducing flows, provided (1) the Reynolds number is defined with respect to the properties (e.g., viscosity) of the Newtonian solvent and (3) the Fanning friction factor is modified as follows ... 

The effects of the concentration of PIB on drag reduction in different solvents have been investigated (65). Viscosity measurements of PIB with different molecular weights in two solvents, namely cyclohexane and xylene showed that a universal drag reduction equation can be used in order to describe the behavior. 

The drag reduction is connected with a reduction in the burst frequency and structure, which is closely associated with the strong polymer-induced increase in elongational viscosity. Here, it must be taken into account that the elongation of the polymer... 

Ting (1972) reported that the degree of drag reduction depends on the content of ionic groups in a series of hydrolyzed PAAm samples exhibiting maximum behavior . He noticed that the reduced viscosity increased sharply with increasing hydrolysis up to 40 % AAm and then decreased, in comparison to the pure polyacrylic acid. Similar investigations with polyacrylic add at different neutralization states have been made by Parker and Banijamali who obtained comparable results. 

Fig. 19. Comparison of the intrinsic viscosity and the drag reduction material function (friction factor versus Reynolds number) dependent on storage time, Mw = 8.1 106 g/mol, c = 50 ppm in distilled water, d = 6.1 mm (Wagner)...

In contrast to this, Armstrong reported that for dilute solutions ( 10 ppm), the drag reduction is independent of the chemical nature of the polymer and relates only to effects on solution viscosity. 

Peyser P, Little RC (1971) The drag reduction of dilute polymer solutions as a function of solvent power, viscosity and temperature J Appl Polym Sci 15 2623... 

Drag reduction increases with polymer concentration until it reaches a maximum. The optimum concentration, and minimum torque in a turbulent Couette experiment with PEO in water decreased with increasing MW. Hunston and Zakin studied the effect of concentration and MW on DR for polystyrene in toluene, a good solvent, and in toluene-isooctane, a poor solvent. They observed increasing DR effectiveness with increasing concentration until offset by viscosity... 

Drag reduction is found generally with dilute solutions of high-molecular-weight linear polymers and is believed to be related to the extension of these flexible molecules at high turbulent shear stress near the wall. The extended molecules increase the local viscosity, which damps the small eddies and leads to increased thickness of the viscous sublayer. With a thicker sublayer at the same... 

Corresponding-states studies of the viscosity-concentration behavior of dilute and semidilute polymer solutions with Robert Simha led one of the authors (JLZ) to their applications in turbulent flows, a phenomenon that is generally called drag reduction. About six decades ago, Mysels [Mysels, 1949 Agoston et al., 1954] and Toms [1949] discovered that small amounts of aluminum soaps and high polymers added to a fluid in turbulent flow could significantly reduce pressure losses. 

Zhang et al. [2005b] studied the effects of various percents of ethylene glycol in water (15,20, and 28%) on cationic surfactant solution properties. Using commercial cationics from Akzo Nobel (Ethoquad 012 and 013), they observed that the cosolvent reduced the upper temperature limit for drag reduction, maximum percent drag reduction, maximum critical wall shear stress, and relative shear viscosity. The formation of TLMs was hampered, but the addition of excess sodium salicylate promoted TLM... 

As indieated in Fig. 7, the emulsion viscosity passes through a minimum at optimum formulation (164). The value of this minimum is quite low, unusually low as it is known that the ulfralow interfacial tension tends to produce small droplets. Actually, this is not necessarily true as will be diseussed later, beeause the droplets formed can coalesce at once. It seems that the low emulsion viscosity is due to the ease of deformation of the droplets along the streaming lines, a phenomenon similar to the drag reduction by polymers (165). 

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