Hoyt and Fabula 



Table 2 



Concentrations (wppm) to Achieve 70% Torque 



Reduction at a Rotating Disk Re = 1,300,000 



(The source and molecular weight of the above 

 inaterials is given in Table 1) 



Rheological Studies 



Since high concentrations (above 1000 wppm) of these polymers are known 

 to be shear-thinning, early explanations of the friction reduction were based on 

 the "non-Newtonian" (i.e., variable) viscosity with rate of shear. Considerable 

 effort was thus placed upon the rheology of these substances and how their 

 shear -thinning behavior could explain drag reduction. 



It was quickly realized, when rheograms were available, that at the concen- 

 trations where maximum friction reductions were obtained, these solutions were 

 not "non- Newtonian, " but of essentially constant viscosity, greater than that of 

 the solvent. It was only at higher concentrations that departures from constant 

 viscosity were evident. For example, Fig. 10 shows a rheogram for guar, and 

 Fig. 11 for poly(ethylene oxide) of 4 million molecular weight.^ At the concen- 

 trations of most interest (under 500 wppm for guar and under 100 wppm for 

 poly(ethylene oxide) it is difficult, from these data, to ascribe a variable vis- 

 cosity with shear to these solutions. The constant viscosity extends to very low 

 shear as shown in Fig. 12. '^ Thus the term "non- Newtonian" is inappropriate 

 for these fluids, unless one allows the possibility that non-steady measurements 

 will show that these solutions display shear rigidities at high frequencies which 

 ideal "Newtonian" fluids would not. J. L. Lumley [8] has recently argued that 

 friction reductions shouldnotbe expected from the purely viscous, non- Newtonian 

 class of fluids. Since many of the effective additives produce highly viscoelastic 

 solutions in higher concentrations, it is possible that the drag reduction phenom- 

 enon is related to viscoelasticity. However, viscoelastic solutions are not nec- 

 essarily effective drag reducers: e.g., Carbopol (Table 1). 



■^These data were obtained under U. S. Navy contract by the Western Company, 

 Research Division, using Fann and Burrel-Severs viscometers. 

 These data were obtained byj. M. Caraher of the Naval Ordnance Test Station, 

 using a new type, helical-coil viscometer of his design. 



952 



