Hoyt and Fabula 



a major portion of the disk. Disk speed and torque are measured using various 

 concentrations of polymer additives in the tank. It can be reasoned that most of 

 the torque is developed near the outer disk edge, so that torque reduction is es- 

 sentially equivalent to friction reduction. Thus these terms are used inter- 

 changeably hereafter. 



An example of the type of data obtained using this apparatus is given in Fig. 

 2. The polymer additive used here is guar gum, the refined endosperm of Cyam- 



opsis tetragonolobus, a plant grown commercially in India, Pakistan, and the 

 United States for food and industrial purposes.^ At constant rotative speed, ad- 

 dition of the polymer produces immediate lowering of the torque until at concen- 

 trations of 300-400 wppm the torque has been reduced to between 30 and 40 per- 

 cent of its pure water value. As the concentration is further increased, the 

 torque is increased somewhat, which can be attributed to the increased viscosity 

 of the solution. 



Much more striking results can be obtained using the synthetic polymer 

 poly(ethylene oxide) which is commercially available in four different molecular 

 weight distributions.^ Figure 3 shows data taken with the 45.7 cm diameter disk 

 at 40 rev/sec for the four molecular weights of the same chemical. As molecu- 

 lar weight is increased, the material becomes more effective, and Fig. 3 shows 

 that 70% torque or friction reduction may be obtained with less than 100 wppm 

 of additive, using the highest molecular weight material. 



Similar tests have been made using a wide variety of natural and synthetic 

 polymers, with the results shown on Table I, where the weight parts per million 

 to achieve a friction reduction of 35% (half way between no effect and the maxi- 

 mum of about 70% observed on this facility at 40 rev/sec) are listed together 

 with the molecular weight of the polymer. 



From the table, it appears that at least three significant parameters affect 

 the ability of a polymer to lower the turbulent frictional resistance of the fluid 

 in which it is dissolved: linearity, molecular weight, and solubility. 



Linearity 



The striking thing about the most effective polymers is that they are "long- 

 chain" materials having an essentially unbranched structure. The chemical for- 

 mulas of guar and poly(ethylene oxide) (Fig. 4) indicate this characteristic, and 

 a photograph of a model of a segment of the poly(ethylene oxide) molecule fur- 

 ther illustrates the thread-like appearance of the material. 



While the exact configuration of these molecules in solution is poorly under- 

 stood, calculations indicate approximate length-to-diameter ratios of from 350 

 to 500 for guar, and from 22,000 to 165,000 for poly(ethylene oxide) of 6 million 

 molecular weight depending on the helix model selected, if we ignore, for the 



The guar guna used in these experiments was "Westco J-Z FP" supplied by the 

 Western Company, Research Division, 1171 Empire Central, Dallas, Texas. 

 ^Supplied by Union Carbide Corp., 270 Park Ave., New York, New York. 



948 



