Turbulence in Viscoelastic Fluids 



DISCUSSION 



Richard L. Hummel 



University of Toronto 



Toronto, Canada 



The authors imply that the drag reduction associated with these dilute poly- 

 meric solutions would be due to a suppression of the high-frequency or small 

 eddies. Is it not correct to believe that the majority of the energy is first 

 picked up by relatively larger eddies through interaction of the bulk stream and 

 the wall layer and then successfully transferred to smaller and smaller eddies 

 where it is more rapidly consumed? If this is so and the suppression of small 

 eddies is due to a more rapid absorption of the energy by these small eddies, I 

 do not see that this would result in any large change in the drag characteristics 

 per se. 



I would presume that for some non -Newtonian fluids, at least, relaxation of 

 stress in a current direction of flow or shear would change the fluids resistance 

 to flow in a new direction by a different amount and that the change might well 

 be of opposite sign. That is, while the resistance to flow for shear in the x di- 

 rection was decreased because of flow in the x direction, resistance to flow or 

 shear in the y or z direction could be increased relative to that of a stationary 

 randomly oriented fluid. Since common turbulence requires movements not only 

 in the primary direction of flow, but also in all other directions such behaviour 

 would suppress the conversion of energy into eddies of any size in the wall re- 

 gion where the flow is most predominantly unidirectional. 



The possible behaviour for the polymeric solutions might be inferred from 

 microscopic physical models of the system. These will depend very much upon 

 the relative interactions between the low-molecular -weight liquid and the high- 

 molecular -weight polymer. If the interactions with the polymer unit were suffi- 

 ciently high, each polymer molecule could be dispersed through the liquid as 

 some sort of thread, possibly tangled. This form would be very strongly aligned 

 by flow shear to give a reduced drag in the direction of flow and considerably 

 increased drag in other directions. If the interaction between liquid and polymer 

 were less favourable, polymer would tend to be forced out of the liquid (or pull 

 itself out, it does not matter which) to form small globules, but in this case 

 there would be almost as strong a tendency to collect large numbers of these 

 molecules to produce fairly sizable micelles as in soap solutions. As noted in 

 the preceding paper these globules themselves tend to become deformed and 

 elongated in the direction of shear, which results in reduced resistance in this 

 direction and increased resistance in others, but to a lesser extent the fragmen- 

 tation of these globules could result in a reduced resistance in all directions. 

 Other possibilities exist depending on the liquid, the polymer units, and the 

 polymer end groups, including the setting up of local or extended gels which are 

 more or less fibrous networks through the liquid. To what extent are these ar- 

 rangements known and how do they affect drag reduction? 



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