Turbulence in Viscoelastic Fluids 

 MACROSCOPIC PHENOMENA, TURBULENT STRUCTURE 



Measurements of the physical properties of viscoelastic fluids more con- 

 centrated than those of general interest in drag reduction have appeared in the 

 rheological literature for some time, though the majority of these do not extend 

 into the high shear rate levels of interest. However, several such studies have 

 appeared (28,51,53), the data of Figs. 1 and 2 being typical. The Weissenberg 

 number (Eq. (3a)) representing a ratio of the elastic to viscous forces is given 

 by the ratio of the ordinates of Fig. 1; the fluid relaxation times (Eq. (1)) cal- 

 culated from similar measurements are shown in Fig. 2. 



10 



10 



10 



lO 



10 10" 10" 



SHEAR RATE, SEC"' 



10* 



lo-' 



Fig. 1 - Rheological properties of viscoelastic 

 fluids: normal and shearing stress measure- 

 ments under steady laminar flow conditions 

 depicted as a function of shear rate. The data 

 are from Ginn and Metzner (28) for 5% solu- 

 tion of polyisobutylene in decalin. 



Several important observations may be made. First the Weissenberg num- 

 ber, hence the importance of elastic effects, may be very great and is an in- 

 creasing function of shear rate. Secondly, relaxation times are typically about 

 10" ^ or 10" ^ second at the shear rate levels of interest and do not seem to be 

 very dependent upon the concentration level of the fluid used in obtaining the 

 results depicted in Fig. 2. Thirdly, and most importantly, such measurements 

 have been recently extended by Oliver (44) to concentrations as low as 100 ppm 

 i.e., well into the range of direct interest —and the same conclusions appear 



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