Tulin 



FLOW TOWARD 

 STAGNATION POINT 



= A< 



FLOW AWAY FROM 

 STAGNATION POINT 



: A >0 



Fig. 4 - Schematic of molecular response 

 in regions of constant rate of extension 



1 - At e 

 p 



( l-Ar )2t/i 



1 - At, 



2 1 + ATp e 



( l+AT^)2t/T^ 



1 + At, 



The behavior of the solution for large times is seen to depend on the value 

 of the nondimensional strain rate (At^) relative to unity, and we see that this 

 simple theory predicts an unlimited strain a^ for values of At^ greater than 

 unity: 



At < 1 (subcritical ); aj 



1 - At, 



1 + ATp • 



At > 1 (supercritical); a^ -» unbounded. 



Of course, the molecules cannot even in the case treated endure unlimited 

 supercritical strains as indicated by theory, for its assumptions become invali- 

 dated first. Nevertheless, we may expect molecules to become greatly extended 

 under certain flow conditions. 



SIMPLE SHEAR 



In a simple shear flow, the radial strain rate is a maximum at an angle of 

 45° to the flow direction and there equals one -half of the maximum strain rate, 

 say (3u/By)/2 . We might thus expect the behavior of molecules in shear flows 

 to be qualitatively different depending on whether Tj(Bu/By) is greater than or 

 less than 2. Of course the molecule is rotating through the region of high shear, 

 so that even in the supercritical case the extension of the molecule will be lim- 

 ited due to the finite time during which the high shear rates act. A careful dis- 

 cussion must involve the effects of rotary dispersion due to Brownian motion, 



10 



