Hydrodynamic Aspects of Macromolecular Solutions 



THEORY 



O 2220 ppm 



experiment:^ a 1440 ppm 



A 10 10 ppm 



Gr' 



10' 



10 —if—> 



0.8 



0.4 





10' 



10' 



10 10 



fi ( cps ) 



10^ 10^ 



fi (cps) 



Fig. 3 - Experimental values (Rouse and Sittel) of dynannic 

 stiffness and viscosity polystyrene (M = 6.2 x 10^) in toluene 

 at 30.3°C 



The considerations of Rouse and others were restricted to small strains 

 from the relaxed state. However, the treatment of large strains is almost cer- 

 tainly essential for an understanding of general flows. 



LARGE STRAINS AND THE CRITICAL STRAIN RATE 



Convecting fluid elements suffer shape distortion (strain) and rotation. The 

 latter is partly associated with changes in streamline direction and partly with 

 the vorticity; the effects of the latter are particularly important and subtle. The 

 strains are due both to vorticity and to the fluid rates of strain associated with 

 the nonvortical (potential) flow. In order easily to gain some understanding of 

 molecular response without restrictions on the magnitude of strain, we consider 

 the simplest case of all: simple extension. This corresponds roughly to the 

 rectilinear potential flow approaching or leaving a symmetrical body along the 

 stagnation streamlines, as indicated in Fig. 4. Assume a constant rate of strain 

 A, as near the stagnation point on a circle or sphere. Then, 



p p 



An exact solution to these dynamic equations for the molecular strain along 

 the streamline (aj) and normal to it {a.^ may be found — with the remarkable 

 result 



