HYDRODYNAMIC ASPECTS OF 

 MACROMOLECULAR SOLUTIONS 



Marshall P. Tulin 



Hydronautics, Incorporated 



Laurel, Md. 



INTRODUCTION 



It is now common knowledge among us that tens or even several parts per 

 million of innocuous large molecules in liquid solution drastically alter some 

 turbulent flows (Refs. 1, 2, and 3, for example). This discovery was not only of 

 very great potential practical importance, but it also meant that hydrodynamics 

 and all of us with it have been brought to the end of a very long age of innocence. 

 We have now discovered for ourselves what those physical chemists, chemical 

 engineers, and mathematicians who call themselves rheologists, have been try- 

 ing to tell us all along: that fluids can store strain energy; that, as a result, the 

 normal pressure in even the simplest shear flow is not an isotropic quantity; 

 that accompanying both shear and extension, fluids in general possess both vis- 

 cosity and stiffness; and that these latter quantities as we would define them, 

 are not physical properties of the fluid, but depend in a rather complicated way 

 upon the flow. 



Perhaps we should not be blamed too much for holding on so long to the 

 gilt-edge security of an old blue-chip like Navier -Stokes, in preference to the 

 frankly rather speculative and volatile issues that have been offered up to us. 

 Now, however, we clearly face the necessity to finance our adventures in 

 polymer land by selling out Navier -Stokes. 



The present work attempts in very brief form to: review some important 

 concepts involving disperse systems (such as thermal forces, entropy, and 

 strain energy); discuss the dynamics of molecular response to the motion of the 

 solvent; introduce and discuss the idea of critical strain rates, which arises 

 naturally in the theory of molecular response; relate molecular strain to fluid 

 stresses through the use of Mohr's circle; and discuss in a speculative way the 

 role of fluid stiffness in turbulent flows, as for example in providing a mode for 

 the extraction of turbulent energy from an eddy through the generation of elastic 

 shear waves. Finally, it is speculated how radiation damping could result in a 

 twofold or threefold thickening of the viscous sublayer. 



DISPERSE SYSTEMS 



Rheological effects occur in all solutions containing a disperse phase — such 

 as colloidal suspensions and polymer solutions. These include most fluids in 



