Stresses for Suspensions of High-Aspect Ratio Particles and Molecules

4 Stresses for Suspensions of High-Aspect-Ratio Particles and Molecules 

Brownian rod-like objects of high aspect ratio are usually molecules, not colloidal particles. As exception is tobacco mosaic virus (TMV), which is a Brownian particle of length 300 nm and diameter 18 nm (Caspar 1963). For completeness, we shall discuss the theory of Brownian rod-like particles in this chapter, with the understanding that the theory for such particles is actually more relevant to long stiff molecules than to rod-like fibers. The behavior of non-Brownian fiber suspensions is covered in Section 6.3.2.2.------------------ 

The stress tensor for solutions or suspensions of cylindrical rods in solution is 

The terms on the right side are the solvent, viscous, and elastic terms, ff , and in that order. The coefficient str is a viscous drag coefficient, which for long, slender fibers is given by (Batchelor 1970) 

From Eqs. (6-26), (6-29), and (6-36)-(6-38), the stresses for arbitrary flows of dilute suspensions of rods can be computed. At low shear rates, 

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