Dois Approximate Solution of the Smoluchowski Equation

(11-3) is multiplied by uu and integrated over the unit sphere, one obtains an evolution equation for the second moment tensor S (Doi 1980 Doi and Edwards 1986). In this evolution equation, the fourth moment tensor (uuuu) appears, but no higher moments, if one uses the Maier-Saupe potential to describe the nematic interactions. Doi suggested using a closure approximation, in which (uuuu) is replaced by (uu) (uu), thereby yielding a closed-form equation for S, namely. 

A closure approximation must also be invoked to express the rotary diffusivity Dr in terms of S. Doi chose the following approximation  

This expression neglects the viscous term, v strD (uuuu). 

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