Constitutive Behavior of Dilute Polymer Solutions

Because the cross-sectional area of the arbitrary plane is c the average stress vector, f, acting on the plane is (F)/c that is. 

Finally, from the definition of the stress tensor t in Eq. (10.5.5), we have 

It can also be shown that the momentum of the beads crossing the plane contributes a term to t, but this term simply adds to the isotropic pressure term p. The total stress T in the polymer solution then is the sum of the solvent stress, which is Newtonian [given by Eqs. (14.2.1) and (14.2.2)], and the polymer stress, which is yet to be calculated but is given formally by Eq. (14.9.6). Thus, 

Note that when there is no flow, D is zero and p r) is given by Eq. (10.2.11). Evaluating the integral in Eq. (14.9.4) gives the following  

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