Theories of Shear Viscosity

Because (dv /dx is y, the viscosity is known if P can be computed. P, in turn, is calculated as the dot product, or scalar product, of the drag force with the velocity vector. 

The work done per unit time against fluid fiiction on a single polymer segment is given as 

Finally, noting that M equals Mq, where Mg is the monomer molecular weight, we have 

When experimental data for the zero-shear viscosity of polymer melts and solutions are examined in light of Eq. (14.8.9), it is found that melts exhibit the expected proportionality with molecular weight (at least for low molecular weights), whereas solutions show a much stronger dependence of the viscosity on molecular weight. The unexpected behavior of solutions apparently results from a dependence of C on M and c. When data are corrected to give viscosities at 

To properly understand why the zero-shear viscosity of an entangled polymer melt or solution increases so rapidly with increasing molecular weight 

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