MATH 559 Homework Assignment IV
University of British Columbia
(due on Nov. 13, 2015 after class)
1. Use the Prager procedure to derive the evolution equation for the tensor < QQ > for a
dilute suspension of Hookean dumbbells.
2. Consider a dilute solution of Hookean dumbbells subject to startup of a homogeneous
uniaxial elongation along the z axis. Write out the rate of change of < Q2z >, and
demonstrate that as De → 1/2, the length increases without bound and no steady state
can be achieved.
3. Bonus problem [2 bonus points]: Evaluate the simple-shear predictions of the FENEP and FENE-CR models. For FENE-P, this involves numerical solution of nonlinear
algebraic equations and plotting of curves.
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