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Homework 6 2008

CM4650 Polymer Rheology
partial solution

    Due:  Wednesday, April 16, 2008 5pm to my mailbox or office.
    (Note:  Firefox does not recognized symbol font; I have described quantities that are rendered in symbol font so that you will recognize them)

    1.  (20 points) 8.15 (Cessation of GLVE)
    2.  (20 points) 8.22 (Given LVE spectrum, calculate material functions)
    3. (20 points) For the generalized Maxwell model parameters given in problem 8.22, calculate the cessation of steady shearing function h-(t) (eta minus) and plot log h-(t) (eta minus) versus log(t) using a computer program.  Does this prediction resemble usual polymer behavior for this flow?
    4.  (20 points) 8.34 (Calculate G', G" Rouse model)
    5.  (20 points)  In lecture 29 there is a plot on page 4 of Einaga's polystyrene solution data of G(t) in step strain.  Estimate the longest relaxation time from this plot and explain how you made this estimate.  In lecture 30 we showed a fit of the generalized Maxwell model to these same data.  What was the longest relaxation time calculated from that fit?  Which number would you used if asked to estimate the longest relaxation time of your material?  When might you need to know the longest relaxation time of your material?
    6.  (20 points) Compare and contrast the Generalized Newtonian fluid models of Chapter 7 and the Generalized Linear Viscoelastic models of Chapter 8.  When are each useful?  List three material behaviors (as discussed in Chapter 6) that are correctly captured by these models and list three material behaviors that are not correctly captured by these models.



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