Level 2

Non-Linear Chains

Problem 1: Use the parameter setting of a = 0, b = 1, flow rate = 0, and chain length = 10. Compare the material properties given in Example 1 for Hookean chains to the results you obtain for the non-linear chains by varying the shear rate for a given chain length. Are the material functions independent of shear rate? You can plot the three material functions versus shear rate to see the shear rate dependence. Notice that the second normal stress coefficient is zero even for non-linear chains.

Problem 2: Observe the chain dynamics of non-linear chains and Hookean chains in the same flows with the same numbers of beads. How do the dynamics differ?

Problem 3: Look carefully at the chain dynamics for shear flow for both Hookean and non-linear chains of various chain lengths. Discuss the difference and similarities of the chain dynamics. Why does the non-linear spring give rise to these differences?

Problem 4: Use the parameter setting of a = 1, b = 1, flow rate = 0, and chain length = 10 from Example 2. Varying the elongation from zero to the maximum rate you can obtain before the chain is pulled apart. Compare this to the maximum rate you measured for Hookean chains.