Stresses in Dilute Solutions of Bead-Nonlinear-Spring Macromolecules. II. Unsteady Flows and Approximate Constitutive Relations

Some numerical calculations of the distribution function for bead positions in a linear-locked-spring dumbbell are presented together with stresses for transient (start-of-shearing) flows. Based upon the idea that this distribution function is sharply peaked in these and other results obtained previously, an approximate constitutive equation of novel form is deduced. The results of stress calculations from the approximate constitutive equations are then compared to those from the numerical work. Some further results for another spring law similar in form to the Langevin spring are also given for comparison. It is concluded that constitutive equations of the type presented are useful for certain classes of flows.