Time‐dependent elongational viscosity of a solution of elastic dumbbells

The elongational viscosity of dilute polymer solutions must always be measured under nonsteady‐state conditions. To predict the time dependence of this viscosity for a polymer solution in which a constant stretching rate is maintained, a simple model is considered in which the polymer molecules are represented by elastic dumbbells. The non‐Hookean elastic force in the dumbbell is determined by the conformational entropy of the chain. Use is made of Peterlin's approximation which replaces the elastic force by a function of the root‐mean‐square end‐to‐end distance. Application to the transient state is straightforward; it can be extended to include the effect of “internal” chain viscosity by means of approximations that are similar to Peterlin's.