Stress Growth at Inception of Steady Elongational Flow

A suspension of rigid dumbbells is a rest for t 0. For f 0 it undergoes a steady elongational flow with steady elongational rate jC(,. Therefore, we will solve the equation 

We imagine a solution of rigid dumbbells in a state of steady elongational flow at a constant elongation rate k for time t 0. Then at t = 0 the stress exerted on the fluid is suddenly removed and the fluid is allowed to recoil. We assume that the fluid will recoil with the same velocity profile as it had during the elongating process, but here k will be ic (t) a function of time. 

The averages in are with respect to the function xp. We assume a solution of the form  

By substituting xp from Eq. (19.3) into Eq. (19.2) and equating like powers of ic we obtain integro-differential equations for the y/. The equations for the first few tp are  

Therefore the ultimate elongational recovery after cessation of steady flow with elongational rate k is  

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Stress Growth at Inception of Steady Elongational Flow... 

Stress growth at inception of steady elongational flow... 

In stress growth at inception of steady elongational flow, both the rigid dumbbells and elastic dumbbells give expressions for... 

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