Transient flows of Gaussian networks in the GT limit

We first study a shear flow with a constant shear rate y along the x-axis, which is started at time r = 0 in a transient network in equilibrium [19]. In the GT limit, we find v°(t) — Vee o where Ve is the unperturbed equilibrium number of the active chains, which stays constant after a steady flow is started. 

The shear component of the stress then takes the form 

Similarly the first and second normal stress differences obey Niit)/kBT = Ve(ytfe o +ava 1 - 

It is easy to see that these stresses are steadily increasing functions they exhibit no overshoot for any large shear rate y. The coupling between the dissociation rate and the chain tension brings about the stress overshoot. 

The stress tensor of the elongational flow (9.116) takes the form (9.133) in the GT limit. The component of the tensor g parallel to the flow direction is given by 

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