EFFECTIVE STRESS RATES OF VISCOELASTIC FREE JETS

We generalize the 1-D theory for viscoelastic free jets of an earlier paper through the introduction of the general tensor rate, equation, involving an arbitrary rate parameter a. The theory can either be obtained as a postulated 1-D theory, as presented, or alternatively derived by integration of the 3-D theory over over the jet cross section. We demonstrate that, in the former approach, the definitions of 1-D tensor rates can be motivated, in the setting of body fixed reference frames, by definitions of tensor rates in the 3-D theory. We apply the theory to axisymmetric free jets, and compare the special cases of a equals 0 (corotational rates), a equals 1 (upper convected rates), a equals minus 1 (lower convected rates) and a continuous within minus 1 less than a less than 1. The jet behavior as a function of stress state at the nozzle is found to differ qualitatively for different choices of the rate parameter.