Taylor-Couette stability analysis for a Doi-Edwards fluid

The stability of Taylor-Couette flow of entangled polymeric solutions to small axisymmetric stationary disturbances is analyzed using the Doi-Edwards constitutive equation in the small gap limit. A previous analysis of Karlsson, Sokolov, and Tanner for the general K-BKZ equation, of which the Doi-Edwards equation is a special case, reduces the problem to one of numerically evaluating seven viscoelastic functions of the shear rate in the gap. Of these seven, only three — two of which are related to the second normal stress difference, and one of them to shear thinning — significantly affect the flow stability. The negative second normal stress difference of the Doi-Edwards fluid stabilizes the flow at low values of the Weissenberg number ₁ , while shear thinning produces strong destabilization at moderate Weissenberg number. Here ₁ is the longest relaxation time. Non-monotonic effects of viscoelasticity on Taylor-Couette stability analogous to those predicted here have been observed in experiments of Giesekus. The extreme shear thinning of the Doi-Edwards fluid is also predicted to produce a large growth in the height of the Taylor cells, a phenomenon that has been seen experimentally by Beavers and Joseph.