Multicritical phenomena in flow of viscoelastic liquids. 2. Zaremba-Fromm-De Witt liquid model generalized to the relaxation time spectrum

The effect of the relaxation time spectrum on the critical, i.e., limiting, conditions of stable shear flow of viscoelastic liquids at small Reynolds numbers was investigated. The approach developed in [1] was generalized to the Zimm, Rouse, Spriggs, and Ferry-Landel-Williams (FLW) viscoelastic relaxation time spectra. The FLW spectrum depicts the plateau of the viscoelasticity of high-molecular-weight polymer melts. The problem of the frequency dependence of the components of the complex shear modulus at different steady-state flow rates for the case of periodic shear directed both parallel to steady-state flow and orthogonal to it was solved for all of the listed models. The results of the experiment on superposition of periodic shear on the steady-state flow of a moderately concentrated solution of polyisobutylene were compared with the results of calculating the effect of steady-state flow on the frequency viscoelastic functions for liquids whose viscoelasticity is approximated by a Spriggs relaxation time spectrum. The calculation showed that in flow of liquids approximated by Rouse, Zimm, or Spriggs spectra, only “parallel and orthogonal” elastic losses of stability occur and dissipative loss of stability does not. Three types of instability (two elastic — “parallel and orthogonal” - and one dissipative — parallel) predict the prospects for use of the FLW spectrum. For this model, like the models using the Rouse and Zimm spectra, the shear rate at which instability is generated, especially dissipative instability, is a function of the number of relaxation times considered in the calculation. It was found that the predicted generation of dissipative instability begins for shear rates q‖D* greater than the critical rates of generation of “elastic parallel” q‖E* and “elastic orthogonal” q⊥E* instabilities, in contrast to the ZFD model which predicts that q‖E*<q‖D*<q⊥E*. The critical shear rates are correlated with the appearance of supermolecular viscoelastic structures caused by shear flow, called elastic-dissipative by analogy with dissipative structures.