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., limi ting, conditions of stable shear flow of viscoelastic liquids at small Reynolds numbers was investigated. The approach developed in [I] was generalized to the Zimm, Rouse, Spriggs, and Ferry-Landel-Williams (FL W) 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 comp lex shear modulus at different steady-state flow rates for the case of periodic shear directed both parallel to steady-state flow and orthog onal to it was solved for all of the listed models. The results of the experiment on superposition of periodic shear on the steady-state flo w of a moderately concentrated solution of polyisobutylene were compar ed 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 calculatio n showed that in flow of liquids approximated by Rouse, Zimm, or Sprig gs spectra, only ''parallel and orthogonal'' elastic losses of stabili ty occur and dissipative loss of stability does not. Three types of in stability (two elastic - ''parallel and orthogonal'' - and one dissipa tive - parallel) predict the prospects for use of the FLW spectrum. Fo r this model, like the models using the Rouse and Zimm spectra, the sh ear rate at which instability is generated, especially dissipative ins tability, is a function of the number of relaxation times considered i n the calculation. It was found that the predicted generation of dissi pative instability begins for shear rates q(parallel to D) greater th an the critical rates of generation of ''elastic parallel'' q(parallel to E) and ''elastic orthogonal'' q(perpendicular to E)* instabilitie s, in contrast to the ZFD model which predicts that q(parallel to E) < q(parallel to D) < q(perpendicular to E)* The critical shear rates are correlated with the appearance of supermolecular viscoelastic stru ctures caused by shear flow, called elastic-dissipative by analogy wit h dissipative structures.