Components of the complex modulus during the periodic shear flow of a viscoelastic fluid

1. In the non-Newtonian region of steady shear flow, the relaxation properties of the flowing melt cannot be determined by a relaxation-time spectrum computed from measured frequency dependencies pf the complex shear modulus G*(ω, q) under conditions where periodic strain is superposed on steady flow. Measured values of G*(ω, q0) reflect both the relaxation characteristics of the flowing material (truncated spectrum) and the effect of a steady-flow disturbance. 2. Integral equations of state of a viscoelastic fluid predict: a) lim η′ '(ω,q0) =dσ12/dq=ηq; ω→0 for parallel superposition, irrespective of the type of equation; b) lim x′ (ω,q0) =d(Pw/2q)/dq ω→0 occurs only in the case of models with a nonlinear memory function, dependent on the straintensor invariants; with a nonlinear relaxation function dependent on strain-rate-tensor invariants for modulus nonlinearity; with a nonlinear memory function dependent or) strainrate invariants for relaxation nonlinearity. 3. When ω < qo, negative values of G′ (ω, qo) are observed, beginning at shear rates corresponding to values of d(Pw/2q)/dq ⩽ 0 only for elastic fluids described by models for which conclusion b) from item 2 is valid. For other models considered, the rates q*o are lower than those preducted by the relationship d(Pw/2q)/dq ⩽ 0 when G′(ω, qo) are negative where ω < qo. 4. Experimental results for a solution of polyisobutylene in cetane in the region of relatively low values of q0 are quantitatively satisfactorily described by a model with a nonlinear memory function, dependent on strain-rate invariants, and modulus nonlinearity. It is established experimentally that q**o > q*e. 5. Asymptotic values of and are obtained for corotational models of a viscoelastic fluid and for values of q*0 which satisfactorily reflect certain results of tests involving the steady flow of melts of linear polymers of narrow molecular-mass distribution. 6. For many polymer solutions, the shear rate q*o coincides with the appearance of a turbulent-flow condition, while in the case of polymer melts, the appearance of turbulent flow coincides with shear rates at which the specimen extrudes from the effective gap in the coneplane rheometer with small angles between the generatrix of the cone and plane.