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Material functions generated by the complex viscosity

Authors:	J Stastna D De Kee

Institution:	(1) Fluid Dynamics Research Institute, University of Windsor, N9B 3P4 Windsor, Ontario, Canada;(2) Department of Chemical Engineering, University of Windsor, N9B 3P4 Windsor, Ontario, Canada

Abstract:	Based on the complex viscosity model various steady-state and transient material functions have been completed. The model is investigated in terms of a corotational frame reference. Also, BKZ-type integral constitutive equations have been studied. Some relations between material functions have been derived. C ^–1 Finger tensor - F], (F ^–1]) Fourier (inverse) transform - $\dot G$ rate of deformation tensor in corotating frame - h(I, II) Wagner's damping function - J (x) Bessel function - m parameter inh (I, II) - m(s) memory function - m _k, n_k integers (powers in complex viscosity model) - P principal value of the integral - parameter in the complex viscosity model - $\dot \gamma$ rate of deformation tensor - $\dot \gamma ,\dot \gamma _0 ,\dot \gamma _\infty$ shear rates - ], ] incomplete gamma function - (a) gamma function - $\eta (\dot \gamma )$ steady-shear viscosity - ^* complex viscosity - , real and imaginary parts of ^* - ₀ zero shear viscosity - ⁺, ₁ ⁺ stress growth functions - ^–, ₁ ^- stress relaxation functions - (s) relaxation modulus - ₁(s) primary normal-stress coefficient - ø(a, b; z) degenerate hypergeometric function - ₁, ₂ time constants (parameters of ^*) - frequency - extra stress tensor

Keywords:	Complex viscosity relaxation modulus material function integral constitutive equation
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