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The memory function and elastic modulus were introduced into the O-W-F type of constitutive equations with the Cauchy-Green and Finger tensors for simple fluid, and then the concrete constitutive equation and material function for polymeric suspensions in the different flow fields were formulated: 1) Viscosity and first normal-stress difference coefficient in the shear flow field; 2) Tensile viscosity at the uni-axial elongation flow field; and 3) Dynamic viscosity and modulus in the dynamic field. Then the dependence of the material function on the deformation rate and weight fraction of fillers was discussed, and the shear flow curves with four characteristic regions ( I-low shear rate plateau region, II-apparent yielding region, III-intermediate rate plateau region, and IV-shear thinning region.) were explained theoretically. Finally, it was verified by a number of experimental values for the rheological suspensions and the viscoelastic and mechanical behaviors can be predicted by the molecular theory of non-linear viscoelasticity for polymeric suspensions.

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