Generalized Newtonian fluid constitutive equation for polymer liquids considering chain stretch and monomeric friction reduction for very fast flows modeling

Abstract

In this work, the recently proposed frame-invariant Generalized Newtonian Fluid (GNF) constitutive equation [M. Zatloukal, “Frame-invariant formulation of novel generalized Newtonian fluid constitutive equation for polymer melts,” Phys. Fluids 32(9), 091705 (2020)] has been modified to provide uniaxial extensional viscosity at a high strain rate limit corresponding to molecular expression for a fully extended Fraenkel chain reported in Ianniruberto et al. [“Melts of linear polymers in fast flows,” Macromolecules 53(13), 5023–5033 (2020)]. It uses basic rheological and molecular parameters together with the ratio of monomeric friction coefficients for equilibrium and fully aligned chains. The modified GNF model was successfully tested by using steady-state uniaxial extensional viscosity data for well-characterized entangled polymer melts and solutions [namely, linear isotactic polypropylenes, poly(n-butyl acrylate), polyisoprenes, and polystyrenes] covering a wide range of strain rates, including those, at which the chain stretch occurs. Only two fitting parameters were sufficient to describe all uniaxial extensional viscosity data, one related to the Rouse stretch time and the other controlling the extensional thinning and thickening behavior at medium and high strain rates. The model was compared to five different advanced viscoelastic constitutive equations, which are based on Doi–Edwards theory and include chain stretch along with a number of important additions. The ability of the proposed GNF model to represent steady uniaxial extensional viscosities under fast flow conditions for entangled polymer fluids has been shown to be superior to the predictions of selected advanced viscoelastic constitutive equations. It is believed that the modified GNF model can be used in the stable modeling of non-Newtonian polymer liquids, especially in very fast steady-state flows where chain stretch begins to occur.