Note on the start-up of Couette flow for viscoelastic fluids

Abstract

This paper is concerned with the numerical modeling of viscoelastic fluids in non-steady shear motions. Time-dependent solutions for three-constant differential models are obtained at the start-up of the planar Couette flows. The influences of (i) the Reynolds number, (ii) the value of κ− material parameter (the ratio between the retardation time and relaxation time), and (iii) the initial condition for the normal stress on the velocity and stresses distributions in the gap are investigated using the numerical solutions obtained with Mathematica software. The focus of the study is the analysis of the Jaumann model (characterized by the corotational derivative) in transitory simple shear rheological tests, as a function of initial conditions for stresses. The steady solutions, corroborated with the non-monotonicity of the steady flow curve, confirm the kink presence in the steady velocity distributions and the formation of shear bandings at Re ≥ 1. The analyses of the strain- and stress-controlled simulations performed at different initial and boundary conditions offer possible explanations of some spurious data recorded in shear measurements of complex viscoelastic fluids. The findings have important consequences for performing transient shear experiments; specifically, it is demonstrated that reproducibility and correlations between the tests require the control of initial normal stresses in the sample.