A numerical and theoretical study on viscoelastic fluid slip flows

Abstract

This work describes a theoretical and numerical investigation of viscoelastic fluid flows, considering slip boundary conditions. The viscoelastic fluid is described by the simplified Phan-Thien-Tanner model, and the governing equations with slip boundary conditions are solved by a finite volume method using (1) a recently proposed methodology to control the growth of the slip velocity along the iterative process (named the SIMPLE-slip method) where some simplifications are assumed at the wall, and also (2) a slip formulation where the complete stress tensor at the wall is taken into account. Analytical and semi-analytical solutions are also provided for the fully developed flow between parallel plates of viscoelastic fluids, assuming Thomson and Troian and Lau and Schowalter non-linear wall slip models. For verification purposes, the numerical results were compared with the analytical solution for fully developed slip-flow in a planar channel using two non-linear slip models. Simulations were carried out in a classical benchmark problem in computational rheology, the viscoelastic fluid flow in a slip-stick geometry, aiming to identify the influence of slip intensity on the flow patterns, velocity, and stress growth at the singularity region.