Newtonian and viscoelastic fluid flows through an abrupt 1:4 expansion with slip boundary conditions

Abstract

In this work, we present a systematic numerical investigation of the 1:4 planar expansion creeping flow under the influence of slip boundary conditions for Newtonian and viscoelastic fluids, the latter modeled by the simplified Phan–Thien–Tanner constitutive model. The linear and nonlinear Navier slip laws were considered with the dimensionless slip coefficient kl* varying in the range 0, 4500 and the slip exponents m = 0.5, 1, and 2. The simulations were carried out for a low Reynolds number, Re = 0.001, and for Deborah numbers (De) between 0 and 100. Convergence could not be achieved for higher values of the Deborah number and large values of the slip coefficient due to the large stress gradients near the singularity point (reentrant corner). The results obtained allow us to conclude that for all De, the increase in slip velocity leads to vortex suppression. The flow characteristics are described in detail for low values of the Deborah number, De ≤ 5, while for higher De the main features are only shown for specific values of the slip coefficient. These results find application in polymer processing, where the use of lubricants that migrate to the wall is common, which promotes slip.