Navier Slip Law Research Articles

Development Length in Planar Channel Flows of Newtonian Fluids Under the Influence of Wall Slip

This technical brief presents a numerical study regarding the required development length (L=Lfd/H) to reach fully developed flow conditions at the entrance of a planar channel for Newtonian fluids under the influence of slip boundary conditions. The linear Navier slip law is used with the dimensionless slip coefficient k¯l=kl(μ/H), varying in the range 0<k¯l≤1. The simulations were carried out for low Reynolds number flows in the range 0<Re≤100, making use of a rigorous mesh refinement with an accuracy error below 1%. The development length is found to be a nonmonotonic function of the slip velocity coefficient, increasing up to k¯l≈0.1-0.4 (depending on Re) and decreasing for higher k¯l. We present a new nonlinear relationship between L, Re, and k¯l that can accurately predict the development length for Newtonian fluid flows with slip velocity at the wall for Re of up to 100 and k¯l up to 1.

Wall slippage with siloxane gum and silicon rubbers

A slip analysis has been developed to calculate the slip velocities from the capillary rheometry data for a polydimethylsiloxane (PDMS) gum, and two silicon rubber compounds. The analysis generalises the classical Mooney method [J. Rheol. 2 (1931) 210–222] to incorporate the influence of die geometry on the slip behaviour. For the PDMS gum, no slippage was observed below a stress level of about 60 kPa, and there was a jump in the slip velocity at a stress level of about 80 kPa. The complex rheological behaviour of the rubbers meant that the analysis was only applicable at higher stress levels. For each material, a reasonable fit to the slip velocity was obtained using a generalised Navier slip law, which can easily be implemented into computational fluid dynamic simulations. Ultimately, a more realistic slip law is required to model the observed flow behaviour correctly.

Numerical Simulation of Twin-Screw Extrusion with Wall Slip

Wall slip boundary condition is first introduced into twin-screw extrusion with the Navier slip law. Three-dimensional isothermal flow in the twin-screw extruder is simulated by using the finite element package POLYFLOW. Profiles of velocity contours in the screw channel and shear rate distributions in the intermeshing region are presented for different slip coefficients. Curves of axial pressure difference, average shear rate and dispersive mixing index vs. the slip coefficient are plotted and discussed. Comparisons are also made between the wall slip conditions and the non-slip condition. The simulation results indicate that, as the level of wall slip decreases, the axial pressure difference rises, the shear effect is intensified and the axial mixing is also enhanced. All these flow characteristics seem to level off with the increase of the slip coefficient. However, because of the inherent limitation of the Navier slip law, use of an overestimated slip coefficient would predict an over-sticky state between the screw surface and the polymer melt.