Annular Poiseuille flow of Bingham fluids with wall slip

Abstract

We consider the annular Poiseuille flow of a Bingham fluid with wall slip. First, the analytical solution is derived for the case in which Navier-slip conditions are applied at the two cylinders. A sliding (pure plug) regime is observed below a critical pressure gradient, and a yielding regime is eventually encountered above another critical pressure gradient in which the material yields near the two walls and moves as a plug in a core region. An intermediate semi-sliding regime is observed when different slip laws apply at the two walls in which the material yields only near the wall corresponding to weaker slip and the unyielded plug slides along the other. Next, we consider the case where wall slip occurs above a critical wall shear stress, the slip yield stress, which is taken to be less than the yield stress, in agreement with experimental observations. In this case, a no-flow regime is observed below a critical pressure gradient, followed by the sliding and yielding regimes. The critical values of the pressure gradient defining the various flow regimes are determined, and the closed-form solutions are provided for all cases. These are compared with available theoretical and experimental results in the literature.