Viscoplastic flow development in tubes and channels with wall slip

The development of Bingham plastic flow in tubes and channels is investigated numerically using the Papanastasiou regularization and finite element simulations. It is assumed that slip occurs along the wall following Navier's law, according to which the slip velocity varies linearly with the wall shear stress. Alternative definitions of the development length are discussed and the combined effects of slip and yield stress at low and moderate Reynolds numbers are investigated. It is demonstrated that even for the Newtonian channel flow using the conventional centerline development length is not a good choice when slip is present. Similarly, the development length definition proposed by Ookawara et al. (2000) for viscoplastic flows results in misleading conclusions regarding the effect of yield stress on flow development. To avoid such inconsistencies a global development length is employed. In general, the global development length is monotonically increasing with the Reynolds and Bingham numbers. As slip is increased, the latter length initially increases exhibiting a global maximum before vanishing rapidly slightly above the critical point corresponding to sliding flow.