VARIATIONAL PRINCIPLE AND VARIATIONAL INEQUALITY FOR A YIELD STRESS FLUID IN THE PRESENCE OF SLIP

Minimum and maximum principles. which have been derived for the creepi ng flows of a yield stress fluid, are extended to flows when wall slip is present. In addition, the minimum principle is shown to lead to a variational inequality when wall slip is absent, and the latter is gen eralised to include inertial effects in specific cases, including hows in pipes and the how past a body at rest due to a uniform flow at inf inity. Moreover, the variational inequality is extended to deal with p roblems when wall slip may be present. Finally, the squeezing flow bet ween two co-axial and parallel disks is re-examined as an application of the variational principles obtained here. (C) 1998 Elsevier Science B.V. All rights reserved.