Uniaxial exchange flows of two Bingham fluids in a cylindrical duct

Buoyancy driven Bows of two Bingham fluids in an inclined duct are consider ed, providing a simplified model for many oilfield cementing processes. The flows studied are near-uniaxial and stratified, with the heavy fluid movin g down the incline, displacing the lighter fluid upwards. Existence and uni queness results are obtained for quite general Bows and for those which sat isfy an axial Bow rate constraint. Parametric dependence of the solutions o n the axial pressure gradient is studied. Flows which satisfy a zero net ax ial Bow constraint result from an axial pressure gradient which minimizes t he viscous dissipation, but not the plastic dissipation. A regularization m ethod is used to compute solutions to these problems for (more or less) arb itrary fluid-fluid interfaces and duct cross-sections. Examples related to a number of practical applications are presented.