Abstract
Buoyancy driven flows of two Bingham fluids in an inclined duct are considered, providing a simplified model for many oilfield cementing processes. The flows studied are near-uniaxial and stratified, with the heavy fluid moving down the incline, displacing the lighter fluid upwards. Existence and uniqueness results are obtained for quite general flows and for those which satisfy an axial flow rate constraint. Parametric dependence of the solutions on the axial pressure gradient is studied. Flows which satisfy a zero net axial flow constraint result from an axial pressure gradient which minimizes the viscous dissipation, but not the plastic dissipation. A regularization method is used to compute solutions to these problems for (more or less) arbitrary fluid-fluid interfaces and duct-cross sections. Examples related to a number of practical applications are presented.
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