The effects of yield stress variation on uniaxial exchange flows of two bingham fluids in a pipe

Buoyancy driven flows of two Bingham fluids in an inclined pipe are conside red, providing a simplified model for flows occurring in the oilfield proce ss of plug cementing. The flows studied are near-uniaxial and strati ed, wi th the heavy fluid moving down the incline, displacing the lighter fluid up wards. Continuity and monotonicity results are given describing parametric dependence of the solutions on the yield stresses. Solutions are found for two specific fluid-fluid interface configurations that are of practical int erest. For these flows there exists a single curve in the dimensionless yie ld stress parameter space, which separates regions of zero and nonzero ow. For the example interface configurations, this curve is determined exactly. For arbitrary interface configurations a rigorous but conservative general result is proven. Heuristic methods are then used to improve this estimate for arbitrary interfaces.