Exchange flows between viscoplastic and Newtonian fluids in vertical and inclined pipes

In this study, we investigate the dynamics of a viscoplastic fluid placed above a Newtonian fluid in an inclined, long tube. The two fluids are miscible and have a density difference, with the viscoplastic fluid always denser. The experimental set-up allows varying inclination angles. Initially, the fluids are separated by a gate valve; upon opening it, distinct flow behaviours are observed, captured using cameras. The flow regimes depend on the interplay between buoyancy (due to the density difference), the yield stress of the viscoplastic fluid and the inclination angle. In tilted tubes, exchange flow with a slumping regime is observed, while in vertical configurations, a stable finger front forms at high values of the yield number ( upper Y Y Y ), representing the ratio of yield stress to buoyancy stress. As upper Y Y Y decreases, helical, disconnected and slug finger regimes emerge. We investigate these flow regimes and quantify their transition boundaries, focusing on finger length and front velocity. Numerically, we develop a three-dimensional model based on the Herschel–Bulkley rheology, implementing the Papanastasiou regularisation and the volume-of-fluid method within the finite-volume framework of OpenFOAM. The simulations provide insights into velocity profiles, finger thickness and the distribution of yielded and unyielded regions. Numerical results indicate the finger tip becomes increasingly eccentric as the pipe is inclined, with a pronounced rise in eccentricity for inclinations exceeding 30 Superscript ring 30 ∘ 30^∘ . These results are particularly relevant to industries like oil and gas, improving well integrity and protecting groundwater and the atmosphere by addressing cementing and sealing challenges.