Interfacial dynamics in immiscible displacements through stationary and rotating inclined pipes

We investigate buoyant immiscible displacements of Newtonian and elasto-viscoplastic fluids in inclined pipes under stationary and axially rotating conditions, motivated by primary cementing applications. Experiments span broad ranges of density contrast, viscosity ratio, interfacial tension, inclination, and both imposed and rotational inertia, yielding flow dynamics governed by multiple dimensionless groups. In stationary pipes, Newtonian displacements form kinked, gravity-dominated fronts, whereas elasto-viscoplastic fluids develop lifted heads with trailing filaments. Head geometry and filament kinematics scale systematically with the Weber and Ohnesorge numbers: increasing inertia and viscosity elongate heads and thicken filaments. Transient filament necking follows an exponential decay captured by a correlation involving the capillary and Deborah numbers. Rotation fundamentally restructures the displacement, generating secondary flows, asymmetric interfaces, and fragmentation of both displacing/displaced fluids; interfacial-wave intensity increases with the rotational Weber number, while wave elongation increases with imposed inertia. Both a higher capillary number and a higher Ohnesorge number result in a longer breakup length and a longer evolution time for fragmented segments. Complementary simulations quantitatively reproduce Newtonian experiments and accurately resolve the evolution of dominant front velocity, interfacial wavelengths, and wave periods while revealing rotation-induced asymmetries and recirculation restructuring. Finally, extensive experimental and numerical data on the relationship between displacement front velocity, Froude number, inclination angle, viscosity ratio, and rotation have been consolidated into a unified correlation applicable to both Newtonian and elasto-viscoplastic fluids.