Buoyant viscoplastic injections in an inclined closed-end pipe

We experimentally and theoretically study the downward injection of a viscoplastic fluid through an inner pipe, into an inclined closed-end pipe hosting a Newtonian fluid, representing a core-annular flow configuration. In our experiments, based on the core viscoplastic fluid behaviour, three distinct flow regimes appear, including the breakup, coiling and buckling (bulging) regimes. In the breakup regime, as the injection continues, at some point the injected core fluid can no longer sustain the progressively-increasing buoyancy force, leading its yielding towards thinning and, finally, breaking up. In the buckling regime, the stresses applied by the annular fluid on the core lead to the yielding of the core fluid towards bulging. For the coiling regime, the core fluid remains largely unyielded and its diameter remains unchanged until the core is deformed into a coiling structure around the pipe wall. In the theoretical part, we develop a lubrication approximation model, along with the Herschel–Bulkley constitutive equation for the representation of the viscoplastic fluid's rheological behaviour. This allows us to successfully classify these flow regimes versus a combination of the governing dimensionless numbers, and make a comparison between experimental and modeling results.