Defying gravity: Injection of viscoplastic fluids in vertical channels

Abstract

We analyze the injection of a heavy viscoplastic fluid into a closed-end, two-dimensional vertical channel filled with a Newtonian fluid, focusing on flow dynamics across a wide range of density differences. Three distinct flow regimes are identified. At low density differences, the displacement flow below the injector is minimal. At high density differences, the injected fluid behaves like a free-falling jet, rapidly giving rise to advective instabilities near the advancing front. In the moderate density range, the injected fluid forms a finger-like interface and displaces the Newtonian fluid beneath the injector. Yet this flow also becomes unstable due to interfacial instabilities near the injection point. Surprisingly, we demonstrate that the heavy fluid ultimately flows upwards, regardless of the density difference. This counterintuitive behavior is attributed to the formation of a progressively more stable, density-stratified layer beneath the injector, which inhibits the downward movement of the heavy fluid. We further characterize the transient displacement flow at moderate density differences, where the front velocity initially becomes steady before re-accelerating at higher density differences. Our findings show that the front velocity is controlled by a balance between local density differences and viscous stresses, and we explain the mechanisms driving the re-acceleration at higher density differences. Remarkably, the interface shape remains consistent across all density differences.