Buoyant miscible displacement flows in vertical pipe

Abstract

The displacement flow of two miscible Newtonian fluids is investigated experimentally in a vertical pipe of long aspect ratio (δ−1 ≈ 210). The fluids have a small density difference and they have the same viscosity. The heavy displacing fluid is initially placed above the light displaced fluid. The displacement flow is downwards. The experiments cover a wide range of the two dimensionless parameters that largely describe the flow: the modified Reynolds number (0 ≤ Ret⪅800) and the densimetric Froude number (0 ≤ Fr ≤ 24). We report on the stabilizing effect of the imposed flow and uncover the existence of two main flow regimes at long times: a stable displacement flow and an unstable displacement flow. The transition between the two regimes occurs at a critical modified Reynolds number RetCritical, as a function of Fr. We study in depth the stable flow regime: First, a lubrication model combined with a simple initial acceleration formulation delivers a reasonable prediction to the time-dependent penetrating displacing front velocity. Second, we find two sub-regimes for stable displacements, namely, sustained-back-flows and no-sustained-back-flows. The transition between the two sub-regimes is a marginal stationary interface flow state, which is also well predicted by the lubrication model. The unstable regime is associated to instabilities and diffusive features of the flow. In addition, particular patterns such as front detachment phenomenon appear in the unstable flow regime, for which we quantify the regions of existence versus the dimensionless groups.