Displacement flows in periodically moving pipe: Understanding multiphase flows hosted in oscillating geometry

Abstract

In the present work, we experimentally study displacement flows of two Newtonian, miscible fluids in a long, vertical moving pipe while comparing the results with the corresponding displacement flows in a stationary pipe. When in motion, the pipe slowly oscillates like an inverted pendulum. The two fluids have a small density difference and a nearly-identical viscosity. The denser displacing fluid is placed above the displaced fluid. Overall, our buoyant displacement flows in a moving pipe are at least controlled by three dimensionless groups, namely the Reynolds number, the densimetric Froude number, and the Rossby number. Experimental images of the penetrating front of the heavy displacing fluid into the light displaced one have been analyzed for a wide range of the dimensionless groups. In particular, three different flow regimes are observed for displacement flows in a moving pipe: a stable flow that is non-diffusive (for Re/Ro≲O102 &Re/Fr2<35), a stable-diffusive flow (for Re/Ro≳O102 &Re/Fr2<35) and an unstable-diffusive flow (for Re/Fr2>35). In addition, penetration front velocities as well as macroscopic diffusion coefficients have been quantified. The results show in detail that depending on the value of the density difference and the mean imposed displacement flow velocity, the geometrical movement can have different and even opposite effects, e.g., slightly increase or decrease the front velocity. The pipe motion seems to also slightly increase the macroscopic diffusion coefficient. While the findings of this study can help understand the leading order effects associated with a flow geometry movement on displacement flows, they can be of great importance for industrial applications and for development of relevant fluid mechanics theories.