Buoyancy driven miscible front dynamics in tilted tubes

The velocity $Vf$ of the fronts of light and heavy fluids in a tilted tube, interpenetrating many diameters, is studied as a function of the fluid viscosity $μ$⁠, Atwood number $At⪡1$ and tilt angle $θ$ from vertical. Three flow regimes are observed: starting from vertical, $Vf$ first increases with $θ$⁠, reaches a plateau and then decreases again. In the first regime, $Vf$ is controlled by segregation and mixing effects, respectively, increasing and decreasing with $θ$⁠. On the plateau, $Vf$ is independent of the fluid viscosity and proportional to $(Atgd)1∕2$⁠, indicating a balance between inertia and buoyancy. In the third regime close to horizontal, the fluids separate into two parallel countercurrents controlled by viscosity. The variations of $Vf$ with $θ$⁠, At, and $μ$ in the second and third regimes and the crossover from one to the other are described by scaling laws based on characteristic viscous and inertial velocities.