Buoyant mixing of miscible fluids of varying viscosities in vertical tubes

Abstract

Gravity-induced mixing of two fluids in long vertical tubes is studied experimentally as a function of the density contrast characterized by the Atwood number At (10−5 to 0.2), the fluid viscosity ν (1 to 16×10−6 m2 s−1) and the tube diameter d (2 to 44 mm). At low density contrasts, a stable counterflow is observed over a large fraction of the tube and its region of existence increases at high viscosities and small tube diameters. For larger density contrasts, the flow is either convective or turbulent and the mean concentration profile C̄(x,t) follows a diffusive spreading law characterized by a diffusivity D. An unexpected increase of D and of the characteristic velocity Vf of random fluid motions is observed when ν increases. This results from the coarser mixing in more viscous fluids which increases local density contrasts and buoyancy forces. Dimensionless plots of the diffusion coefficient D/ν as a function of the Reynolds number of the flow indicate a transition between two different diffusive regimes. Scaling arguments are put forward to account for the dependence of Vf and of the characteristic diffusion length in the convective–diffusive regime.