Effect of diffusing layer thickness on the density-driven natural convection of miscible fluids in porous media: Modeling of mass transport

In this study, density-driven natural convection in porous media associated with Rayleigh-Taylor instability was visualized by X-ray computed tomography to investigate the effect of the thickness of the diffusing interface on convection. The thickness of the interface was changed by molecular diffusion with time, and the effective diffusivity in a porous medium was estimated. Compared with the thick interface, for the thin interface, many fine fingers formed and extended rapidly in a vertical direction. The onset time of natural convection increased proportionally with the thickness of the interface, being correlated with Rayleigh number and Peclet number. For the thinner initial interface, the finger number density increased more rapidly after onset and reached a higher value. Next, we discussed the mass transport in Rayleigh-Taylor convection to show how dispersion affects mass transport based on finger extension velocity and concentration in fingers. Increasing the interface thickness delayed the onset of convection, while the finger extension velocity remained the same. The reduced finger extension velocity changed nonlinearly with the Peclet number, reflecting the effect of dispersion. High transverse dispersion and longitudinal dispersion quickly reduced finger density. Transverse dispersion between ascending and descending fingers decreased the density; the density decreased linearly along the finger on both sides of the symmetric plane. As a result, the Sherwood number was proportional to the Rayleigh number, whereas the coefficient changed nonlinearly with Peclet number because of dispersion, reflecting the nonlinear dependences of the reduced velocity and the reduced density difference on Peclet number.