  We report a pore-scale numerical study of salt finger convection in porous
media, with a focus on the influence of the porosity in the non-Darcy regime,
which has received little attention in previous research. The numerical model
is based on the lattice Boltzmann method with a multiple-relaxation-time scheme
and employs an immersed boundary method to describe the fluid-solid
interaction. The simulations are conducted in a two-dimensional,
horizontally-periodic domain with an aspect ratio of 4, and the porosity is
varied from 0.7 to 1, while the solute Rayleigh number ranges from 4*10^6 to
4*10^9. Our results show that, for all explored Rayleigh number, solute
transport first enhances unexpectedly with decreasing porosity, and then
decreases when porosity is smaller than a Rayleigh number-dependent value. On
the other hand, while the flow strength decreases significantly as porosity
decreases at low Rayleigh number, it varies weakly with decreasing porosity at
high Rayleigh number and even increases counterintuitively for some porosities
at moderate Rayleigh number. Detailed analysis of the salinity and velocity
fields reveals that the fingered structures are blocked by the porous structure
and can even be destroyed when their widths are larger than the pore scale, but
become more ordered and coherent with the presence of porous media. This
combination of opposing effects explains the complex porosity-dependencies of
solute transport and flow strength. The influence of porous structure
arrangement is also examined, with stronger effects observed for smaller
porosity and higher Rayleigh number. These findings have important implications
for passive control of mass/solute transport in engineering applications.

Fluid Dynamics