Transition from diffusion to advection controlled contaminant adsorption in saturated chemically heterogeneous porous subsurfaces

Journal article, 2023

We show the impact that scalar structure deformation and mixing have on the fate of plumes of waterborne contaminant transported through a chemically heterogeneous, partially adsorbing porous medium at a typical Péclet number characterizing saturated flows in subsurfaces, Pe=O(1). Via pore-scale lattice Boltzmann simulations, we follow the dynamic of a passive scalar injected in a packed bed consisting of a mixture of chemically inert and adsorbing spherical particles. By varying the fraction of adsorbers ξ randomly and uniformly distributed in the porous volume, we find that the waterborne solute forms concentration plumes emerging between pairs of adsorbing particles. This deformation is a consequence of the different mechanisms of transport characterizing the transport of molecules in the proximal and remote pores relative to the adsorbers, diffusion and advection, respectively. The resulting isoscalar surface embedding the plumes grows at a rate proportional to the average pore-scale velocity U and inversely proportional to the adsorbers' interparticle dimensionless distance, i.e., γ∝U/ℓξ. We provide a quantification of the characteristic diffusive timescale of the plume tη∝ℓ2ξ/Dm, which dissipates the concentration differences in the vicinity of the adsorbers, with Dm being the molecular diffusion coefficient. Thus, by quantifying the relative importance of the advection-sustained stretching rate γ and plume mixing rate 1/tη for different values of fractions of adsorbers ξ, we establish a transition from diffusion- to advection-dominated macroscopic adsorption, whose time evolutions scale as ∝√t and ∝t, respectively. Such a transition is determined by the number of adsorbers within the medium, with diffusion and advection dominating at high and low fractions, respectively. Our numerical analysis provides ℓξ/d≈4/ln(2)Pe−1 as the critical distance between adsorbers that sets the transition, with d being the pore size.