We investigate the interplay between adsorption and transport
in
a two-dimensional porous medium by means of an extended Lattice Boltzmann
technique within the Two-Relaxation-Time framework. We focus on two
canonical adsorption thermodynamics and kinetics formalisms: (1) the
Henry model in which the adsorbed amount scales linearly with the
free adsorbate concentration and (2) the Langmuir model that accounts
for surface saturation upon adsorption. We simulate transport of adsorbing
and nonadsorbing particles to investigate the effect of the adsorption/desorption
ratio k, initial free adsorbate concentration c
0, surface saturation Γ∞, and Peclet numbers Pe on their dispersion behavior. In all cases,
despite marked differences between the different adsorption models,
the three following transport regimes are observed: diffusion-dominated
regime, transient regime and Gaussian or nearly Gaussian dispersion
regime. On the one hand, at short times, the intermediate transient
regime strongly depends on the system’s parameters with the
shape of the concentration field at a given time being dependent on
the amount of particles adsorbed shortly after injection. On the other
hand, at longer times, the influence of the initial condition attenuates
as particles sample sufficiently the adsorbed and nonadsorbed states.
Once such dynamical equilibrium is reached, transport becomes Gaussian
(i.e., normal) or nearly Gaussian in the asymptotic regime. Interestingly,
the characteristic time scale to reach equilibrium, which varies drastically
with the system’s parameters, can be much longer than the actual
simulation time. In practice, such results reflect many experimental
situations such as in water treatment where dispersion is found to
remain anomalous (non-Gaussian), even if transport is considered over
long macroscopic times.