The nonlinear adsorptive kinetics of solute transport in soil does not change with pore-water velocity: Demonstration with pore-scale simulations

Abstract

Summary The adsorptive kinetics of reactive solutes in soils is usually measured in batch experiments by keeping the water stagnant. One concern over such measured parameters is their representative of describing the adsorption in field where the water is not stagnant but moves in a spatially variable velocity. Answer to this question appears to be conflict in the literature with some finding a dependence of the adsorptive kinetics on water flow rate and others showing contradiction. Since the adsorption occurring at water–solid interface is inaccessible, affected by various physical and biochemical processes, the existing explanations about an dependence, or independence, of the adsorptive kinetics on water flow rate are not consensus. In this paper a pore-scale model was developed to investigate the adsorptive kinetics of solute in soil. It was assumed that each water–solid interface has a limited number of adsorptive sites to adsorb solute, and that the rate at which the interface adsorbs solute is proportional to the number of the adsorptive sites that still remain unoccupied by solute particles. In the meantime, each adsorbed solute particle can come off the interface at a given probability to become desorbed. Water flow and solute transport through the void space was simulated using a lattice Boltzmann method, and the simulated solute distribution at pore scale was then spatially averaged to yield two profiles: one for solute in fluid and one for solute adsorbed on the fluid–solid interface, in an attempt to test if the spatial average leads to a macroscopic adsorptive kinetics that changes with water flow rate. The results indicated that when the microscopic adsorptive kinetics is homogeneous in that the adsorption and desorption rates operating on the fluid–solid interface are both constants, the associated macroscopic adsorptive rates do not change with water flow rate and their values measured in batch experiments can accurately predict solute displacement under different pore-water velocities. When the microscopic adsorptive kinetics becomes spatially heterogeneous, however, the macroscopic adsorption rates measured in the batch experiments are no longer able to describe solute displacement. The results presented in this paper provide some insight into the adsorptive kinetics of solute in soils, suggesting that the reported dependence of adsorptive rates on water flow rate could be due to an inappropriate use of adsorptive models in describing the heterogeneous adsorption in soil, rather than truly that a change in pore-water velocity indeed results in a change in adsorption rates.