Lattice Boltzmann model for agrochemical transport in soils

Agrochemical transport in soils is complicated and involves physical, chemical and biochemical reactions; its mathematical modelling remains a challenging task. This paper presents a lattice Boltzmann model to simulate the agrochemical movement. The lattice Boltzmann model is a microscopic and process-based model, simulating the transport process by tracking chemical particles. The model presented in this paper is for one-dimensional vertical leaching and assumes that the chemical particles at the microscopic level move in five directions: one stagnant, two in vertical direction and two in an internal horizontal direction bounded by two reactive walls. Reactions at the walls are assumed to take place at two different rates, one in fast rate where the chemicals in the solution and on the wall are in an instant equilibrium, and the other in slow rate where the mass exchange rate between the chemicals in the solution and on the wall is a first-order kinetic. The reactions on both walls are assumed to occur instantly when the chemical particles moving in the internal direction hit the walls. To test the model, we measured the leaching of atrazine through soil columns in the laboratory. The results simulated with the lattice Boltzmann model are compared with the measured breakthrough curves and the non-equilibrium two-site convection-dispersion model; they all show close agreement. The transport parameters needed in the models are obtained from the measurement of adsorption isotherm of atrazine, bromide leaching in the same soil columns and calibration.