Discrete-Continuum Multiphase Model for Structure Formation in Soils Including Electrostatic Effects

Abstract

Structure formation and self organization in soils determine soil functions and regulate soil processes. Mathematically based modeling can facilitate the understanding of organizing mechanisms at different scales, provided that the major driving forces are taken into account. In this research we present an extension of the mechanistic model for transport, biomass development and solid restructuring that was proposed in [RayRuppPrechtel2017]. Three main extensions are implemented. First, arbitrary shapes for the building units (e.g. spherical, needle-like or platy particles), and also their compositions are incorporated into the model. Second, a gas phase is included in addition to solid, biofilm, and fluid phases. Interaction rules within and between the phases are prescribed using a cellular automaton method (CAM) and a system of partial differential equations (PDEs). These result in a structural self organization of the respective phases which define the time-dependent composition of the computational domain. Within the non-solid phases, chemical species may diffuse and react. In particular a kinetic Langmuir isotherm for heterogeneous surface reactions and a Henry condition for the transfer from/into the gas phase are applied. As third important model extension charges and charge conservation laws are included into the model for both the solid phase and ions in solution, as electrostatic attraction is a major driving force for aggregation. The ions move obeying the Nernst-Planck equations. A fully implicit local discontinuous Galerkin (LDG) method is applied to solve the resulting equation systems. The operational, comprehensive model allows to study structure formation as a function of the size and shape of the solid particles. Moreover, the effect of attraction and repulsion by charges is thoroughly discussed. The presented model is a first step to capture various aspects of structure formation and self organization in soils, it is a process-based tool to study the interplay of relevant mechanisms in silico.