Multiscale mathematical modelling of the fate of TMs after digestate land applications

Abstract

Biofilm-driven processes have emerged as a potential approach for remediation of heavy metal contaminated soils. Designed as intricate biological aggregates, biofilms have potential abilities that can be exploited for removal of pollutants within soil and wastewater systems. Nevertheless, biofilm growth in porous media is dificult to understand because it involves a variety of processes each occurring at different scales in space and time simultaneously. Experimental studies addressing these complexities are often time-consuming and costly, necessitating the use of mathematical models to explore the effective parameters influencing bioremediation and to optimize system performance.

This thesis develops a comprehensive multiscale mathematical model to describe the biosorption of heavy metals by multispecies biofilms in porous soil. The model is designed to accommodate the complex interplay of biological and hydrological processes across multiple scales, without constraints on the number of bacterial species or substrates involved. Three different models are presented, each progressively addressing more realistic and complex scenarios of biofilm growth and biosorption within soil media. The first model, based on state-of-the-art literature, assumes separate growth of biofilm species within soil pores, while the second introduces a novel framework for modeling mixed-culture biofilm growth. The third model extends the mixed-culture biofilm framework to simulate heavy metal biosorption, accounting for biofilm interactions and their impact on soil purification processes.

The resulting three models are formulated as systems of hyperbolic non-linear partial differential equations, reflecting the multiscale nature of biofilm dynamics. These models were numerically implemented using the Uniformly Accurate Central Scheme of order 2 (UCS2) in MatLab. Through extensive numerical simulations, the models offer insights into the microbial interactions, biofilm expansion, and the biofilm-soil-hydrology interdependence. The findings demonstrate that these models provide a robust tool for optimizing biofilm-mediated bioremediation processes, offering practical implications for field-scale applications and wastewater treatment in bioreactors.