Emergence in porous media

Emergence in natural porous media

Participants: Nadja Ray, Alexander Prechtel, Andreas RuppSerge Kräutle, Simon Zech, Alice Lieu

The grand goal of this group is the development, analytical, and numerical investigation of a mechanistic model describing processes of formation, stability, and turnover of soil micro-aggregates, i.e., particles in the range up to 250 micrometers. They are the fundamental building blocks of soils and thus determine important soil functions, such as water retention, biological activity and habitat, and the storage and biogeochemical cycling of carbon [Totsche et al. 2018]. To assess the complex coupling of biological, chemical and physical processes, we developed a mechanistic model.

In contrast to existing conceptual aggregation models and compartment models for carbon turnover and aggregation, we focus on specific, experimentally identified transformation processes of soil microaggregates.
Since we are interested in giving an improved mechanistic, qualitative and even quantitative description of aggregation, we transfer the gained insights of 1. to a mechanistic model in terms of ordinary differential equations (ODEs), partial differential equations (PDEs), and perhaps algebraic equations (AEs). To that end, we aim to take into account information/identified processes on different spatial scales as well as spatial heterogeneity and variability. All our modeling is done in a rigorous, deterministic way and our modeling concepts are based on continuum mechanics, i.e. a description via concentrations and not a description considering single particles. We start our investigations at the pore scale and apply multiscale techniques to obtain a comprehensive mathematical model at the macroscale (bottom up). In particular, the interplay of geochemistry and microbiology is considered, and also their link to soil functions.

The coupled ODE/PDE systems and complex micro-macro problems can not be treated numerically with standard software packages. The number of species, nonlinearity of the processes and heterogeneity of the medium results in a high computational effort that requires accurate and efficient discretization methods and solution algorithms. Moreover sophisticated numerical multiscale methods have to be applied.
In our simulations, we do not aim to recreate reality in every detail. Instead, we aim to illustrate, compare, and reveal influencing factors and mechanisms by abstracting relevant processes.

The model currently combines reactive transport of solutes and charges, prescribed by means of partial differential equations, with solid restructuring and biomass development, realized in a cellular automaton framework (CAM) [Ray et al. 2017, Rupp et al. 2018, Rupp 2019]. As the evolving computational domain leads to discrete discontinuities, we apply the local discontinuous Galerkin (LDG) method for the transport equations.

Two videos illustrate studies performed within the framework of the research unit RU 2179 “MAD Soil – Microaggregates: Formation and turnover of the structural building blocks of soils” (DFG RU 2179).


In this simulation, we distributed bacteria and particulate organic matter (POM) sources in a pore space given from a CT scan of a microaggregate (courtesy of Vincent Felde, Universität Kassel) of size 128*128 µm. For the chosen saturation of 0.5 the gas and liquid phase were distributed following a morphological model, similar to [Hu et al. 2014]. Dissolved organic carbon is hydrolized by a first order kinetics from the POM sources. The bacteria strains grow based on Michaelis-Menten kinetics due to the uptake of DOC and shrink due to respiration of CO2. Realistic parameter values for the diffusion coefficent and reaction rates were taken from [Portell et al. 2018]. The video illustrates the movement of bacteria towards nutrient sources. Additionally, global biodegradation kinetics integrated over the whole computational domain are presented. For more details, see Preprint [Zech et al. 2021].


The formation of microaggregates’ smaller building units is largely determined by aggregation processes of fine-sized mineral and organic microaggregate forming materials. In this simulation, inspired by laboratory experiments from [Dultz et al. 2019], we randomly distributed oppositely charged prototypic minerals illite and goethite for varying mixing ratios. The particles are able to rotate and move within a size dependent stencil and form larger composites due to electrostatic attraction. Largest aggregates were found for mixtures closest to the point of zero charge. For more details, see [Zech et al. 2020]. In the video, excerpts of the computational domain for three different mixing ratios are shown.



Totsche et al. (2018): https://doi.org/10.1002/jpln.201600451

Ray et al. (2017): https://doi.org/10.1016/j.advwatres.2017.04.001

Rupp et al. (2018): https://doi.org/10.3389/fenvs.2018.00096

Rupp (2019): https://opus4.kobv.de/opus4-fau/frontdoor/index/index/year/2019/docId/11252

Hu et al. (2014): https://doi.org/10.1016/j.jhydrol.2014.10.057

Portell et al. (2018): https://doi.org/10.3389/fmicb.2018.01583

Dultz et al. (2019): https://doi.org/10.1016/j.clay.2019.01.002

Zech et al. (2020): https://doi.org/10.1016/j.clay.2020.105845

Zech et al. (2021): https://www1.am.uni-erlangen.de/research/preprint/pr412.pdf

Friedrich-Alexander-Universität Erlangen-Nürnberg