Research Project C01

We investigate the flow structure and the porosity-permeability relationship of porous media that undergo morphology modifications due to evaporation or microbially induced calcite precipitation, as well as wettability modifications of the solid-fluid interface due to fluid pH, composition, or salt con¬centration changes. We develop simulation methods based on coupled multi-phase and multi-component Lattice-Boltzmann and solute molecular dynamics simulations, capable of reproducing these processes in detail on the pore scale, yielding results to be used to improve existing continuum models.

Multiphase/multicomponent lattice Boltzmann with electrokinetics: Using automatic code generation frameworks, we implemented the Shan-Chen pseudopotential method for simulating multiphase and multicomponent flows with lattice Boltzmann. The Shan-Chen method is a diffuse interface method, the demixing of fluid phases or components depends on the strength of the pseudopotential.  No-slip boundaries were introduced using the bounce-back algorithm. Wetting properties of surfaces can be adjusted by introducing an interaction between boundaries and each fluid component of the same form as the Shan-Chen pseudopotential. To simulate charged solutes in the multicomponent system, we implemented a finite-volume-based solver for the electrokinetic equations. Each solute species is treated as a dilute charged continuum subject to diffusion, electrostatic interactions and advection with the underlying fluids.
Additionaly, the solutes interact with with the fluids via a ion-solvent specific force, which can cause separation of solutes when placed in a multicomponent fluid.

Bacteria and Biofilm: As a first step for biofilm formation, the location of biofilm initiation must be found. In a porous environment with external flow, these locations are determined by the interplay of bacterial motility, confinement and local flows.  We developed a model to simulate the run-and-tumble motility pattern that is observed in many bacterial species.  Here, straight swimming phases (runs) are interrupted by sudden changes in orientation (tumbles). We match the statistical properties of run and tumble durations as well as the reorientation angle to experimentally measured values for E. coli bacteria. We applied the calibrated model to a simplified porous geometry consisting of a rectangular channel with one cylindrical obstacle.  We observe accumulation of bacteria behind the obstacle when the bacteria are motile and an external flow is present.  To further advance the bacterial model and come closer to modelling the whole process of biofilm formation on porous media, we added an algorithm for surface attachment. The attachment is reversible, for example strong flows can remove a bacterium from a surface.

The next step is biofilm growth, which happens on a much larger timescale than the swimming and attachment. In our model, individual bacteria grow until reaching a length threshold, at which point the parent cell is replaced by two daughter cells which together occupy the same space that the parent alone occupied before.  We implemented several growth models, the simplest of which being exponential growth with a constant doubling time as observed for bacteria that are supplied with a surplus of nutrients. Placing the biofilm in a flow field allows us to investigate the interplay between the forces inside the biofilm and the viscous drag exerted by the fluid on the biofilm surface.
Biofilm and fluid are coupled in both ways, so the growing biofilm also affects the flow field. The full model of biofilm growth has been applied to a simple porous geometry, see to show how the permeability is reduced until the biofilm clogs the whole system.

We will extend the electrokinetics lattice Boltzmann algorithm to also include a model for evaporation and precipitation. We can then combinbe it with the bacterial model to simulate the process of microbially induced calcite precipitation. With our models, we will be able to simulate biofilm growth depending on nutrients (simulated as a solute in the lattice Boltzmann electrokinetics) and the release of enzymes by the bacteria. Then we can make the pecipitation dependent on enzyme concentration an determine the locations of likely precipitation.