Numerical solution of a single-species biofilm model on non-orthogonal grids

Ali, Md Afsar
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University of Guelph

Biofilms are collections of microbes attached to either a smooth or a rough surface. Within biofilms, bacteria interact with each other using a signalling communication method known as quorum sensing, which enables bacteria to execute gene-expression. Our research focuses on studying a density-dependent, diffusion-reaction-based single-species biofilm model, in which the biomass growth equation exhibits two non-linear degeneracy effects: (i) a porous medium degeneracy as biomass density vanishes, (ii) a super-diffusion singularity as it approaches unity. Previously, a semi-implicit numerical method was developed to solve this model on orthogonal grids. We improve and extend the existing semi-implicit method to solve the biofilm model on non-orthogonal grids. In this process, governing equations are transferred to general non-orthogonal curvilinear grids, and are discretized by the cell-centered finite volume method. At the faces of a control volume, the diffusive flux is split into orthogonal and non-orthogonal components. The orthogonal component is handled in a conventional manner, while the non-orthogonal component is handled explicitly and treated as a part of the source term. While discretizing the non-orthogonal term at the midpoint of a control volume face, the values of a dependent variable at the corners of the control volume face are calculated using values available at the centroid locations by an area-weighted linear interpolation scheme. The semi-implicit treatment of the non-orthogonal flux component works efficiently if the maximum deviation in orthogonality in the grid is within 15−20 degrees. The developed method is applied to study the effect of surface roughness on the substrate diffusivity and biofilm activity. The results show that under the nutrient-rich condition, substratum roughness does not have a pronounced effect on biofilm activity, but under the nutrient-low condition, the biofilm growth activity and structure are affected. To study the effect of substratum roughness on quorum sensing activity in biofilm, we further solve a single-species quorum sensing model using the developed numerical formulation. The results indicate that QS induction is dependent not only on the size of the bacterial population, but also on the diffusion properties of the signalling molecules according to the surface roughness properties.

Simulation, Non-orthogonal Grid, Rough Surface