The functioning of natural and engineered porous media, like soils and filters, depends in many cases on the interplay between biochemical processes and hydrodynamics. In such complex environments, microorganisms often form surface-attached communities known as biofilms. Biofilms can take the shape of clusters, which alter the distribution of fluid flow velocities within the porous medium, subsequently influencing biofilm growth. Despite numerous experimental and numerical efforts, the control of the biofilm clustering process and the resulting heterogeneity in biofilm permeability is not well understood, limiting our predictive abilities for biofilm-porous medium systems. Here, we use a quasi-2D experimental model of a porous medium to characterize biofilm growth dynamics for different pore sizes and flow rates. We present a method to obtain the time-resolved biofilm permeability field from experimental images and use the obtained permeability field to compute the flow field through a numerical model. We observe a biofilm cluster size distribution characterized by a spectrum slope evolving in time between -2 and -1, a fundamental measure that can be used to create spatio-temporal distributions of biofilm clusters for upscaled models. We find a previously undescribed biofilm permeability distribution, which can be used to stochastically generate permeability fields within biofilms. An increase in velocity variance for a decrease in physical heterogeneity shows that the bioclogged porous medium behaves differently than expected from studies on heterogeneity in abiotic porous media.
Keywords: biofilm cluster dynamics; fluid flow velocities; permeability heterogeneity; porous media.