Modeling of Symbiotic Bacterial Biofilm Growth with an Example of the Streptococcus-Veillonella sp. System.

We present a multi-dimensional continuum mathematical model for modeling the growth of a symbiotic biofilm system. We take a dual-species namely, the Streptococcus-Veillonella sp. biofilm system as an example for numerical investigations. The presented model describes both the cooperation and competition between these species of bacteria. The coupled partial differential equations are solved by using an integrative finite element numerical strategy. Numerical examples are carried out for studying the evolution and distribution of the bio-components. The results demonstrate that the presented model is capable of describing the symbiotic behavior of the biofilm system. However, homogenized numerical solutions are observed locally. To study the homogenization behavior of the model, numerical investigations regarding on how random initial biomass distribution influences the homogenization process are carried out. We found that a smaller correlation length of the initial biomass distribution leads to faster homogenization of the solution globally, however, shows more fluctuated biomass profiles along the biofilm thickness direction. More realistic scenarios with bacteria in patches are also investigated numerically in this study.

Biofilm formation by the oral pioneer colonizer Streptococcus gordonii: an experimental and numerical study.

For decades, extensive research efforts have been conducted to improve the functionality and stability of implants. Especially in dentistry, implant treatment has become a standard medical practice. The treatment restores full dental functionality, helping patients to maintain high quality of life. However, about 10% of the patients suffer from early and late device failure due to peri-implantitis, an inflammatory disease of the tissues surrounding the implant. Peri-implantitis is caused by progressive microbial colonization of the device surface and the formation of microbial communities, so-called biofilms. This infection can ultimately lead to implant failure. The causative agents for the inflammatory disease, periodontal pathogenic biofilms, have already been extensively studied, but are still not completely understood. As numerical simulations will have the potential to predict oral biofilm formation precisely in the future, for the first time, this study aimed to analyze Streptococcus gordonii biofilms by combining experimental studies and numerical simulation. The study demonstrated that numerical simulation was able to precisely model the influence of different nutrient concentration and spatial distribution of active and inactive biomass of the biofilm in comparison with the experimental data. This model may provide a less time-consuming method for the future investigation of any bacterial biofilm.

Noise-driven interfaces and their macroscopic representation.

We study the macroscopic representation of noise-driven interfaces in stochastic interface growth models in (1+1) dimensions. The interface is characterized macroscopically by saturation, which represents the fluctuating sharp interface by a smoothly varying phase field with values between 0 and 1. We determine the one-point interface height statistics for the Edwards-Wilkinson (EW) and Kadar-Paris-Zhang (KPZ) models in order to determine explicit deterministic equations for the phase saturation for each of them. While we obtain exact results for the EW model, we develop a Gaussian closure approximation for the KPZ model. We identify an interface compression term, which is related to mass transfer perpendicular to the growth direction, and a diffusion term that tends to increase the interface width. The interface compression rate depends on the mesoscopic mass transfer process along the interface and in this sense provides a relation between meso- and macroscopic interface dynamics. These results shed light on the relation between mesoscale and macroscale interface models, and provide a systematic framework for the upscaling of stochastic interface dynamics.

Estimation of effective parameters for a two-phase flow problem in non-Gaussian heterogeneous porous media.

In this paper we discuss estimates of effective parameters for an upscaled model for buoyant counter flow of DNAPL and water in a closed box filled with heterogeneous porous material. The upscaling procedure is based on the assumption that the flow is dominated by capillary forces on the small scale and that the fluids are segregated. The upscaled model has the same form as the usual two-phase flow model with an effective capillary pressure function and an effective mobility function Λ. Effective parameters are then estimated in two different ways. Stochastic theory can be applied to calculate the effective parameters to first order in the parameter fluctuations. This approach does not take into account that different parameter ranges of the heterogeneous field may be connected or isolated, yielding very different macroscopic residual saturations. Therefore, the second estimate of effective parameters takes connectivity of parameter ranges into account. In this case, the univariate parameter distribution of the heterogeneous field and the values that mark connected materials are the only information about heterogeneity that is used. Effective parameters are then estimated using mean field theory (the Maxwell approach). The upscaled model and the estimation of effective parameters are applied to a numerical test case. Buoyant counter flow in heterogeneous parameter fields with different structures is simulated numerically and compared to the solutions of the quasi-1d upscaled model with differently estimated parameters. It is demonstrated that connectivity of the different parameter ranges is an important information that determines typical time scales for the flow process and the macroscopic residual saturation. Even simple estimates of effective parameters based on little information may capture the typical time scales, provided that information about connected parameter ranges is taken into account.