Moving boundary problem for the detachment in multispecies biofilms

The work presents the qualitative analysis of the free boundary value problem related to the detachment process in multispecies biofilms. In the framework of continuum approach to one-dimensional mathematical modelling of multispecies biofilm growth, we consider the system of nonlinear hyperbolic partial differential equations governing the microbial species growth, the differential equation for the biomass velocity, the differential equation that governs the free boundary evolution and also accounts for detachment, and the elliptic system for substrate dynamics. The characteristics are used to convert the original moving boundary equation into a suitable differential equation useful to solve the mathematical problem. We also provide another form of the same equation that could be used in numerical applications. Several properties of the solutions to the free boundary problem are shown, such as positiveness of the functions that describe the microbial concentrations and estimates on the characteristic functions. Uniqueness and existence of solutions are proved by introducing a suitable system of Volterra integral equations and using the fixed point theorem

Towards a reduction of greenhouse gas emission from wastewater treatment plants: a new plant wide experimental and modelling approach

The increasing interest in greenhouse gas (GHG) emissions from wastewater treatment plants (WWTPs) has led to the development of new tools for their design and management. Studies about gas emissions show that the sewer collection and the wastewater treatment plant are anthropogenic GHG potential sources, so they contribute to the climate change and air pollution. A wastewater treatment plant receives wastewater from sewers and, while produces treated water for discharge into surface water, emits the three major greenhouse gases, CO2, CH4, and N2O, during the treatment processes, and additional amounts of CO2 and CH4 from the energy demands (Bani Shahabadi et al., 2009). Indeed, energy consumption can be considered as an indirect source of GHGs. Greenhouse-gas emissions are generated by water-line and sludge- line processes and by the on-site combustion of biogas and fossil fuels for energy generation. GHGs may also be produced during sludge disposal or reuse (transportation and degradation of remaining biosolids off-site), off-site energy production and off-site chemicals production. In recent years, increasing attention is given to the assessment of N2O emissions from WWTPs. N2O is a powerful greenhouse gas that is almost 300 times stronger than CO2. Nevertheless, the source and magnitude of N2O are relatively unknown and the knowledge is still incomplete. This paper presents the first results of an ongoing research project aiming at setting-up an innovative mathematical model platform (Decision Support System—DSS) for the design and management of WWTPs. The project is constituted by four research units (UOs) and its final goal is to minimize, by means of this platform, the environmental impact of WWTPs through their optimization in terms of energy consumptions and pollutants, sludge and GHG emissions

Continuum and discrete approach in modeling biofilm development and structure: a review

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions