Russo, Fabiana (2022) Free boundary approach to model granular biofilms: application to wastewater treatment. [Tesi di dottorato]

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The present dissertation relates to the mathematical modelling of innovative biotechnologies for wastewater treatment. Novel mathematical models are derived and presented, with the aim of investigating new treatment processes and examining crucial aspects of such biological processes never or not exhaustively explored by mathematical models present in literature. In the first study, the mathematical model simulates the metals leaching from electronic waste induced by dark fermentation effluents. It consists of a system of non-linear ordinary differential equations (ODEs), accounting for the main biological, chemical, and physical processes occurring during the fermentation of soluble biodegradable substrates and the dissolution process of metals in an anaerobic environment. The second part of the thesis deals with biofilm modelling and focuses on the genesis and formation of granular biofilms, with a special interest in anaerobic granules, anammox granules and oxygenic photogranules. The models presented here are formulated as spherical free boundary problems under the assumption of radial symmetry, which describe the evolution of granular biofilms. Such biofilm models are conceived in the framework of continuum mathematical modelling of biofilm growth, and consists of systems of partial differential equations (PDEs): non-linear hyperbolic PDEs model the advective transport and growth of sessile biomasses which constitute the biofilm solid matrix; quasi-linear parabolic PDEs govern the diffusive transport and conversion of soluble substrates; and quasi-linear parabolic PDEs describe the invasion phenomena and conversion of planktonic cells suspended in the surrounding environment. The free boundary evolution is governed by an ODE, which accounts for the growth of sessile biomass as well as exchange fluxes with the bulk liquid. In addition, a system of ODEs derived from mass balance considerations is accounted to describe the dynamics of dissolved substrates and suspended biomasses within the bulk liquid. In the second study, a multiscale model on the genesis and growth of granular biofilms within a completely mixed continuous reactor is presented. The mathematical model is derived for a generic granular-based bioreactor and applied to the anaerobic granulation process to test the model behaviour and study the formation, evolution and ecology of anaerobic granules. In the third study, the qualitative analysis of the initial formation of a multispecies granular biofilm, through the modelling of the initial attachment by pioneer microbial cells, is addressed. A theorem of existence and uniqueness of the solutions, based on the fixed-point theorem, is presented. In the fourth study, the mathematical model derived in the second study is applied to the partial nitritation/anammox process occurring in a granular-based system. It mainly addresses the invasion phenomena influence on the de novo granulation process of anammox granules and on the microbial stratification. The multiscale approach of the model allows to simulate both the evolution of anammox granules and dynamics of the bioreactor where granules develop. Finally, the fifth model is aimed at describing for the first time the metals biosorption process on oxygenic photogranules, recognized as a promising alternative technology for the contextual removal of organic and inorganic compounds from wastewater. Such model describes the genesis and growth processes of oxygenic photogranules within a sequencing batch reactor (SBR) and metals adsorption on their solid matrix. The main factors influencing both granulation and adsorption processes, the symbiotic and competitive microbial mechanisms driving the treatment process, and the key role that phototrophs and EPS play on metals adsorption are included in the model. All models are integrated numerically through the development of original code in MatLab platform. The main numerical methods used are the method of characteristics and method of lines. Furthermore, numerical simulations are carried out to analyze aspects and factors influencing the biological processes investigated in the present dissertation.

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