The Theoretical Analyses And Simulations On Fractal Structure Of Biofilms

Microbial biofilm is a kind of universal biological community in the complicated environment, which can be applied comprehensively in the environmental science, life science and geosciences field etc. Biofilms form a very complex biological community as an open, multi-level, multi-scale, nonlinear system far from equilibrium in which many species of microorganisms exist and a variety of complex physical, chemical and biological reactions occur. Fundamental theoretical depiction is still lacked on biofilm wastewater treatment systems up to today.Nonlinear dynamic features of biofilms growth play important roles in the operation of bioreactor. A mechanistic nonlinear reaction diffusion model for biofilms formation in plug flow reactor (PFR), taking account of the transformation between planktonic bacteria and adherent bacteria and some parametric effects of biofilms formation and stabilization, was proposed. By analytical investigations on the washout equilibrium and the existence of a nontrivial steady state, the physics for the start-up (i.e. biofilms formation) in PFR was revealed. Some suggestions on successful startup and operation of PFR in wastewater treatment engineering were provided.The process of biofilms formation is the typical example of fractal structure formation in the physics. A modified fractal growth model based on diffusion-limited aggregation (DLA) with spatial restriction of a random walk in 1st quadrant of the coordinate plane is considered. By utilizing it, fractal structure of biofilms in one colonization site is simulated. By theoretical and numerical analyses, the factors influencing fractal structure of biofilms, such as the fractal dimension, growth efficiency, finishing maximum radius, maximum aspect ratio etc, are discussed. Qualitative investigations are carried out and suggestions on industrial applications are then proposed.Biofilms essentially is a complicated, non-equilibrium thermodynamics system, whose formation is a self-organizing process of plentiful microbial cells. Biofilms microscopic dynamics may be described by maximum flux principle (MFP): an open system far from equilibrium always seeks an optimization process so that the obtained flux from outside is maximal under given prices or constrains. By theoretical analyses on fractal structure of biofilms, the important nonlinear characteristics in biofilms formation, such as cooperation, competition, the transformation of phase, replication, inheritance and hierarchical structure etc, were discussed. On the basis of MFP, the expression of fractal dimension was derived from the new model of biofilm fractal growth. Parameterξthat denotes fractal structure of biofilms was gained via training in the Self-Organizing Feature Map(SOM), and the fractal dimension of biofilm was then figured out byξ. After further analyses on microscopic dynamics of biofilms structure, the applications on both science and engineering were proposed.