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VAN DOORSLAER , PHILIPPE M. HEYNDERICKX , JO 1KERMIT, Department of Applied Mathematics, Biometrics and Process Control, Faculty of Bioscience Engineering, Ghent University, Coupure links 653, 2EnVOC, Department of Sustainable Organic Chemistry and Technology, Faculty of Bioscience Engineering, Ghent University, Coupure links 653, B-9000 Ghent, Cellular automata (CA) appeared for the first time in literature in the first half of the 20th century and are mathematical models in which thetime, spatial and state domain are discrete [1, 5, 7]. Although CA havebeen successfully employed in the study of several (a)biological processes,overcoming some of the issues inherent to the more classical modeling meth-ods as well as providing researchers with novel insights in these processes,papers on CA-based models within the field of chemical engineering are stillscarce. To this day, partial differential equation based models dominatethe field of chemical engineering, although they have difficulties handlingthe complexity of many systems encountered in this field. Therefore, inthis work, we opted to elaborate a CA-based model to study the photocat-alytic degradation of fluoroquinolones (FQ), enabling researchers to studythis complex, stochastic system that is difficult to describe with classicalmodeling methods even when the governing equations are simplified [4].
∗ Submitted to Summer Solstice 2011: Discrete Models of Complex Systems, satellite workshop at Unconventional Computation 2011, June 6-10 2011, Turku 2. Modeling photolytic degradation using cellular automata Fluoroquinolones are a family of synthetic broad-spectrum, antibacterial com- pounds that are not completely metabolized in the body and are con-sequently par- tially (up to 50%) excreted in their pharmaceutically activeform. Due to their lim- ited biodegradability, widespread use and incom-plete removal in wastewater treat- ment plants, they are released in theenvironment and cause adverse effects on (aquatic) organisms [3, 6]. Asthe environmental laws and regulations are becom- ing more stringent, re-search is directed towards novel methods to obtain complete mineralizationof organic poluants, such as FQ, with TiO2-assisted photocatalysis beingone of the most promising methods. When irradiated with UV-light and inthe presence of O2, TiO2 catalysts generate highly reactive radical specieswhich can converse organic compounds to CO2, H2O and mineral acids,rendering them harm- less. Although photocatalysis is gaining importance,the surface structure of TiO2 is not completely elucidated and there is noconsensus on the complex mechanism behind photocatalysis, which hampersthe development of a model. Therefore, we designed a stochastic CA-basedmodel to provide reseachers with a tool to study this system and gain in-sight into the underlying mechanism, by determining the model parametersthrough inverse problem solving, i.e. deducing a (set of) CA rule(s) startingfrom the observed data [5].
In this work, we consider a stochastic CA-based model that makes use of a square tessellation, aMoore neighborhood function and a set of states S ={H2O,TiO2, FQ}. The transition function consists of two parts, being diffu-sion and reaction respec- tively, whereby we introduce stochasticity into thereaction part through parameters that express the probability of adsorptionpads and desorption pdes of FQ on the catalyst as well as parameters thatcapture degradation of FQ through UV-light pfot and catalysis pcat. Specialattention is given to the relation between the physical values characterizingthe process to be simulated and the parameters of its CA-based model, forwhich no systematic approach exists thus far. We focused for this work onhow to initialize the tessellation, the choice of the relationship between realtime and a discrete time step of the model, the diffusion coefficient and thechoice of the appropriate update mechanism [2, 7]. Further, data obtainedin the laboratory are used to parameterize the model through inverse prob-lem solving [5, 6]. In a first series of simulations, the influence of photolysis,the degradation of FQ solely through UV-light, is investigated, resultingin a value for pfot. In a second series of simulations, the behavior of theCA-based model when photolysis as well as photocatalysis are taken intoaccount, is studied, also making use of experimental data for parameteri-zation. We focused on the workability of the suggested CA-based model to create an intuitive and practical modeling tool for performing calculationswith real data instead of developing a CA-based model that merely givesqualitative results, as was often done in the past in the field of chemicalengineering [5].
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