Abstract: Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined.

Abstract: Photocatalysis has been labeled for decades as a promising technique for air purification. The principle seems straightforward and requires a photocatalyst that is immobilized on a substrate, and one or more UV sources to activate the photocatalyst. No waste products are produced, the reactions occur in mild conditions and the supplies are relatively cheap. Yet it seems that the commercialization of photocatalytic systems does not break through on the global market. The aim of this thesis is to identify and tackle the bottlenecks that impede commercialization from an application-oriented approach. The problem of indoor air pollution is enhanced by the fact that people spend more and more time indoors and that ventilation is kept to a minimum as an energy-saving measure. This inevitably leads to an accumulation of volatile organic compounds (VOCs) that are emitted by e.g. building materials, paint and furniture. Human exposure to VOCs is directly related to the sick building syndrome leading to complaints such as headache, fatigue, dizziness and lack of concentration. In addition, exposure to VOCs is related to serious long-term health effects such as cancer or respiratory diseases. Therefore, significant research efforts are focused on advanced indoor air purification methods. Integration or retrofitting of a photocatalytic (PCO) air purifying unit into heating, ventilation and air conditioning (HVAC) equipment has been chosen as an interesting approach. As a starting point of this thesis, the operational conditions of a ventilation system were mapped. These systems are characterized by high flow rates and the necessity of minimal pressure losses. Pressure losses increase the energy demand and can lead to failure of the ventilation fan and thereby undermine the proper functioning of the ventilation system. A suitable substrate must allow the contaminated air to pass through with a minimal pressure drop, allow sufficient contact time between VOC and photocatalyst, have a large surface area available for coating with excellent adhesion, and be transparent to UV light. Therefore, the permeability and the available exposed surface were selected as main selection criteria. After a thorough quantitative analysis of potential substrates, borosilicate glass tubes were selected. Glass tubes can easily be stacked to constitute a transparent monolithic multi-tube reactor, with their length parallel to the air flow in order to minimize the pressure drop. Moreover, borosilicate glass is relatively inexpensive and has excellent UV-A light transmitting properties. Based on a literature study, a sol-gel coating procedure was selected that is extremely suitable for coating glass substrates. The next step was to optimize the amount of P25 (commercial titanium dioxide) in the photocatalytic sol-gel coating for its application. More P25 in the sol-gel coating results in a higher adsorption capacity and consequently a higher photocatalytic activity, but greatly reduces the transparency of the coating. After an in-depth study, the concentration of 10 g L-1 P25 was selected as the most feasible for multi-tube reactors. Since the operation of photocatalytic reactors is based on a complex interaction of physical and chemical processes, mathematical models were developed, supported by experimental data, that include all these phenomena as a tool for reactor design and optimization. By making use of such models, time-consuming and expensive experimental research can be minimized. However, the experimental validation of models is of utmost importance to prove its reliability and accuracy. Intrinsic kinetic parameters provide the fundamentals for these models as they describe the photocatalytic reaction rate, independent of fluid dynamics, reactor geometry and radiation field. In this work they were estimated by means of a Computational Fluid Dynamics (CFD) study, based on FTIR (Fourier-transform infrared spectroscopy) experiments with a lab scale multi-tube reactor. The kinetic parameters were validated by an alternative analytic approach, emphasizing the accuracy and reliability of the simulations. Finally, the aforementioned CFD approach, based on the simultaneously modelling of airflow, mass transfer, UV light irradiation and photocatalytic reactions, was used to obtain insights for the light source configuration in upscaled multi-tube reactors. After taking all these insights and some practical implications into account, a final upscaled multi-tube reactor design was proposed and converted into a first built prototype. Subsequently, it was evaluated according the CEN-EN-16486-1 standard for VOC removal by the external scientific research center ‘CERTECH’. The scientific results, regarding the mineralization of the VOCs and photocatalytic efficiency of the reactor, demonstrated the feasibility for indoor air purification by the upscaled multi-tube reactor and the possible implementation in ventilation systems.