Optimization of the thickness of a photocatalytic film on the basis of the effectiveness factor

In a supported ‘‘thick’’ photocatalytic film, internal diffusion of the reactant and transport of the photons might hinder the reactivity of the material and limit the obtainable rate of removal of the organic pollutant substrate. The effectiveness factor of the photocatalytic film is the index of the extent of the limitation. Two dimensionless parameters affect the effectiveness factor: the optical thickness and the ratio, alpha, of the characteristic time of diffusion with respect to the characteristic time of reaction. The analysis demonstrates that the process is controlled by the diffusion of the substrate when the parameter alpha is high and it is controlled by the transport of the photons when the optical thickness is high. It is also shown that different results are obtained if the film is illuminated from the fluid–film interface (PF) or from the glass–film interface (CF). In PF the observed rate of degradation increases with the film thickness, but no further enhancement of the rate of degradation is obtained when the thickness exceeds the depth where a substantial depletion of the photons or of the substrate takes place. In CF the rate of degradation reaches a maximum at an optimal thickness. Finally, a new simple procedure to estimate the parameters and then to predict the best thickness is illustrated.