are you asking about the rate? It is generally assumed to be the same as diffusion since that should be the slow step when using light as an energy source.
Before dye degradation experiment, the mixture of photocatalyst and dye solution should keep in dark to reach adsorption-desorption equilibrium. Here i dont know what is adsorption-desorption equilibrium and i dont know whether adsorption-desorption equilibrium will affect the efficiency of photocatalyst.
It is probably a safe bet to assume the equilibrium will be reach after a couple hours at the very most. It will be system dependent.
The equilibrium process itself is just the reactants associated with the photocatalyst (absorption) and then diffusing away (desorption) this happens at a rate that is specific to the order of the system. In general for catalysis you want to push equilibrium towards absorption as the catalytic process will not occur in the desorbed state. you can do this by increasing the concentration of the reactant.
but again equilibrium should be reached shortly after the components are mixed together, but you may want to wait an hour or so before inducing the reaction with light.
Alex even I found a peculiar sort of absorbance versus time (hr) when performing arsenite adsorption on TiO2 after 24 hr stirring. The graph showed zigzag behaviour, it was embarassing observation. Till today I couldn't get any sort of explanation of those graphs.
Before irradiation, it is essential for the target pollutants to get adsorbed on the selected photocatalyst by stirring in dark for 30 to 60 minutes. More adsorption on the catalyst reaction site leads to enhanced degradation.