In this talk, we will present a spatial model describing the growth of a photosynthetic microalgae biofilm. In this model we consider photosynthesis, extracellular matrix excretion, and mortality. These mechanisms are described precisely using kinetic laws that take into account some saturation effects which limit the reaction rates and involve different components that we treat individually. In particular, to obtain a more detailed description of the microalgae growth, we consider separately the lipids they contain and the functional part of microalgae (proteins, RNA, etc ...), the latter playing a leading role in photosynthesis. We also consider components dissolved in liquid phase such as CO2. The model is based on mixture theory and the behaviour of each component is described on the one hand by mass conservation, which takes into account biological features of the system, and on the other hand by conservation of momentum, which describes the physical properties of the components. Some numerical simulations will be presented and show that the model is able to estimate accurately the biofilm productivity. This work has been done in collaboration with O. Bernard and M. Ribot.