The Photoinhibistat: Operating Microalgae Culture under Photoinhibition for Strain Selection**This work was supported by the French ANR Facteur 4 (ANR-12-BIME-0004) and Purple Sun (ANR-13-BIME-0004) projects

Theory of turbid microalgae cultures

Microalgae can be cultivated in closed or open photobioreactors (PBR). In these systems, light rapidly decreases as it passes through the culture due to the turbidity of the medium. Thus, microalgae experiment different light intensities depending on their position in the medium. In this paper, we study theoretically how the growth rate of microalgae is affected by different factors; incident light intensity, form of the PBR, microalgae population density, turbidity of non-microalgae components, and light path-length of the reactor. We show that for different types of PBR the average growth rate is completely determined by the incident light intensity and the optical depth. In the case of vertical cylindrical PBRs illuminated from above (e.g. race-way or panel-type reactors), we described (and we prove under general assumptions) in details the dependence of the AGR on the aforementioned factors. Finally, we discuss some implications of our analysis; the occurrence of the Allee effect, if light ostensibly limits or inhibits the growth rate in outdoor cultures, and how the geometry of the PBR affects microalgae growth rate and productivity.