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Mixotrophic cultivation holds great promise to significantly enhance the productivities of biomass and valuable metabolites from microalgae. In this study, a new kinetic model is developed, explicitly describing the effect of the most influential environmental factors on both biomass growth and the production of the high-value product lutein. This extensive study of multinutrient kinetics for Tetradesmus obliquus in a mixotrophic regime covers various nutritional conditions. Crucial nutrients governing the model include nitrate, phosphate, and glucose. Using seven state variables and 13 unknown parameters, the model's accuracy was ensured through a well-designed two-factor, four-level experimental setup, providing ample data for reliable calibration and validation. Results accurately predict dynamic concentration profiles for all validation experiments, revealing broad applicability. Optimizing nitrogen availability led to significant increases in biomass (up to fourfold) and lutein production (up to 12-fold), with observed maximum biomass concentration of 6.80 g L−1 and lutein reaching 25.58 mg L−1. Noticeably, the model exhibits a maximum specific growth rate of 4.03 day−1, surpassing reported values for photoautotrophic and heterotrophic conditions, suggesting synergistic effects. Valuable guidance is provided for applying the method to various microalgal species and results are large-scale production-ready. Future work will exploit these results to develop real-time photobioreactor operation strategies. -- Keywords : Biomass production ; Lutein production ; Microalgae ; Mixotrophic conditions ; Multinutrient kinetic model.

Publisher's description: The use of geometric methods in classical mechanics has proven fruitful, with wide applications in physics and engineering. In this book, Professor Marsden concentrates on these geometric aspects, especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, including the double spherical pendulum and the classical rotating water molecule.