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This paper focuses on mixing strategies to enhance the growth of microalgaein a raceway pond. The flow is assumed to be laminar and the Han modeldescribing the dynamics of the photosystems is used as a basis to determinegrowth rate as a function of light history. A device controlling the mixing isassumed, which means that the order of the cells along the different layers canbe rearranged at each new lap according to a permutation matrix P. The order ofcell depth hence the light perceived is consequently modified on a cyclicalbasis. The dynamics of the photosystems are computed over K laps of the racewaywith permutation P. It is proven that if a periodic regime is reached, it willbe periodic immediately after the first lap, which enables to reducesignificantly the computational cost when testing all the permutations. In viewof optimizing the production, a functional corresponding to the average growthrate along depth and for one lap is introduced. A suboptimal but explicitsolution is proposed and compared numerically to the optimal permutation andother strategies for different cases. Finally, the expected gains in growthrate are discussed.

Optimizing microalgal productivity in raceway ponds through a controlled mixing device