  This paper focuses on mixing strategies to enhance the growth of microalgae
in a raceway pond. The flow is assumed to be laminar and the Han model
describing the dynamics of the photosystems is used as a basis to determine
growth rate as a function of light history. A device controlling the mixing is
assumed, which means that the order of the cells along the different layers can
be rearranged at each new lap according to a permutation matrix P. The order of
cell depth hence the light perceived is consequently modified on a cyclical
basis. The dynamics of the photosystems are computed over K laps of the raceway
with permutation P. It is proven that if a periodic regime is reached, it will
be periodic immediately after the first lap, which enables to reduce
significantly the computational cost when testing all the permutations. In view
of optimizing the production, a functional corresponding to the average growth
rate along depth and for one lap is introduced. A suboptimal but explicit
solution is proposed and compared numerically to the optimal permutation and
other strategies for different cases. Finally, the expected gains in growth
rate are discussed.
