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Dispersion of microorganisms is a key issue in bio-physics and has many applications in the fields of algae cultivation, biomass energy, and wetland ecology. However, there has been limited exploration of the effects of settling behavior and initial release conditions on the transient dispersion of gyrotactic microorganisms. This paper explores the transient dispersion of settling gyrotactic microorganisms in an open channel flow. The moment equations derived from the Smoluchowski equation are solved by the biorthogonal expansion method, and the results are compared with random walk simulations, showing good agreement. The time variations of concentration distribution, drift velocity, and dispersivity of settling gyrotactic microorganism suspension are explored in detail under typical initial release conditions. As illustrated and characterized, settlement weakens the gravitactic focusing of microorganisms near the free surface, leads to accumulation at the bottom, and increases the dispersivity; from a line source release, the relaxation time is shortest, and the microorganisms scatter fastest in the longitudinal direction, while the point source at the water surface leads to the most concentrated longitudinal distribution and the highest drift velocity; furthermore, the initial release condition assumes an important role in shaping the concentration distribution and drift velocity.
Zeng et al. (Sun,) studied this question.