Transport–reaction coupling under hydrodynamic mixing in batch systems

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Abstract
Mixing plays an important role in microalgae cultivation as it directly affects nutrient transport, light exposure, and overall reactor performance. However, the extent to which improvements in hydrodynamic mixing enhance biomass productivity remains unclear, particularly under batch conditions where nutrients are limited. This study investigates that question through numerical simulations of a coupled fluid–microalgae model, in which biomass and substrate are transported as scalar fields within an incompressible flow and interact through Monod growth kinetics. Four jet-driven flow configurations are examined alongside a no-flow reference and three complementary limiting regimes: a diffusion-limited case, an intermediate spatially uniform substrate model, and a fully mixed limit. Simulations are initialized from highly segregated conditions to isolate the role of transport processes. The central finding is that, despite marked differences in mixing efficiency across configurations, domain-averaged biomass trajectories converge to within 0.5%, with peak biomass gains confined to a narrow 2–3% range. In the absence of advection, substrate remains inaccessible to biomass, causing net biomass loss driven by endogenous respiration. When flow is introduced, substrate and biomass rapidly come into contact within O(200 s), activating growth. This convergence is explained by a transport–reaction decoupling argument: once advection overcomes the initial segregation and the system enters the reaction-limited regime (Da≪1), integrated yield becomes insensitive to the details of the flow field. Biomass production is then governed primarily by substrate inventory rather than mixing intensity, a result explained by the clear separation between hydrodynamic and biological timescales.
Funding Information
  • Conseil Régional Aquitaine (AAPR2022-2022-17538910)

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