Decoupling mixing from mass transfer through fluid dynamics to shape microalgal blooms and carbon reservoir stability

Fluid dynamics shapes microalgal growth and carbon sequestration, yet the underlying mechanisms and quantitative metrics remain poorly understood. By experimentally decoupling mixing from mass transfer, we developed a cross-scale mathematical model to elucidate and quantify atmospheric carbon assimilation by microalgae. This approach revealed a previously unrecognized behavioral pathway: the bubble-microalgae anchored carbon pump. In this mechanism, microalgae construct an extracellular liquid membrane that connects with the gas membrane of bubbles to enhance carbon uptake while maintaining homeostatic inorganic carbon partitioning. Without this pathway, maximum predicted assimilation reached only 10.0%-38.9% of observations. Fluid dynamics regulates this process through two independent factors: mixing and mass transfer. Mixing controls substance migration from macroscopic reservoirs to microscale carbon pools and modulates photochemical electron transport, thereby governing population expansion. Mass transfer dominates molecular exchange at micro-membrane interfaces, determining individual biomass. Specific mixing force (SF_mix), introduced as a unified metric, quantifies convective and diffusive carbon fractions and membrane interaction times. It exhibits an exponentially time-sensitive transition (R = 0.914, p < 0.05). Under equilibrium diffusion (SF_mix<0.0051 m/s²), carbon transfer from gas to liquid membranes is governed by mass transfer; during non-equilibrium relaxation (SF_mix=0.0051-0.1769 m/s²), mixing and mass transfer act synergistically. Notably, hydrodynamic enhancement, long considered beneficial for carbon capture, simultaneously weakens biological carbon-reservoir stability by accelerating dissolved organic carbon release. The model further guides reactor modification, where minor geometric changes can produce substantial shifts in hydrodynamics (SF_mix=0.003-0.067 m/s²) and carbon assimilation (0.237-2.099 g/L). This study provides new mechanistic insights into the interactions among fluid dynamics, microalgal behavior, and carbon dynamics.