Influence of biomass layer thickness in a photobioreactor on the growth rate of Tetraselmis viridis

Most models describing the effect of light on the growth rate of optically dense microalgal cultures rely on the classical Beer–Lambert–Bouguer law, and the mismatch between theory and experiment is typically compensated by introducing empirical correction factors. Although these factors reflect the increase in light scattering as culture density rises, they offer no biological interpretability. As an alternative, an analytical model is proposed that describes the spatial distribution of photon flux within a microalgal culture. Rather than invoking the physics of absorption and scattering in colloidal media, the model is grounded in the experimentally observed linear growth of microalgae: photon flux density decreases hyperbolically with increasing biomass concentration and exponentially with increasing optical path length. To validate this approach, Tetraselmis viridis was cultivated in batch mode in photobioreactors with various biomass layer thicknesses under identical surface irradiance. Under all experimental conditions, the cultures exhibited an extended linear growth phase characteristic of light limitation. Relationships were obtained between transmittance, optical path length, and biomass concentration. The experimental data were fitted using both the proposed analytical model and the Beer–Lambert–Bouguer law; each provided adequate accuracy. A quantitative relationship was derived linking the productivity of Tetraselmis viridis in the linear growth regime to the biomass layer thickness. These expressions apply only under light-limited conditions. The modeling results indicate that the proposed theoretical framework is appropriate and has both scientific and practical value, particularly for predicting Tetraselmis yield in industrial-scale cultivation.

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