Theoretical Analysis of Culture Growth in Flat-Plate Bioreactors:
The Essential Role of Timescales
Y. Zarmi, G. Bel, and C. Aflalo
Qualitative characteristics of biomass production in ultrahigh density algal bioreactors with a small optical path (specifically, thin flat-plate reactors) are analyzed and explained in terms of models, which combine the random motion of cells across the optical path with simple models for the photosynthetic process. Characteristics of different models at extreme densities are compared with existing data. An analogy between flashing light illumination and the light regime experienced by the randomly moving cells provides basic insight into the important role of timescales in reactor performance. The emergence of an optimal culture density (OCD), at which the volumetric and areal production rates are maximal, is understood in simple terms. While higher density implies an increase in the number of photosynthesizing cells, it leads to narrowing of the illuminated (photic) zone, hence to a decrease in the time spent by these cells in the photic zone. When the time spent by cells in the photic zone is longer than the time needed to collect the photons required for the photosynthetic process, the addition of cells increases the volumetric production rate. When the time spent by cells in the illuminated zone falls below the time needed for the collection of photons, the volumetric production rate is decreased. The combined effects of changes in density are the cause of the emergence of an OCD. At the OCD, the time spent by cells in the thin illuminated layer of the culture and the time needed for the collection of the photons required for the photosynthetic process coincide.