Temporal scaling of the growth dependent optical properties of microalgae

The optical properties of microalgae are basic parameters for analyzing light field distribution in photobioreactors (PBRs). With the growth of microalgae cell, their optical properties will vary with growth time due to accumulation of pigment and lipid, cell division and metabolism. In this work, we report a temporal scaling behavior of the growth dependent optical properties of microalgae cell suspensions with both experimental and theoretical evidence presented. A new concept, the temporal scaling function (TSF), defined as the ratio of absorption or scattering cross-sections at growth phase to that at stationary phase, is introduced to characterize the temporal scaling behavior. The temporal evolution and temporal scaling characteristics of the absorption and scattering cross-sections of three example microalgae species, Chlorella vulgaris, Chlorella pyrenoidosa, and Chlorella protothecoides, were experimentally studied at spectral range 380-850 nm. It is shown that the TSFs of the absorption and scattering cross-sections for different microalgae species are approximately constant at different wavelength, which confirms theoretical predictions very well. With the aid of the temporal scaling relation, the optical properties at any growth time can be calculated based on those measured at stationary phase, hence opens a new way to determine the time-dependent optical properties of microalgae. The findings of this work will help the understanding of time dependent optical properties of microalgae and facilitate their applications in light field analysis in PBRs design.