# Growth-dependent radiative properties of *Chlorella vulgaris* and its influence on prediction of light fluence rate in photobioreactor

## Abstract

The radiative properties of microalgae (the absorption cross-section, scattering cross-section, and scattering phase function) are essential for analyzing the light transfer in photobioreactors (PBRs). Due to the growth of microalgal cells, their radiative properties will vary with time. However, the growth-dependent radiative properties of microalgal cells have been rarely considered in the literature in analyzing light fluence rate in the PBRs and its influence on the accuracy of light fluence rate prediction is not well evaluated. In this work, the growth-dependent radiative properties of *Chlorella vulgaris* are studied via a semi-analytical approach. The growth-dependent cell size distribution of *C. vulgaris* is taken from experimental data in the literature. The temporal evolution of the scattering and absorption cross-sections and scattering phase function of *C. vulgaris* is determined based on the Lorenz-Mie theory combined with the growth-dependent cell size distributions and pigment content. The relative deviation of the radiative properties of microalgae at different growth phase with that at stationary phase microalgae is investigated. The deviation of predicted light fluence rate in a flat-plate PBR using the growth-dependent radiative properties and the radiative properties at stationary phase is evaluated. The results show that the relative deviation of absorption, scattering, and extinction cross-sections is significant, especially at exponential growth phase (over 18%). The relative deviation of the predicted light fluence rate is over 40% at exponential growth phase. As a result, the growth-dependent radiative properties have to be applied in order to accurately predict the light fluence rate in PBRs during different growth phases. A simple model is presented and demonstrated good performance to predict the growth-dependent radiative properties of *C. vulgaris* over the whole growth phase. The presented analysis will facilitate the design and optimization of the optical configuration of PBRs for microalgal cultivation.

## Keywords

Microalgae*Chlorella vulgaris*Growth-dependent radiative properties Photobioreactors Growth model

## Notes

### Funding information

The supports by the National Nature Science Foundation of China (Nos. 51276051, 51336002) are greatly acknowledged.

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