Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

Committee Chair(s)

Jia Zhao


Jia Zhao


Luis Gordillo


Ronald Sims


Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). The experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory experimental findings. The predictive mathematical model development is coordinated with laboratory experiments of biofilm areal productivity associated with ammonia and inorganic phosphorus uptake by RABRs. The unified experimental and theoretical tool is used to investigate the effects of RABR rotating velocity, duty cycle, and light intensity on algae biofilm growth, areal productivity, nutrient uptake efficiency, and energy efficiency in wastewater treatment. Our framework indicates that maintaining a reasonable light intensity range results in better biomass areal productivity and nutrient uptake efficiency. Our framework also indicates that faster RABR rotation benefits biomass areal productivity. However, maximizing the nutrient uptake efficiency requires a reasonably low RABR rotating speed. Meanwhile, energy efficiency is strongly correlated with RABR rotating speed and duty cycle. Following these developments, we then extend our model to become a partial differential equation (PDE) based model that takes into consideration the spatial heterogeneity present in the reactor, by incorporating the spatial resolution of the substratum on which the algae biofilm grows within the RABR. In the proposed model extension, we conduct an extensive series of numerical simulations to better understand algae biofilm growth in an outdoor setting. Our primary focus in these simulations is to investigate the impact of various harvesting strategies and frequencies on the overall biomass productivity of the algae biofilm. Our model and numerical results provide valuable insights into optimizing algae biofilm growth and harvesting techniques in RABR systems in the context of a heterogeneous system.