Rotating algal biofilm reactors (RABRs) are innovative systems designed to cultivate microalgae biofilms efficiently. In this paper, we have developed a novel mathematical model to accurately capture the growth dynamics of algae biofilms within RABR. By considering the spatial heterogeneity of the RABR, we introduce a PDE-based model that addresses the spatial variations across the substratum, enabling a more accurate simulation of biofilm growth in RABRs. The photosynthesis process is modeled through reactive kinetics, driving the growth of the algae biofilm. To analyze the system's behavior, we employ finite difference numerical methods to solve the complex PDE model. We then conduct extensive numerical simulations to understand algae biofilm growth in the RABR environment under various operational factors and environmental conditions. One primary focus in these simulations is to investigate the impact of various harvesting strategies, harvesting frequencies, light intensity, and light exposure on the overall biomass productivity of the algae biofilm. The numerical results provide valuable insights into optimizing algae biofilm growth and designing harvesting techniques in RABR systems. Our proposed novel mathematical model provides an effective platform for the theoretical investigation and design of RABRs for wastewater treatment.

中文翻译：

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用于废水处理的异质旋转藻类生物膜反应器（RABR）中微藻生物膜生长的计算模型

旋转藻类生物膜反应器 (RABR) 是一种创新系统，旨在有效培养微藻生物膜。在本文中，我们开发了一种新颖的数学模型来准确捕获 RABR 内藻类生物膜的生长动态。通过考虑 RABR 的空间异质性，我们引入了一种基于偏微分方程的模型，该模型可以解决整个基质的空间变化，从而能够更准确地模拟 RABR 中的生物膜生长。光合作用过程通过反应动力学进行建模，驱动藻类生物膜的生长。为了分析系统的行为，我们采用有限差分数值方法来求解复杂的 PDE 模型。然后，我们进行广泛的数值模拟，以了解在各种操作因素和环境条件下 RABR 环境中藻类生物膜的生长情况。这些模拟的一个主要重点是研究各种收获策略、收获频率、光强度和光照对藻类生物膜整体生物量生产力的影响。数值结果为优化藻类生物膜生长和设计 RABR 系统中的收获技术提供了宝贵的见解。我们提出的新颖数学模型为废水处理 RABR 的理论研究和设计提供了有效的平台。