Abstract A simple interaction by exchange with the mean (IEM) mixing model is implemented to describe the glucose concentration segregations in industrial and laboratory scale bioreactors. This approach is coupled with a population balance model (PBM) for the growth rate adaptation and a metabolic model dependent on the individuals state, both from the literature [1] . The model formulation is validated against different published experiments and it is shown that the IEM model reduces the computational costs when just the segregation of few species is of interest. A model for the maintenance costs of Escherichia coli subject to glucose concentration fluctuation is also presented and implemented in the context of the IEM mixing model. An Eulerian formulation of the effects of the substrate fluctuations on the maintenance rate is proposed and tied to a more intuitive Lagrangian vision. The study of these metabolic changes due to substrate heterogeneities helps the understanding of the relationships between hydrodynamics and cells metabolism and it improves the agreement between numerical and experimental data.

中文翻译：

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用概率方法模拟底物波动对生物反应器维持率的影响

摘要 通过交换与平均 (IEM) 混合模型的简单交互被实施来描述工业和实验室规模生物反应器中的葡萄糖浓度分离。这种方法与用于增长率适应的人口平衡模型 (PBM) 和依赖于个体状态的代谢模型相结合，均来自文献 [1]。该模型公式针对不同的已发表实验进行了验证，结果表明，当仅关注少数物种的分离时，IEM 模型降低了计算成本。在 IEM 混合模型的上下文中，还提出并实施了受葡萄糖浓度波动影响的大肠杆菌维持成本模型。提出了底物波动对维持率影响的欧拉公式，并将其与更直观的拉格朗日视觉联系起来。研究由于底物异质性引起的这些代谢变化有助于理解流体动力学和细胞代谢之间的关系，并提高数值和实验数据之间的一致性。