可渗透生物膜的孔隙尺度模型：数值模拟与实验
A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments
摘要：
在本文中，我们推导出一个孔隙尺度模型的可渗透生物膜形成的二维孔隙。孔隙分为两相：水和生物膜。假设生物膜由四种组分组成：水、胞外聚合物（EPS）、活性细菌和死细菌。水的流动由斯托克斯方程模拟，而营养物质的运输涉及扩散-对流方程。在水/生物膜界面处，考虑了由于水通量引起的营养物运输和剪切力。在生物膜中，考虑了水流的Brinkman方程、由于扩散和对流引起的营养物质的运输、由于细菌的繁殖/死亡引起的生物膜组分的位移以及EPS的产生。采用分离有限元法求解数学方程组。根据实验确定的参数进行数值模拟。应力系数与实验数据进行了拟合。为了确定关键模型参数，进行了敏感性分析。输入参数的Sobol灵敏度指数基于标称参数值的$\pm 10 \%$的均匀扰动来计算。敏感性分析证实，任何参数的变异性或不确定性都不应被忽略。
英文摘要：
In this paper we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided in two phases: water and biofilm. The biofilm is assumed to consist of four components: water, extracellular polymeric substances (EPS), active bacteria, and dead bacteria. The flow of water is modeled by the Stokes equation whereas a diffusion-convection equation is involved for the transport of nutrients. At the water/biofilm interface, nutrient transport and shear forces due to the water flux are considered. In the biofilm, the Brinkman equation for the water flow, transport of nutrients due to diffusion and convection, displacement of the biofilm components due to reproduction/dead of bacteria, and production of EPS are considered. A segregated finite element algorithm is used to solve the mathematical equations. Numerical simulations are performed based on experimentally determined parameters. The stress coefficient is fitted to the experimental data. To identify the critical model parameters, a sensitivity analysis is performed. The Sobol sensitivity indices of the input parameters are computed based on uniform perturbation by $\pm 10 \%$ of the nominal parameter values. The sensitivity analysis confirms that the variability or uncertainty in none of the parameters should be neglected.
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