论文标题
浓度极化和渗透效应的有限元模型
A finite element model for concentration polarization and osmotic effects in a membrane channel
论文作者
论文摘要
在本文中，我们研究了一个数学模型，该数学模型代表了逆渗透跨流通道中具有多孔膜的浓度极化和渗透作用。使用Navier-Stokes方程对流体进行建模，而Darcy定律用于在膜上施加动量平衡。该方案包括一种符合有限元方法，该方法与Navier-Stokes方程的速度压力公式以及对流扩散方程的原始方案组成。 Nitsche方法用于在整个膜上施加渗透率。进行了几个数值实验以显示该方法的鲁棒性。最终的模型准确地复制了分析模型，并预测了与以前的工作相似的结果。发现淹没的配置具有最高的渗透率产生，但也具有所研究的所有三种配置的压力损失最大。
In this paper we study a mathematical model that represents the concentration polarization and osmosis effects in a reverse osmosis cross-flow channel with porous membranes at some of its boundaries. The fluid is modeled using the Navier-Stokes equations and Darcy's law is used to impose the momentum balance on the membrane. The scheme consist of a conforming finite element method with the velocity-pressure formulation for the Navier-Stokes equations, together with a primal scheme for the convection-diffusion equations. The Nitsche method is used to impose the permeability condition across the membrane. Several numerical experiments are performed to show the robustness of the method. The resulting model accurately replicates the analytical models and predicts similar results to previous works. It is found that the submerged configuration has the highest permeate production, but also has the greatest pressure loss of all three configurations studied.
