Multilayered membrane filters, which consist of a stack of thin porous membranes with different properties (such as pore size and void fraction), are widely used in industrial applications to remove contaminants and undesired impurities (particles) from a solvent. It has been experimentally observed that the performance of well-designed multilayer structured membranes is markedly better than that of equivalent homogeneous membranes. Mathematical characterization and modeling of multilayered membranes can help our understanding of how the properties of each layer affect the performance of the overall membrane stack. In this paper, we present a simplified mathematical model to describe how the pore-scale properties of a multilayered membrane affect the overall filter performance. Our results show that, for membrane stacks where the initial layer porosity decreases with depth, larger (negative) porosity gradients within a filter membrane are favorable for increasing throughput and filter lifetime, but at the expense of moderately poorer initial particle retention. We also found that the optimal layer thickness distribution that maximizes total throughput corresponds to a membrane stack with larger (negative) porosity gradients in which layer thickness increases slightly between successive layers in the depth of the membrane.

多层膜过滤器由堆叠的具有不同特性（例如孔径和空隙率）的薄多孔膜组成，已广泛用于工业应用中，以从溶剂中去除污染物和不希望的杂质（颗粒）。实验上已经观察到，设计良好的多层结构膜的性能明显优于等效的均质膜。多层膜的数学表征和建模可以帮助我们了解每一层的特性如何影响整个膜叠层的性能。在本文中，我们提供了一个简化的数学模型来描述多层膜的孔径特性如何影响整体过滤器性能。我们的结果表明，对于初始层孔隙度随深度降低的膜叠堆而言，滤膜内较大的（负）孔隙率梯度有利于增加通量和过滤器寿命，但以适度较差的初始颗粒保留为代价。我们还发现，使总生产量最大化的最佳层厚度分布对应于具有较大（负）孔隙率梯度的膜堆，其中，在膜的深度中，各连续层之间的层厚度略有增加。