标题： 渗透性膜间隙中扩散传输的有效渗透条件 显示英文标题

标题： Effective permeability conditions for diffusive transport through impermeable membranes with gaps

摘要： 膜在各种工业和生物应用中调节运输。 膜的微观几何结构可以显著影响通过膜的整体运输，但这种多尺度耦合的精确性质通常没有被很好地表征。 受跨细菌膜运输应用的启发，本文我们使用形式多尺度分析来推导二维不渗透膜上周期性间隔缝隙处宏观运输的有效耦合条件，并通过数值模拟验证这些条件。 我们推导了与膜相关的有效宏观量的解析表达式，例如渗透率，这些表达式是基于微观几何结构的。 我们的结果将经典的构成膜耦合条件推广到更广泛的膜几何结构和时间变化的情况。 具体而言，我们证明了如果外部浓度随时间变化，对于具有长通道的膜，运输会具有记忆特性，其中耦合条件取决于系统的历史。 通过在小分子通过称为孔蛋白的细菌膜缝隙运输的背景下应用我们的有效条件，我们预测细菌膜渗透率主要由膜的厚度主导。 此外，我们预测了膜微观结构的变化，例如通过改变孔蛋白表达，可能会影响整体运输，包括当外部浓度随时间变化时的情况。 这些结果将适用于具有类似膜结构的各种物理应用，从医疗和工业过滤到碳捕获。 显示英文摘要

摘要： Membranes regulate transport in a wide variety of industrial and biological applications. The microscale geometry of the membrane can significantly affect overall transport through the membrane, but the precise nature of this multiscale coupling is not well characterised in general. Motivated by the application of transport across a bacterial membrane, in this paper we use formal multiscale analysis to derive explicit effective coupling conditions for macroscale transport across a two-dimensional impermeable membrane with periodically spaced gaps, and validate these with numerical simulations. We derive analytic expressions for effective macroscale quantities associated with the membrane, such as the permeability, in terms of the microscale geometry. Our results generalise the classic constitutive membrane coupling conditions to a wider range of membrane geometries and time-varying scenarios. Specifically, we demonstrate that if the exterior concentration varies in time, for membranes with long channels, the transport gains a memory property where the coupling conditions depend on the system history. By applying our effective conditions in the context of small molecule transport through gaps in bacterial membranes called porins, we predict that bacterial membrane permeability is primarily dominated by the thickness of the membrane. Furthermore, we predict how alterations to membrane microstructure, for example via changes to porin expression, might affect overall transport, including when external concentrations vary in time. These results will apply to a broad range of physical applications with similar membrane structures, from medical and industrial filtration to carbon capture.