We present a realistic phenomenological description of liquid transport through defective, layered membranes. We derive general expressions based on conventional models of laminar flow and extend the formalism to accommodate slip flow. We consider different types of defects including in-layer vacancies that provide an activation-free tortuous path through the membrane. Of the many factors that affect flow, the most important is the radius of in-layer vacancy defects, which enters in the fourth power in expressions for the flux density. We apply our formalism to water transport through defective multilayer graphene oxide membranes and find the flow to remain in the laminar regime. Our results show that observed high water permeability in this system can be explained quantitatively by a sufficient density of in-layer pores that shorten the effective diffusion path.

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液体流过有缺陷的分层膜的现象学描述

我们提出了通过有缺陷的分层膜的液体传输的现实现象学描述。我们基于传统的层流模型推导了一般表达式，并扩展了形式主义以适应滑流。我们考虑了不同类型的缺陷，包括提供穿过膜的无激活曲折路径的层内空位。在影响流动的许多因素中，最重要的是层内空位缺陷的半径，它在通量密度的表达式中输入四次方。我们将形式主义应用于通过有缺陷的多层氧化石墨烯膜的水传输，并发现流保持在层流状态中。