Dispersion controlled by permeable surfaces: surface properties and scaling
Dispersion controlled by permeable surfaces: surface properties and scaling
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DOI：
10.1017/jfm.2016.431
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发表时间：
2016-08-01
影响因子：
3.7
通讯作者：
Battiato, Ilenia
中科院分区：
文献类型：
--
作者：
Ling, Bowen;Tartakovsky, Alexandre M.;Battiato, Ilenia
渗透性和渗透性表面在天然和工程系统中很常见。在这种表面上的流动和传输明显受表面性质的影响，例如基质的孔隙度和渗透率。然而，这些性质与宏观溶质输运之间的关系在很大程度上是未知的。在这项工作中，我们重点研究了在完全发展的层流条件下，具有可渗透多孔壁的二维通道中的质量传输。利用摄动理论和渐近分析方法，导出了描述通道-多孔-基质耦合系统中质量输运的升阶方程组，并给出了弥散系数与表面性质即孔隙率和渗透率之间的关系的解析表达式。我们的分析表明，它们对弥散系数的影响强烈地依赖于Peclet数的大小，即扩散和平流质量传输之间的相互作用。此外，我们展示了不同的尺度行为的弥散系数的薄或厚多孔矩阵。我们的分析表明，对于给定的Peclet数，可以通过主动机制(即改变操作条件)或被动机制(即控制基质的有效性质)来控制色散系数，即横向混合。通过阐明基质孔隙率和渗透率对溶质传输的影响，我们扩展的模型为更好地理解、控制和设计具有针对性的宏观传输特性的微孔涂层奠定了基础。
Permeable and porous surfaces are common in natural and engineered systems. Flow and transport above such surfaces are significantly affected by the surface properties, e.g. matrix porosity and permeability. However, the relationship between such properties and macroscopic solute transport is largely unknown. In this work, we focus on mass transport in a two-dimensional channel with permeable porous walls under fully developed laminar flow conditions. By means of perturbation theory and asymptotic analysis, we derive the set of upscaled equations describing mass transport in the coupled channel-porous-matrix system and an analytical expression relating the dispersion coefficient with the properties of the surface, namely porosity and permeability. Our analysis shows that their impact on the dispersion coefficient strongly depends on the magnitude of the Peclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviours of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transverse mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Peclet number. By elucidating the impact of matrix porosity and permeability on solute transport, our upscaled model lays the foundation for the improved understanding, control and design of microporous coatings with targeted macroscopic transport features.