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Macroscale transport in channel-matrix systems via integral transforms
Physical Review Fluids ( IF 2.7 ) Pub Date : 2021-04-12 , DOI: 10.1103/physrevfluids.6.044501
B. Ling , C. B. Rizzo , I. Battiato , F. P. J. de Barros

Flow and transport in coupled channel-matrix systems are ubiquitous to many environmental and engineering applications such as flows in fractured porous media over canopies and in membrane filtration units. The multiscale nature of such systems, where the horizontal length scale is often orders of magnitude larger than the vertical one, allows one to employ vertically averaged descriptions of the system. As a result, two-dimensional transport in the channel and the matrix can be upscaled to a coupled system of transient one-dimensional advection-dispersion equations, where matrix and channel properties can be analytically related to macroscopic transport observables. In this work, we first develop a semianalytical solution based on integral transforms that can be employed to predict macroscopic transport in channel-matrix shear flows in a computationally efficient manner. Then we demonstrate that under appropriate dynamic conditions, the coupled system at the macroscale can be further simplified to a single upscaled one-dimensional advection-dispersion equation, which admits an analytical closed-form solution, thus enabling real-time macroscale concentration estimates in relevant applications.

中文翻译:

通过积分变换在通道矩阵系统中进行宏观传输

耦合通道-矩阵系统中的流动和运输在许多环境和工程应用中是普遍存在的,例如在冠层和膜过滤单元中破裂的多孔介质中的流动。这种系统的多尺度性质,其中水平长度尺度通常比垂直尺度大几个数量级,因此人们可以采用该系统的垂直平均描述。结果,通道和矩阵中的二维传输可以按比例放大到瞬态一维对流扩散方程的耦合系统,其中矩阵和通道属性可以分析地与宏观传输观测值相关。在这项工作中,我们首先开发基于积分变换的半解析解决方案,该解决方案可用于以计算有效的方式预测通道矩阵剪切流中的宏观传输。然后,我们证明了在适当的动态条件下,可以将宏观尺度上的耦合系统进一步简化为一个单一的放大的一维对流弥散方程,该方程式允许采用解析的封闭形式解,从而可以在相关的情况下实时进行宏观尺度浓度估计。应用程序。
更新日期:2021-04-12
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