Analytical solutions of drying in porous media for gravity-stabilized fronts.
Analytical solutions of drying in porous media for gravity-stabilized fronts.
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重力稳定前沿多孔介质中干燥的解析解。
DOI：
10.1103/physreve.85.046308
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Y. Yortsos
中科院分区：
文献类型：
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作者：
A. Yiotis;Dominique Salin;E. Tajer;Y. Yortsos
本文建立了重力作用下多孔介质干燥的数学模型。该模型结合了角流通过宏观液体膜，形成在孔壁的空腔中，传质介质的干燥区域中的扩散，表面上的外部传质，和重力的影响。我们考虑两种不同的情况下：当重力反对液体流动的角落膜，并导致一个稳定的渗滤干燥前，当它在相反的方向上的行为。在这一部分中，我们开发的分析结果时，问题可以被视为一个等效的连续和描述为一个一维（1D）的问题。当重力通过反向角流而对干燥起作用时，或者当重力通过增加角膜流而增强干燥但它足够小时，总是这种情况。我们获得了所有相关变量的结果，包括干燥速率、宏观薄膜区域的范围以及恒速期和降速期两种不同状态的界限。考察了键数、毛细管数和舍伍德数等无因次变量对外部传质的影响。当重力作用于增强干燥时，如果适当定义的瑞利数高于临界阈值，则仍然可以得到1D解决方案。在此条件下，我们得到了一个模型问题的线性稳定性分析，验证了前稳定性。进一步分析这个问题，当瑞利数低于临界值时，需要一个孔隙网络模拟器，这将是未来工作的重点。
We develop a mathematical model for the drying of porous media in the presence of gravity. The model incorporates effects of corner flow through macroscopic liquid films that form in the cavities of pore walls, mass transfer by diffusion in the dry regions of the medium, external mass transfer over the surface, and the effect of gravity. We consider two different cases: when gravity opposes liquid flow in the corner films and leads to a stable percolation drying front, and when it acts in the opposite direction. In this part, we develop analytical results when the problem can be cast as an equivalent continuum and described as a one-dimensional (1D) problem. This is always the case when gravity acts against drying by opposing corner flow, or when it enhances drying by increasing corner film flow but it is sufficiently small. We obtain results for all relevant variables, including drying rates, extent of the macroscopic film region, and the demarkation of the two different regimes of constant rate period and falling rate period, respectively. The effects of dimensionless variables, such as the bond number, the capillary number, and the Sherwood number for external mass transfer are investigated. When gravity acts to enhance drying, a 1D solution is still possible if an appropriately defined Rayleigh number is above a critical threshold. We derive a linear stability analysis of a model problem under this condition that verifies front stability. Further analysis of this problem, when the Rayleigh number is below critical, requires a pore-network simulator which will be the focus of future work.