Effective macroscopic transport parameters between parallel plates with constant concentration boundaries
Effective macroscopic transport parameters between parallel plates with constant concentration boundaries
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DOI：
10.1016/j.advwatres.2007.04.004
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发表时间：
2007-09
影响因子：
4.7
通讯作者：
D. Webster;D. Felton;Jian Luo
中科院分区：
文献类型：
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作者：
D. Webster;D. Felton;Jian Luo
本文建立了一个宏观输运模型，采用泰勒剪切弥散分析方法，求解具有恒定浓度的平行平板间的二维层流剪切流。这种理想化的几何模型污染物溶解在孔隙尺度的污染物源区和流动在岩石裂缝溶解壁。我们升级的宏观瞬态传输模型的平均速度，宏观分散，和一阶传质速率的有效传输系数。为了验证宏观模型的平均浓度，协方差，和壁浓度梯度的对流扩散方程和Graetz解决方案的数值模拟的结果进行了比较。结果表明，在定浓度边界和局部尺度变化的情况下，放大后的平均速度和宏观扩散系数与Taylor-Aris扩散不同，一级传质模型描述的传质通量大于定壁面的扩散通量.此外，宏观模型中放大的一级传质系数仅取决于板间隙和扩散系数。因此，放大的一阶传质系数与平均速度和行进距离无关，导致恒定的孔尺度舍伍德数为12。由扩散质量通量确定的有效舍伍德数在小Peclet数时是Peclet数的函数，在大Peclet数时接近常数10.3。
A macroscopic transport model is developed, following the Taylor shear dispersion analysis procedure, for a 2D laminar shear flow between parallel plates possessing a constant specified concentration. This idealized geometry models flow with contaminant dissolution at pore-scale in a contaminant source zone and flow in a rock fracture with dissolving walls. We upscale a macroscopic transient transport model with effective transport coefficients of mean velocity, macroscopic dispersion, and first-order mass transfer rate. To validate the macroscopic model the mean concentration, covariance, and wall concentration gradient are compared to the results of numerical simulations of the advection–diffusion equation and the Graetz solution. Results indicate that in the presence of local-scale variations and constant concentration boundaries, the upscaled mean velocity and macrodispersion coefficient differ from those of the Taylor–Aris dispersion, and the mass transfer flux described by the first-order mass transfer model is larger than the diffusive mass flux from the constant wall. In addition, the upscaled first-order mass transfer coefficient in the macroscopic model depends only on the plate gap and diffusion coefficient. Therefore, the upscaled first-order mass transfer coefficient is independent of the mean velocity and travel distance, leading to a constant pore-scale Sherwood number of 12. By contrast, the effective Sherwood number determined by the diffusive mass flux is a function of the Peclet number for small Peclet number, and approaches a constant of 10.3 for large Peclet number.