Partial Reversibility of Dispersion in Heterogeneous Porous Media

非均质多孔介质中的溶质运移是近四十年来研究的热点问题。众所周知，溶质扩散，测量溶质羽流的增加的不规则性，不同于溶质混合，量化溶质羽流与其周围的质量交换。前者先于后者，但只有后者有利于混合控制反应。到目前为止，还没有一个理论可以很好地预测大规模的非菲克扩散和溶质混合。既不给现有的理论进行大规模的保守传输实验，以量化溶质混合的实际建议。拟议的项目建立在这样的事实上，纯粹的运动学变形的水包裹携带溶质在异质地层是完全可逆的，而扩散混合是不可逆的。变形和小规模的扩散混合在溶质输运在这样的地层之间的相互作用导致部分可逆性的溶质扩散：在流动逆转的空间范围的溶质羽收缩，但不恢复到原来的初始状态。该项目将分析具有均匀平均流的非均质多孔介质中的溶质羽流的二阶中心矩（其中一半的变化率定义了弥散系数）。申请人假定，在相同时间的向前和向后运动之后，分散的不可逆分数可以作为溶质混合的度量。在非径向推拉实验中，目标量是注入/提取横截面中返回溶质的穿透曲线的扩展。分析是通过在3-D虚拟区域中的粒子跟踪随机行走模拟，通过一阶随机扰动方法用于空间矩的理论分析，通过发展一种新的相关连续时间随机行走方法与先前步骤的记忆和随机交换的平均值用于时间矩的分析，并通过在一个案例中的实验来完成的。2 m × 1 m准二维流动域，使用折射率匹配流体优化光透射成像检测。实验将包括检测返回溶质的穿透曲线。据推测，线性随机理论预测合奏和有效的时刻，以及轻度异质性的情况下。增加逆Péclet数，非均匀性程度及其各向异性应增加分散的不可逆部分。二次中心力矩预计会在气流逆转时收缩，并在羽流中心到达其原始位置之前再次增加。收缩时间和对系综色散的可逆贡献应该与局部Péclet数成比例。该项目开发了新的理论和实验方法来区分非均质多孔介质中的扩散和混合，这控制了反应性化合物的行为。

Solute transport in heterogeneous porous media has been the topic of intensive research in the last four decades. It is well established that solute spreading, measuring the increasing irregularity of solute plumes, differs from solute mixing, quantifying the mass exchange of a solute plume with its surrounding. The former precedes the latter, but only the latter facilitates mixing-controlled reactions. To date there is no theory that is good in predicting both large-scale non-Fickian spreading and solute mixing. Neither give existing theories practical advice on performing large-scale conservative-transport experiments to quantify solute mixing. The proposed project builds on the fact that purely kinematic deformation of water parcels carrying solutes in heterogeneous formations is fully reversible, whereas diffusive mixing is irreversible. The interaction between deformation and small-scale diffusive mixing in solute transport in such formations cause partial reversibility of solute spreading: Upon flow reversal the spatial extent of a solute plume shrinks, but does not revert to the original initial state. The project will analyze second-central moments of solute plumes (of which half the rate of change define dispersion coefficients) in heterogeneous porous media with uniform-in-the-mean flow subject to flow reversal. The applicant presumes that the irreversible fraction of dispersion, after equal times of forward and backward motion, can be taken as a metric of solute mixing. In non-radial push-pull experiments the target quantity is the spread of the breakthrough curve of the returning solute in the injection/extraction cross-section. The analysis is done by particle-tracking random-walk simulations in 3-D virtual domains, by first-order stochastic-perturbative methods for the theoretical analysis of spatial moments, by the development of a new correlated Continuous-Time Random-Walk approach with memory of preceding steps and random exchange with the mean for the analysis of temporal moments, and by experiments in a ca. 2m × 1m quasi 2-D flow domain using refractive-index matching fluids to optimize detection by light-transmission imaging. The experiments will include detecting the breakthrough curve of the returning solute. It is hypothesized that linear stochastic theory predicts ensemble and effective moments well for cases with mild heterogeneity. Increasing the inverse Péclet number, the degree of heterogeneity, and its anisotropy should increase the irreversible fraction of dispersion. Second-central moments are expected to shrink upon flow reversal and increase again before the plume center reaches its original position. The shrinking time and the reversible contribution to ensemble dispersion should scale with the local Péclet number. This project develops new theoretical and experimental approaches to distinguish spreading and mixing in heterogenous porous media, which controls the behavior of reactive compounds.