Application of Stochastic Theories and Three-Dimensional Particle Tracking Velocity (3D-PTV) Experiments to Study Anomalous Dispersion

0003878 Cushman模型开发用于模拟多孔介质，通常认为污染物种类的分散通量与浓度梯度成正比，通过一个常数或时间相关的分散系数。 这些模型是一个粗糙的近似在多孔介质中的传输与不断变化的尺度上的观测的异质性。 可以说，如果色散张量是常数，则多孔介质以菲克方式表现，如果张量是时间依赖的，则多孔介质是准菲克，如果通量是卷积，则多孔介质是卷积菲克。 色散通量的更一般形式是可能的，并且在任何情况下，本文提出的一个主要目的是利用现有的混合过程模型和三维粒子跟踪速度（3D-PTV）相结合，研究扩散通量与浓度梯度之间的比例关系，并将其应用于混合过程的模拟中。来研究这些理论对于各种异质性的准确性。 此外，建议通过使用完整的中间散射函数和非线性动力学的概念，如有限大小的李雅普诺夫指数来扩展这些模型。 具体的实验目标是：（i）构建一系列匹配指数，非均匀，多孔基质流体混合物：（ii）使用3D-PTV重建拉格朗日粒子轨迹;（iii）使用轨迹来确定均方位移、速度分布、速度相关性（单粒子和多粒子）函数，经典色散张量，自部分和完全中间散射函数，广义波矢量和频率相关的色散张量，和有限大小的李雅普诺夫指数;（iv）调查浮力驱动的空气流甘油在匹配的指数形成，均质和非均质的实验室规模。 具体的理论目标是：（i）用实验数据检验现有非均匀介质中输运模型的充分性;（ii）发展非均匀介质中有限尺寸李雅普诺夫指数与色散之间的关系;（iii）发展一种具有发展不均匀性的多孔介质中的色散理论，该理论依赖于多粒子相关函数，完全中间散射函数，和有限大小的李雅普诺夫指数;及（iv）测试新的理论与实验获得的数据。

0003878CushmanModel developed to simulate in porous media often consider the dispersive flux of the contaminant species to be proportional to the concentration gradient via a constant, or time-dependent dispersion coefficient. These models are a crude approximation for transport in porous media with evolving scales of heterogeneity on the scale of observation. It is said that a porous medium behaves in a fickian fashion if the dispersion tensor is constant, it is quasi-fickian if the tensor is time dependent, and it is convolution fickian if the flux is a convolution. More general forms of the dispersive flux are possible, and in any case, dispersive fluxes are called anomalous if there is no constant coefficient of proportionality between the dispersive flux and the gradient of concentration.A main purpose of the proposed effect is to use existing models of the mixing process in conjunction with three-dimensional particle tracking velocity (3D-PTV) to study the accuracy of these theories for various types of heterogeneity. In addition, it is proposed to extend these models by using the full intermediate scattering function and concepts from nonlinear dynamics such as finite-size Lyapunov exponents. The specific experimental objectives are: (i) to construct a sequence of matched index, heterogeneous, porous-matrix fluid mixtures; (ii) to use 3D-PTV to reconstruct lagrangian particle trajectories; (iii) to use the trajectories to determine mean square displacements, velocity distributions velocity correlation (single and multiparticle) functions, classical dispersion tensors, self-part and full intermediate scattering functions, generalized wave-vector and frequency dependent dispersion tensors, and finite-size Lyapunov exponents; (iv) to investigate buoyancy driven flow of air in glycerol in matched index formations, both homogeneous and heterogeneous on the lab scale. The specific theoretical objectives are: (i) to examine the adequacy of existing models of transport in heterogeneous media using experimental data: (ii) to develop the relationship between the finite-size Lyapunov exponents and dispersion in heterogeneous media; (iii) to develop a theory of dispersion in porous media with evolving heterogeneity which relies upon multiparticle correlation functions, the full intermediate scattering function, and the finite-size Lyapunov exponents; and (iv) to test the new theory with data obtained experimentally.