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

0003878 cushman用于模拟多孔介质的模型通常认为污染物种类的分散通量通过一个常数或时变分散系数与浓度梯度成正比。这些模型是多孔介质中运移的粗略近似，在观测尺度上具有不断变化的非均质尺度。如果色散张量是常数，则多孔介质表现为菲克式；如果张量与时间有关，则为准菲克式；如果通量是卷积，则为卷积菲克式。色散通量的更一般形式是可能的，在任何情况下，如果色散通量和浓度梯度之间没有恒定的比例系数，则色散通量被称为反常。提出的效应的一个主要目的是利用现有的混合过程模型，结合三维粒子跟踪速度（3D-PTV）来研究这些理论对各种非均质性的准确性。此外，还提出了利用全中间散射函数和有限尺寸李雅普诺夫指数等非线性动力学概念对这些模型进行扩展。具体的实验目标是：(i)构建一系列匹配的指数，非均质，多孔基质流体混合物；（ii）利用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（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色散张量以及有限大小的李雅普诺夫指数；（iv）在实验室规模上研究在匹配的指数地层（均质和非均质）中由浮力驱动的空气在甘油中的流动。具体的理论目标是：(i)使用实验数据检查现有的异质介质中输运模型的充分性；（ii）发展有限尺寸Lyapunov指数与异质介质中弥散之间的关系；（iii）建立基于多粒子相关函数、完整中间散射函数和有限大小Lyapunov指数的多孔介质非均质演化色散理论；（四）用实验得到的数据检验新理论。

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.