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

应用随机理论和三维粒子跟踪速度（3D-PTV）实验研究反常色散

• 批准号: 0003878
• 负责人: John Cushman
• 金额: $ 28万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-01-15 至 2004-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0003878&HistoricalAwards=false
• 关键词: Application; Stochastic; Theories; Three; Dimensional

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.

0003878Cushman 开发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常数或时间相关的分散系数与浓度梯度成正比。 这些模型是多孔介质中传输的粗略近似，在观察尺度上具有不断变化的异质性尺度。 据说，如果色散张量恒定，则多孔介质表现为菲克行为；如果张量与时间相关，则多孔介质表现为拟菲克行为；如果通量为卷积，则多孔介质表现为卷积菲克行为。 色散通量的更一般形式是可能的，并且在任何情况下，如果色散通量和浓度梯度之间不存在恒定的比例系数，则色散通量被称为反常。所提出的效果的主要目的是使用现有模型混合过程与三维粒子跟踪速度 (3D-PTV) 相结合，研究这些理论对于各种类型的异质性的准确性。 此外，还建议通过使用完整的中间散射函数和非线性动力学概念（例如有限大小的李亚普诺夫指数）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、非均质、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、广义波矢和频率相关色散张量以及有限-大小李雅普诺夫指数； (iv) 在实验室规模上研究匹配指数形成中甘油中浮力驱动的空气流动，包括均质和非均质。 具体的理论目标是：（i）使用实验数据检查异质介质中现有传输模型的充分性：（ii）建立有限尺寸李雅普诺夫指数与异质介质中色散之间的关系； (iii) 发展一种具有不断演化的异质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、完整的中间散射函数和有限大小的李亚普诺夫指数； (iv) 用实验获得的数据检验新理论。