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.

0003878为在多孔培养基中模拟的0003878 CUSHMANMODEL通常认为污染物物种的色散通量与浓度梯度通过常数或时间依赖性的分散系数成正比。 这些模型是在观察尺度上具有不断发展的异质性尺度的多孔介质中传输的粗略近似。 据说，如果分散量张量是恒定的，则多孔培养基的行为会以五核的方式行为，如果张张量依赖于时间，则是准纤维式的，如果通量是卷积，则是卷积的fickian。 可能会出现更一般的色散通量形式，无论如何，如果分散通量与浓度梯度之间没有恒定的比例系数，则称为分散通量被称为异常。拟议效果的主要目的是使用混合过程中的现有模型在三维粒子跟踪velocity（3DD-DD-PPTV）中使用各种类型异质性。 此外，建议通过使用来自有限大小的Lyapunov指数等非线性动力学的完整中间散射函数和概念来扩展这些模型。 特定的实验目标是：（i）构建一系列匹配的指数，异质，多孔 - 矩阵流体混合物； （ii）使用3D-PTV重建拉格朗日粒子轨迹； (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）研究在实验室尺度上均匀和异质的匹配指数地层中甘油中空气的浮力驱动流动。 具体的理论目标是：（i）使用实验数据检查异质介质中现有运输模型的充分性：（ii）开发有限尺寸的lyapunov指数与异质介质中的分散性之间的关系； （iii）在具有不断发展的异质性的多孔培养基中发展一个分散理论，该理论依赖于多片段相关函数，完整的中间散射函数和有限大小的lyapunov指数； （iv）通过实验获得的数据测试新理论。