Coupling Stochastic and Chaotic-Dynamic Theories with 3d-pptv Experiments to Study Flow and Anomalous Dispersion in Porous Media

正在进行的理论工作得到了创新的实验室实验的支持，这些实验集中在单流体多孔介质系统中的分散。实验由意大利的莫罗尼教授指导，理论和数据分析由普渡大学的PI负责。实验使用了指数匹配的流体和固体系统以及三维摄影测量粒子跟踪测速（3D-PPTV）。这个想法是使用小气泡作为反射性的被动示踪粒子来跟踪穿越空间和时间的流动。从这些轨迹中，可以推导出粒子动力学的各种测量，这些测量将用于测试色散和相关体行为的理论。具体目标包括：1)开发用于三维分析的三摄像头系统；2)使用带有单个摄像头的可移动光片来获得多孔固体的详细几何形状；3)构建全局非静止但局部静止的异质介质；自相似介质；4)利用三维轨迹获得均方位移、局部和全局速度分布、速度相关函数以及各种其他措施。总之，pi将开发一种粒子跟踪技术，使用可移动的光片获得多孔基质的详细几何形状，构建全局非静止但局部静止的非均匀介质，并使用3D轨迹收集数据以测试各种非均匀性的输运模型。实现更有效地模拟各种天然和人工多孔介质中的湍流和化学输运的目标，对保护地下水质量有重要贡献。首次应用3D-PPTV和混沌动力学的集成为验证新的建模思想和推进基础理论提供了一个有价值的新工具。

Cushman0310029Ongoing theoretical work is supported by innovative laboratory experiments focused on dispersion in single-fluid porous media systems. The experiments are being directed by Prof. Moroni in Italy, and the theory and data analysis are pursued by the PI at Purdue. The experiments use index-matched fluid and solid systems and three-dimensional photogrammetric particle-tracking velocimetry (3D-PPTV). The idea is to use small air bubbles as reflective passive tracer particles to track flow through space and time. From these trajectories, various measures of particle dynamics would be derived, and these measures would be used to test theories on dispersion and related bulk behavior. The specific objectives include 1)Development of a three-camera system for three-dimensional analysis, 2)Use of a moveable light sheet with a single camera to obtain detailed geometry of the porous solid, 3)Construction of globally nonstationary, but locally stationary, heterogeneous media; self similar media; and homogeneous media with graded particle size distribution, and 4)Use of 3D trajectories to obtain the mean-square displacement, local and global velocity distributions, velocity correlation functions, and a variety of other measures. In summary, the PIs would develop a particle-tracking technique, use a moveable light sheet to obtain detailed geometry of the porous matrix, construct a globally non stationary but locally stationary heterogeneous media, and use 3D trajectories to gather data to test transport models for various types of heterogeneity. Accomplishing the goal of more effective modeling of turbulent flow and chemical transport in a wide variety natural and built porous media makes an important contribution to the protection of groundwater quality. The first-time application of an integration of 3D-PPTV and chaotic dynamics provides a valuable new tool for use in validating new modeling ideas and in advancing fundamental theory.