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

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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.