NSF Award
0003878
0003878<br/>Cushman<br/>Model 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.<br/><br/>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.
