title: Anomalous transport and chaotic advection in homogeneous porous media.
abstract: The topological complexity inherent to all porous media imparts persistent chaotic advection under steady flow conditions, which, in concert with the no-slip boundary condition, generates anomalous transport. We explore the impact of this mechanism upon longitudinal dispersion via a model random porous network and develop a continuous-time random walk that predicts both preasymptotic and asymptotic transport. In the absence of diffusion, the ergodicity of chaotic fluid orbits acts to suppress longitudinal dispersion from ballistic to superdiffusive transport, with asymptotic variance scaling as σ(L)(2)(t)∼t(2)/(ln t)(3). These results demonstrate that anomalous transport is inherent to homogeneous porous media and has significant implications for macrodispersion.
authors.affiliation: Mathematics, Informatics and Statistics, CSIRO, PO Box 56, Highett, Victoria 3190, Australia and School of Civil, Environmental and Chemical Engineering, Royal Melbourne Institute of Technology, Melbourne, Victoria 3001, Australia.
authors.forename: D R
authors.initials: DR
authors.lastname: Lester
authors.affiliation: Materials Science and Engineering, CSIRO, PO Box 56, Highett, Victoria 3190, Australia.
authors.forename: G
authors.initials: G
authors.lastname: Metcalfe
authors.affiliation: Land and Water, CSIRO, Private Bag 5, Wembley, Western Australia 6913, Australia and School of Earth and Environment, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia.
authors.forename: M G
authors.initials: MG
authors.lastname: Trefry
mesh_terms: D004396:Coloring Agents; D009038:Motion; D017711:Nonlinear Dynamics; D016062:Porosity
chemical_list: D004396:Coloring Agents