Lester D R, Metcalfe G, Trefry M G
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.
Materials Science and Engineering, CSIRO, PO Box 56, Highett, Victoria 3190, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Dec;90(6):063012. doi: 10.1103/PhysRevE.90.063012. Epub 2014 Dec 19.
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.
所有多孔介质固有的拓扑复杂性在稳定流动条件下会产生持续的混沌平流，这与无滑移边界条件共同作用，会产生反常输运。我们通过一个模型随机多孔网络来探究这种机制对纵向弥散的影响，并开发了一种连续时间随机游走模型，该模型可以预测预渐近和渐近输运。在没有扩散的情况下，混沌流体轨道的遍历性会抑制纵向弥散，使其从弹道输运转变为超扩散输运，渐近方差的标度为σ(L)(2)(t)∼t(2)/(ln t)(3)。这些结果表明，反常输运是均匀多孔介质所固有的，并且对宏观弥散具有重要意义。
