Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, 35032 Marburg, Germany.
Laboratory of Electron Kinetics, Institute of Solid State Physics, Russian Academy of Sciences, Academician Ossipyan Strasse 2, 142432 Chernogolovka, Russia.
Phys Rev E. 2017 Jun;95(6-1):063108. doi: 10.1103/PhysRevE.95.063108. Epub 2017 Jun 19.
Solute dispersion in fluid flow results from the interaction between advection and diffusion. The relative contributions of these two mechanisms to mass transport are characterized by the reduced velocity ν, also referred to as the Péclet number. In the absence of diffusion (i.e., when the solute diffusion coefficient D_{m}=0 and ν→∞), divergence-free laminar flow of an incompressible fluid results in a zero-transverse dispersion coefficient (D_{T}=0), both in ordered and random two-dimensional porous media. We demonstrate by numerical simulations that a more realistic realization of the condition ν→∞ using D_{m}≠0 and letting the fluid flow velocity approach infinity leads to completely different results for ordered and random two-dimensional porous media. With increasing reduced velocity, D_{T} approaches an asymptotic value in ordered two-dimensional porous media but grows linearly in disordered (random) structures depending on the geometrical disorder of a structure: a higher degree of heterogeneity results in a stronger growth of D_{T} with ν. The obtained results reveal that disorder in the geometrical structure of a two-dimensional porous medium leads to a growth of D_{T} with ν even in a uniform pore-scale advection field; however, lateral diffusion is a prerequisite for this growth. By contrast, in ordered two-dimensional porous media the presence of lateral diffusion leads to a plateau for the transverse dispersion coefficient with increasing ν.
在流体流动中，溶质的弥散是由于对流和扩散相互作用的结果。这两种机制对传质的相对贡献由无量纲速度 ν 来表征，也称为 Peclet 数。在没有扩散的情况下（即当溶质扩散系数 D_{m}=0 且 ν→∞时），不可压缩流体的无旋层流在有序和随机二维多孔介质中都会导致横向弥散系数 D_{T}=0。通过数值模拟，我们证明了使用 D_{m}≠0 并使流体流速趋近于无穷大来更真实地实现 ν→∞的条件，会导致有序和随机二维多孔介质的结果完全不同。随着无量纲速度的增加，在有序二维多孔介质中 D_{T}趋近于渐近值，但在无序（随机）结构中线性增长，这取决于结构的几何无序程度：结构的异质性越高，D_{T}随 ν 的增长就越强。所得结果表明，即使在均匀的孔隙尺度对流场中，二维多孔介质的几何结构中的无序也会导致 D_{T}随 ν 的增长；然而，横向扩散是这种增长的前提条件。相比之下，在有序二维多孔介质中，随着 ν 的增加，横向弥散系数的存在会导致弥散系数出现一个平台。
