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The role of stagnant zones in hydrodynamic dispersion is studied for creeping flow through a fixed bed of spherical permeable particles, covering several orders of characteristic time and length scales associated with fluid transport. Numerical simulations employ a hierarchical model to cope with the different temporal and spatial scales, showing good agreement with our experimental results on diffusionlimited mass transfer, transient, and asymptotic longitudinal dispersion. These data demonstrate that intraparticle liquid holdup in macroscopically homogeneous porous media clearly dominates over contributions caused by the intrinsic flow field heterogeneity and boundary-layer mass transfer. DOI: 10.1103/PhysRevLett.88.234501 PACS numbers: 47.15.Gf, 05.60. -k, 47.55.Mh A detailed understanding of transport in porous media over the intrinsic temporal and spatial scales is important in many technological and environmental processes [1]. For example, natural and industrial materials such as soil, rock, filter cakes, or catalyst pellets often contain lowpermeability zones with respect to hydraulic flow of liquid through the medium or even stagnant regions which then remain purely diffusive. The relevance of stagnant zones stems from their influence on dispersion: Fluid molecules entrained in the deep diffusive pools cause a substantial holdup contribution and thereby affect the time scale of transient dispersion, as well as the value of the asymptotic dispersion coefficient (if the asymptotic long-time limit can be reached at all) [2][3][4]. Consequently, the associated kinetics of mass transfer between fluid percolating through the medium and stagnant fluid becomes rate limiting in a number of dynamic processes, including the separation and reaction efficiency of chromatographic columns and reactors, or economic oil recovery from a reservoir.In this respect, transport phenomena observed in model systems such as random packings of spheres may help to characterize materials with a higher disorder [5][6][7]. For random packings of nonporous (impermeable) particles, for example, the long-time longitudinal dispersion coefficient is dominated by the boundary-layer contribution (due to the no-slip condition at the solid-liquid interface) or by medium and large-scale velocity fluctuations in the flow field depending on the actual disorder of the medium and the Peclet number, Pe u ay d p D m (with u ay , the average velocity; d p , particle diameter; and D m , the molecular diffusivity) [6,8]. This behavior contrasts with random packings of porous (permeable) particles. In that case, liquid holdup associated with stagnant zones inside the particles may dominate dispersion when convective times t c uayt dp significantly exceed the dimensionless time for diffusion, t d. In many situations, however, both a macroscopic flow heterogeneity and solute trapping in stagnant zones contribute to transient and asymptotic dispersion [3,7,9].Despite numerous theoretical, experimental, and numerical studies (e.g., [1,7,8,[10][11][12]),...

SUMMARYA generic, mass conservative local grid reÿnement technique for the lattice-Boltzmann method (LBM) is proposed. As a volumetric description of the lattice-Boltzmann equation is applied, mass conservation can be imposed by allowing the lattice-Boltzmann particles to move from coarse grid cells to ÿne grid cells and vice versa in the propagation step. In contrast to most existing techniques, no spatial and temporal interpolation of particle densities is applied. Moreover, since the communication between the coarse and the ÿne grids is independent on the collision step, the method can be used for any LBM scheme.It was found that the method is second-order accurate in space for 2-D Poiseuille ow and di erent grid setups. The method was also applied to the case of 2-D lid driven cavity ow at Re = 1000, where half of the cavity was locally reÿned. It was found that the locations of the two lower vortices could be captured accurately. Finally, a direct numerical simulation (DNS) of turbulent channel ow at Re = 360 was performed where the grid was locally reÿned near the walls of the channel. Good ÿrst-and second-order turbulence statistics were obtained, showing the applicability of the local grid reÿnement technique for complex ows.

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