Inspired by recent observations of granular flow, we examine how rotational vortices contribute to heat or mass transfer enhancement in a fluid. We use a tracer method to simulate both diffusion and advection in systems of differing intrinsic diffusivities D 0 , vortex sizes R, vortex rotation frequencies f, and vortex lifetimes . The results reveal that these systems exhibit an effective diffusive behavior, characterized by an effective diffusivity

PACS 47.56.+r -Flows through porous media PACS 47.60.Dx -Flows in ducts and channels PACS 89.75.Hc -Networks and genealogical trees Abstract -We investigate the hydraulic permeability of complex channel networks by expressing analytically the system tortuosity in terms of topology. The tortuosity is shown to be strongly dependent on the covariance between the flow velocity in the channels and their length, and we demonstrate that in isotropic networks no covariance means impermeability. The derived analytical expression for the tortuosity is assessed against numerical simulations of various proximity-based and topology-based isotropic complex networks, and is then used to explain why the permeability of the latter networks is typically lower than the former. The new formula and findings have vast applications in biology, geology, hydrology and in engineering transport systems.

PACS 47.56.+r -Flows through porous media PACS 47.60.Dx -Flows in ducts and channels PACS 89.75.Hc -Networks and genealogical trees Abstract -This study focuses on the loss of permeability and connectivity of hydraulic networks induced by channel clogging. Five network attack scenarios are considered that consist of clogging an increasing number of channels, selected according to their pressure drop and flow rate. By simulating the flow in the network before and after each attack, we show that some strategies only marginally affect the permeability and lead to a loss of connectivity only after a large proportion of channels are clogged. By contrast, other strategies strongly decrease the permeability and lead to a loss of connectivity after a small proportion of channels are clogged. These findings, interpreted in terms of change in porosity and network tortuosity, should help the prediction of the effect of network attacks in biological systems, hydrogeology and microfluidics.

We investigate the transfer properties of idealised porous materials comprising a diffusive solid pervaded by an array of channels. Using a tracer method, we study how a liquid flowing through these channels may reduce the cooling time of the solid. Accordingly, we define an effective transfer efficiency, which we systematically measure in systems of differing diffusivities, channel radii, lengths and spacings, average flow velocities and flow fields -namely plugged and Hagen-Poiseuille flows. We show that the transfer efficiency scales with a key dimensionless number involving the Péclet number and the channel to solid volume fraction. This scaling exhibits three regimes. Based on the analysis of the advection and diffusion processes in the systems, we introduce a semi-empirical model that captures the entire range of results.

Abstract. In sheared granular media, particle motion is characterized by vortex-like structures; here this is demonstrated experimentally for disks system undergoing indefinite deformation during simple shear, as often imposed by the rock masses hosting earthquake fault gouges. In traditional fluids it has been known for years that vortices represent a major factor of heat transfer enhancement via convective internal mixing, but in analyses of heat transfer through earthquake faults and base planes of landslides this has been continuously neglected. Can research proceed by neglecting heat convection by internal mixing? Our answer is astonishingly far from being yes.