Solute transport through homogeneous media has long been assumed to be scale-independent and can be quantified by the second-order advection-dispersion equation (ADE). This study, however, observed the opposite in the laboratory, where transport of CuSO4 through relatively homogeneous silica-sand columns exhibits sub-diffusion growing with the spatial scale. Only at a very small travel distance...

We use Lattice Boltzmann models to simulate solute transport in porous media traversed by larger conduits and fit the resulting solute breakthrough curves with macroscopic Continuous Time Random Walk (CTRW) models. In this paper, the porous media are simulated using a real-numbered coefficient that partially damps the inertial components of the flow and, when the damping is large enough, leads ...

We study the dynamics defined by the Boltzmann equation set in the Euclidean space R in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As...

solute transport in unsaturated porous media can be viewed as a coupled phenomenon with waterand heat transport, together with mechanical behaviour of media. in this paper, solute transport is formulatedmathematically considering heat and water flow in deformable porous media. advection, dispersion anddiffusion of chemical species in the liquid phase are considered. convection and conduction fo...

a new mathematical model for identifying pollution sources in aquifers is presented. the model utilizes lagrange constrained optimization method (lcom) and is capable to inversely solve unsteady fluid flow in saturated, heterogeneous, anisotropic confined and/or unconfined aquifers. throughout the presented model, complete advection-dispersion equation, including the adsorption as well as retar...

[1] A physically based description is provided for the transverse dispersion coefficient in porous media as a function of Péclet number, Pe. We represent the porous medium as lattices of bonds with square cross section whose radius distribution is the same as computed for Berea sandstone and describe flow (Stokes equation) and diffusion (random walk method) at the pore scale ( mm) to compute th...