Related papers: Models and measures of mixing and effective diffus…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different…
We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a…
Over three decades ago the advection-diffusion equation for a steady fluid velocity field was homogenized, leading to a Stieltjes integral representation for the effective diffusivity, which is given in terms of a spectral measure of a…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
We deal with the problem of separation of time-scales and filamentation in a linear drift-diffusion problem posed on the whole space $\mathbb{R}^2$. The passive scalar considered is stirred by an incompressible flow with radial symmetry. We…
We are concerned with flow enhanced mixing of passive scalars in the presence of diffusion. Under the assumption that the velocity gradient is suitably integrable, we provide upper bounds on the exponential rates of enhanced dissipation.…
We solve the advection-diffusion equation for a stochastically stationary passive scalar $\theta$, in conjunction with forced 3D Navier-Stokes equations, using direct numerical simulations in periodic domains of various sizes, the largest…
Streamer electrical discharges are often investigated with computer simulations of density models (also called drift-diffusion-reaction models). We review these models, detailing their physical foundations, their range of validity and the…
Periodic forcing of flow in compressible porous media is an important driver for solute dispersion and mixing in geological and engineered porous media subject for example to tides, pumping and recharge cycles, or fluid injection and…
The effect of oscillatory shear flows on turbulent transport of passive scalar fields is studied by numerical computations based on the results provided by E. Kim [\emph{Physics of Plasmas}, {\bf 13}, 022308, 2006]. Turbulent diffusion is…
We apply a pulsed-light interferometer to measure both the intensity and the phase of light that is transmitted through a strongly scattering disordered material. From a single set of measurements we obtain the time-resolved intensity,…
Swimming bacteria create long-range velocity fields that stir a large volume of fluid and move around passive particles dispersed in the fluid. Recent experiments and simulations have shown that long-time mean-squared displacement of…
The statistics of a passive scalar randomly emitted from a point source is investigated analytically. Our attention has been focused on the two-point equal-time scalar correlation function. The latter is indeed easily related to the…
We study a passive scalar equation on the two-dimensional torus, where the advecting velocity field is given by a cellular flow with a randomly moving center. We prove that the passive scalar undergoes mixing at a deterministic exponential…
We present direct numerical simulations (DNS) of the mixing of the passive scalar at modest Reynolds numbers (10 =< R_\lambda =< 42) and Schmidt numbers larger than unity (2 =< Sc =< 32). The simulations resolve below the Batchelor scale up…
The shearing instability of a dilute granular mixture composed of smooth inelastic hard spheres or disks is investigated. By using the Navier-Stokes hydrodynamic equations, it is shown that the scaled transversal velocity mode exhibits a…
The advection of a passive scalar by a quenched (frozen) incompressible velocity field is studied by extensive high precision numerical simulation and various approximation schemes. We show that second order self consistent perturbation…
We quantitatively study the interaction between diffusion and mixing in both the continuous, and discrete time setting. In discrete time, we consider a mixing dynamical system interposed with diffusion. In continuous time, we consider the…
When polydisperse granular systems are sheared, the transverse dynamics is characterized by the interplay of size segregation and diffusion. Segregation in nonuniform and confined shearing flows is studied using annular shear cell…
The dispersion of a passive scalar by wall turbulence, in the limit of infinite Peclet number, is analyzed using frozen velocity fields from the DNS by our group. The Lagrangian trajectories of fluid particles in those fields are integrated…