Brownian diffusion in a dilute field of traps is Fickean but non-Gaussian
Serge Mora and Yves Pomeau
Motivated by experimental observations, we look for the diffusion of Brownian particles in a medium where they can be either trapped in randomly disposed deep traps or where they diffuse by the regular Fick’s law outside of the traps. This process can be represented by two coupled equations—one valid inside the traps and another one outside —yielding the probability distribution of the distance run as a function of time. This probability depends on a unique dimensionless parameter λwhich is proportional to the product of the (small) density of the traps times the long time of staying in the traps. The mean-square displacement is proportional to the lag time, and for finite or large λ the probability density is no longer Gaussian but exponential on intermediate time scales.
Viscoinertial regime of immersed granular flows
Lhassan Amarsid, J-Y Delenne, Patrick Mutabaruka, Yann Monerie, Frédéric Perales, Farhang Radjai
By means of extensive coupled molecular dynamics–lattice Boltzmann simulations, accounting for grain dynamics and subparticle resolution of the fluid phase, we analyze steady inertial granular flows sheared by a viscous fluid. We show that, for a broad range of system parameters (shear rate, confining stress, fluid viscosity, and relative fluid-grain density), the frictional strength and packing fraction can be described by a modified inertial number incorporating the fluid effect. In a dual viscous description, the effective viscosity diverges as the inverse square of the difference between the packing fraction and its jamming value, as observed in experiments. We also find that the fabric and force anisotropies extracted from the contact network are well described by the modified inertial number, thus providing clear evidence for the role of these key structural parameters in dense suspensions.