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International audience; Suffusion refers to a special form of internal erosion characterized by the selective erosion of the finest particles of a soil under the action of an internal fluid flow. In this work, the microscopic mechanism of particle detachment in binary mixtures subjected to suffusion under different flow directions is analyzed. We use the coupled lattice Boltzmann method (LBM) and discrete element method (DEM) to simulate the suffusion process in a granular sample subjected to an anisotropic stress state. When the macro flow direction is aligned with the principal direction of compression, it is found that the fluid flow is more intense, which increases erosion. The stress anisotropy also influences the detachment direction that is not necessarily correlated with the macroscopic flow direction. The sample's anisotropic stress state is responsible for directional variations in microstructural properties during the suffusion under different flow directions. From a micro scale point of view, a contact sliding index P and a particle detachment index Δ are defined to demonstrate that fluid-induced sliding dominates for particles about to detach.

In this paper, we rigorously obtain all the equilibria of collision kernels of type ``two particles give two particles'' appearing in weak turbulence theory under very general assumptions, thus completing the ``equality case'' in Boltzmann's H-theorem for those models. We also provide some rigorous results for collision kernels of type ``two particles give one particle'', under assumptions which include some of the most classical kernels of this type. The method of proof is inspired by the quantitative estimates obtained for the Landau equation by Desvillettes in [J. Funct. Anal. 269:1359-1403, 2015].