Universal Distribution of Non-Fickian Particle Kinetics in Three-Dimensional Porous Media.

We study particle transport in three-dimensional random packings of monodispersed spheres at different particle P\'eclet numbers using Lagrangian simulations. We find a universal non-exponential function that describes the observed particle velocity probability distributions when non-Fickian behavior occurs. The function also reproduces results from particle tracking experiments and yields the Maxwell-Boltzmann distribution in the Fickian limit. We discuss the implications of the new function, with emphasis on its ability to explain non-Fickian behavior, which arises because of energy dissipation events during particle deposition even in mildly heterogeneous media.