Universal Particle Kinetic Distribution in Crowded Environments

We study many-particle transport in heterogeneous, crowded environments at different particle P\'{e}clet numbers ($Pe^*$). We demonstrate that a modified Nakagami-$m$ function describes particle velocity probability distributions when particle deposition occurs. We assess the universality of said function through comparison against new Lagrangian simulations of various particle types as well as experimental data from the literature. We construe the function's physical meaning as its ability to explain particle deposition in terms of $Pe^*$ and the competition between distributions of energy barriers for particle release and particles' diffusive energy.