  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.
