The onset of turbulence in particle-laden pipe flows

We propose a scaling law for the onset of turbulence in pipe flow of neutrally buoyant suspensions. This scaling law, based on a large set of experimental data, relates the amplitude of the particle-induced perturbations ($\epsilon$) to the critical suspension Reynolds number, $Re_{s,c}$. Here $\epsilon$ is a function of the particle-to-pipe diameter ratio and the volume fraction of the suspended particles, $\epsilon = (d/D)^{1/2} \phi^{1/6}$. $Re_{s,c}$ is found to scale as $\epsilon^{-1}$. Furthermore, the perturbation amplitude allows a distinction between classical, intermediate and particle-induced transition.