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 ε to the critical suspension Reynolds number Res,c. Here ε is a function of the particle-to-pipe diameter ratio and the volume fraction of the suspended particles, ε=(d/D)1/2ϕ1/6. Res,c is found to scale as ε−1. Furthermore, the perturbation amplitude allows a distinction between classical, intermediate, and particle-induced transitions.