Fluid forces or impacts, what governs the entrainment of soil particles in sediment transport mediated by a Newtonian fluid?

To sustain steady sediment transport, the loss of transported particles that become trapped in the soil bed must be balanced by the entrainment of bed particles through fluid forces or energetic impacts of transported particles. Here we show that the transition to fully impact-sustained transport occurs at a critical impact number $\mathrm{Im}=\Theta\mathrm{Re}\sqrt{s}\approx3$, where $\Theta$ is the Shields number, $\mathrm{Re}$ the particle Reynolds number, and $s$ the particle-fluid-density ratio. Hence, fluid entrainment is negligible for most regimes, including turbulent bedload transport.