An Instability Mechanism For Particulate Pipe Flow

We present a linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles, two-way coupled to the fluid velocity field via Stokes drag (Saffman, J. Fluid Mech., vol. 13 (01), 1962, pp. 120-128). We extend previous analysis in a channel (Klinkenberg et al., Phys. Fluids, vol. 23 (6), 2011, 064110) to allow for the initial distribution of particles to be inhomogeneous in a similar manner to Boronin (Fluid Dyn., vol. 47 (3), 2012, pp. 351-363) and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability offering an alternative route to turbulence within this problem.