Unraveling the Complexity of Dusty Channel Flow: A Comprehensive Stability Analysis

We investigate the stability of dusty channel flow, driven by an imposed pressure gradient, where particles are in a dilute suspension. Saffman¹, and later, Klinkenberg et al² studied the stability under homogeneous particle loading. Klinkenberg et al² found that the addition of particles results a small suppression of exponentially growing modes. 

In contrast, our work incorporates a more realistic base mass fraction profile, inspired by experiments on dusty channel flows. We include Stokes drag as well as the viscosity variation caused by particles, based on Einstein's viscosity formula.

Combining numerical and analytical methods, we conduct a comprehensive investigation. Intriguingly, our results are  remarkable and unexpected: the presence of even small quantities of particles leads to significant destabilization.

1. Saffman, P. G. (1962). On the stability of laminar flow of a dusty gas. J. Fluid Mech. 13(1):120-128.

2. Klinkenberg, J., De Lange, H., and Brandt, L. (2011). Modal and non-modal stability of particle-laden channel flow. Phys. Fluids, 23, 0064110.