Influence of immersed particles on the stability of the liquid-liquid interface in a two-layer channel flow

The current study investigates the global linear stability of a two-layer channel flow with a train of solid particles flowing near the liquid-liquid interface. Three different mechanisms of instability (shear, interfacial and migration modes) are identified, and their interactions are examined. The interfacial instability, associated with the viscosity jump at the liquid-liquid interface, is found to be coupled to the migration of the particle. The stability of the flow configuration is evaluated for various governing parameters, including fluid viscosities and flow rate ratios, particle position, inter-particle distance, and Reynolds and capillary numbers. Our numerical results are compared with the particle-free flow configuration, indicating that the presence of the particle in the more viscous fluid promotes the destabilization of the interface. Remarkably, under certain flow parameters, the presence of the particle stabilizes the interface when flowing in the less viscous liquid. The impact of particles is more significant as the capillary number increases or the Reynolds number decreases.