Solid particles moving parallel to a deformable liquid–liquid interface in a micro-channel: migration forces

This work focuses on the dynamics of a train solid particles, separated by distance $L$ , flowing near deformable interface formed two co-flowing immiscible fluids in microchannel height $h$ . Our study includes systematic analysis influence governing parameters (fluids viscosity ratio, and particle positions, Reynolds $Re$ capillary $Ca$ numbers inter-particle ) hydrodynamic force $f$ exerted particle. In pure inertial regime with non-deformable interfaces $Ca=0$ is driven towards wall (interface) when close to (wall). Up three neutral equilibrium positions $f=0$ them stable, are found this limit. The contrary obtained $Re=0$ limit, we also carried out an asymptotic distinguished limits very large small surface tension. latter case, amplitude deformation induced large, comparable its diameter, but limited region upstream downstream limit tension, presence modifies shape length $2\lambda$ much larger than diameter $d$ parameter $\lambda$ introduces additional characteristic that determines behaviour flow properties