Stability of particle laden interfaces of drops flowing through a pore

When a drop laden with solid particles and suspended in a liquid passes through a narrow pore, its interface experiences strong shear and elongation, and the raft of particles may accumulate toward the back of the drop. Using well-controlled formulations of Pickering drops driven at set pressure, we determine the two conditions for which solid particles are expelled from the oil-water interface after a Pickering drop passes a converging-diverging pore: (i) particles accumulation at the rear of the drop is such that surface pressure builds up at the interface and (ii) surface pressure relaxation by buckling is impaired by geometrical constraints. These two conditions are rationalized using three nondimensional numbers: the capillary number, the particle to pore size ratio, and the drop to particle size ratio, which allow us to account for the viscous shear at the interface, the stability of the lubricating film between the pore wall and the drop, the drag on the raft of particles adsorbed at the interface, and its mechanical behavior.