Swimming droplets in 1D geometries: an active Bretherton problem

We investigate experimentally the behavior of self-propelled water-in-oil droplets, confined in capillaries different square and circular cross-sections. The droplet's activity comes from formation swollen micelles at its interface. In straight velocity droplet decreases with increasing confinement. However very high confinement, converges toward a non-zero value, so that even long droplets swim. Stretched are then used to explore higher lubrication layer around takes non-uniform thickness which constitutes significant difference usual flow-driven passive droplets. A neck forms rear droplet, deepens eventually undergoes successive spontaneous splitting events for large enough Such observations stress critical role interface on under propose an analytical formulation by integrating transport problem into classical Bretherton approach. model accounts convergence finite value non-classical shape layer. further discuss saturation concentration along interface, would explain divergence leading division.