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