  Few simulations exist for microswimmers near deformable interfaces. Here, we
present numerical simulations of the hydrodynamic flows associated with a
single microswimmer embedded in a binary fluid mixture. The two fluids demix,
separated by a penetrable and deformable interface that we assume to be
initially prepared in its planar ground-state. We find that the microswimmer
can either penetrate the interface, move parallel to it or bounce back off it.
We analyze how the trajectory depends on the swimmer type (pusher/puller) and
the angle of incidence with respect to the interface. Our simulations are
performed in a system with periodic boundary conditions, corresponding to an
infinite array of fluid interfaces. A puller reaches a steady state in which it
either swims parallel to the interface or selects a perpendicular orientation,
repeatedly penetrating through the interface. In contrast, a pusher follows a
bouncing trajectory between two interfaces. We discuss several examples in
biology in which swimmers penetrate soft interfaces. Our work can be seen as a
highly simplified model of such processes.
