  Transport of material across liquid interfaces is ubiquitous for living cells
and is also a crucial step in drug delivery and in many industrial processes.
The fluids that are present on either side of the interfaces will usually have
different viscosities. We present a physical model for the dynamics of
microswimmers near a soft and penetrable interface that we solve using computer
simulations of Navier-Stokes flows. The literature contains studies of similar
isoviscous fluid systems, where the two fluids have the same viscosity. Here we
extend this to the more general case where they have different viscosities. We
investigate the effect of the fluid viscosity ratio on the movement patterns of
microswimmers. We find that swimmers systematically reorientate towards the
region containing the lower viscosity fluid. Ultimately this is expected to
drive the swimmers to behave as if they are more inclined to swim in low
viscosity fluids. Furthermore, in addition to the types of swimming already
reported in the isoviscous system, i.e. bouncing, sliding and penetrating, we
observed a hovering motion, in which strong pullers swim parallel to the
interface with a certain distance, which is consistent with the dynamics of
such swimmers near the solid wall.
