  The interplay of inertia and deformability has a substantial impact on the
transport of soft particles suspended in a fluid. However, to date a thorough
understanding of these systems is still missing and only a limited number of
experimental and theoretical studies is available. We combine the
finite-element, immersed-boundary and lattice-Boltzmann methods to simulate
three-dimensional suspensions of soft particles subjected to planar Poiseuille
flow at finite Reynolds numbers. Our findings confirm that the particle
deformation and inclination increase when inertia is present. We observe that
the Segr\'e-Silberberg effect is suppressed with respect to the particle
deformability. Depending on the deformability and strength of inertial effects,
inward or outward lateral migration of the particles takes place. In
particular, for increasing Reynolds numbers and strongly deformable particles,
a hitherto unreported distinct flow focusing effect emerges which is
accompanied by a non-monotonic behaviour of the apparent suspension viscosity
and thickness of the particle-free layer close to the channel walls. This
effect can be explained by the behaviour of a single particle and the change of
the particle collision mechanism when both deformability and inertia effects
are relevant.
