  Small heavy particles in a fluid flow respond to the flow on a time-scale
proportional to their inertia, or Stokes number St. Their behaviour is thought
to be gradually modified as St increases. We show, in the steady
spatially-periodic laminar Taylor-Green flow, that particle dynamics, and their
effective diffusivity, actually change in an irregular, non-monotonic and
sometimes discontinuous manner, with increasing St. At Stokes of order one, we
show chaotic particle motion, contrasting earlier conclusions for heavy
particles in the same flow (Wang et al. 1992). Particles may display trapped
orbits, or unbounded diffusive or ballistic dispersion, with the vortices
behaving like scatterers in a soft Lorentz gas (Klages et al. 2019). The
dynamics is non-ergodic. We discuss the possible consequences of our findings
for particulate turbulent flows.
