Polymer transport is investigated, in the limit of the so-called
dumb-bell model, for two paradigmatic laminar flows having pen and
closed streamlines, respectively. For both types flows we find
transport depletion wing to the action of the polymers elastic degree
of freedom. For flows with closed streamlines the leading mechanism for
the observed transport reduction is the ( dynamical) formation of
barriers. For flows with open streamlines the reduction of transport is
induced by the renormalization of the bare diffusion coefficient.
Results have been obtained by means of Lagrangian simulations.