  Complex fluids in shear flow and biased dynamics in crowded environments
exhibit counterintuitive features which are difficult to address both at
theoretical level and by molecular dynamic simulations. To understand some of
these features we study a schematic model of highly viscous liquid, the 2D
Kob-Andersen kinetically constrained model, driven into non-equilibrium steady
states by a uniform non-Hamiltonian force. We present a detailed numerical
analysis of the microscopic behavior of the model, including transversal and
longitudinal spatial correlations and dynamic heterogeneities. In particular,
we show that at high particle density the transition from positive to negative
resistance regimes in the current vs field relation can be explained via the
emergence of nontrivial structures that intermittently trap the particles and
slow down the dynamics. We relate such spatial structures to the current vs
field relation in the different transport regimes.
