  We study the question of periodic homogenization of a variably scaled
reaction-diffusion problem with non-linear drift posed for a domain crossed by
a flat composite thin layer. The structure of the non-linearity in the drift
was obtained in earlier works as hydrodynamic limit of a totally asymmetric
simple exclusion process (TASEP) process for a population of interacting
particles crossing a domain with obstacle.
  Using energy-type estimates as well as concepts like thin-layer convergence
and two-scale convergence, we derive the homogenized evolution equation and the
corresponding effective model parameters for a regularized problem. Special
attention is paid to the derivation of the effective transmission conditions
across the separating limit interface in essentially two different situations:
(i) finitely thin layer and (ii) infinitely thin layer.
  This study should be seen as a preliminary step needed for the investigation
of averaging fast non-linear drifts across material interfaces -- a topic with
direct applications in the design of thin composite materials meant to be
impenetrable to high-velocity impacts.
