  Describing particle transport at the macroscopic or mesoscopic level in
non-ideal environments poses fundamental theoretical challenges in domains
ranging from inter and intra-cellular transport in biology to diffusion in
porous media. Yet, often the nature of the constraints coming from many-body
interactions or reflecting a complex and confining environment are better
understood and modeled at the microscopic level.
  In this paper we investigate the subtle link between microscopic exclusion
processes and the mean-field equations that ensue from them in the continuum
limit. We derive a generalized nonlinear advection diffusion equation suitable
for describing transport in a inhomogeneous medium in the presence of an
external field. Furthermore, taking inspiration from a recently introduced
exclusion process involving agents with non-zero size, we introduce a modified
diffusion equation appropriate for describing transport in a non-ideal fluid of
$d$-dimensional hard spheres.
  We consider applications of our equations to the problem of diffusion to an
absorbing sphere in a non-ideal self-crowded fluid and to the problem of
gravitational sedimentation. We show that our formalism allows one to recover
known results. Moreover, we introduce the notions of point-like and extended
crowding, which specify distinct routes for obtaining macroscopic transport
equations from microscopic exclusion processes.
