  Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of
high interest because of its role in biological processes such as transport in
cell membranes. In partially phase-separated solutions, gradient-driven
diffusion affects microstructure, which in turn affects diffusivity; a key
question is how this complex coupling controls both transport and pattern
formation. To examine these mechanisms, we study a two-dimensional
multi-component lattice gas model, where "tracer" molecules diffuse between a
source and a sink separated by a solution of sticky "crowder" molecules that
cluster to form dynamically evolving obstacles. In the high temperature limit,
crowders and tracers are miscible and transport may be predicted analytically.
At intermediate temperatures, crowders phase separate into clusters that drift
toward the tracer sink. As a result, steady-state tracer diffusivity depends
non-monotonically on both temperature and crowder density and we observe a
variety of complex microstructures. In the low temperature limit, crowders
rapidly aggregate to form obstacles that are kinetically arrested; if crowder
density is near the percolation threshold, resulting tracer diffusivity shows
scaling behavior with the same scaling exponent as the random resistor network
model. Though highly idealized, this simple model reveals fundamental
mechanisms governing coupled gradient-driven diffusion, phase separation, and
microstructural evolution in crowded solutions.
