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Gradient-driven diffusion in crowded, multicomponent mixtures is a topic ofhigh interest because of its role in biological processes such as transport incell membranes. In partially phase-separated solutions, gradient-drivendiffusion affects microstructure, which in turn affects diffusivity; a keyquestion is how this complex coupling controls both transport and patternformation. To examine these mechanisms, we study a two-dimensionalmulti-component lattice gas model, where "tracer" molecules diffuse between asource and a sink separated by a solution of sticky "crowder" molecules thatcluster 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 drifttoward the tracer sink. As a result, steady-state tracer diffusivity dependsnon-monotonically on both temperature and crowder density and we observe avariety of complex microstructures. In the low temperature limit, crowdersrapidly aggregate to form obstacles that are kinetically arrested; if crowderdensity is near the percolation threshold, resulting tracer diffusivity showsscaling behavior with the same scaling exponent as the random resistor networkmodel. Though highly idealized, this simple model reveals fundamentalmechanisms governing coupled gradient-driven diffusion, phase separation, andmicrostructural evolution in crowded solutions.

Gradient-driven diffusion and pattern formation in crowded mixtures