Inter-particle ratchet effect determines global current of heterogeneous particles diffusing in confinement

Abstract

In a model of N volume-excluding spheres in a d-dimensional tube, we consider how differences between the drift velocities, diffusivities, and sizes of particles influence the steady-state distribution and axial particle current. We show that the model is exactly solvable when the geometrical constraints prevent any particle from overtaking all others—a notion we term quasi-one-dimensionality. Then, due to a ratchet effect, the current is biased towards the velocities of the least diffusive particles. We consider special cases of this model in one dimension, and derive the exact joint gap distribution for driven tracers in a passive bath. We describe the relationship between phase-space structure and irreversible drift that makes the quasi-one-dimensional (q1D) supposition key to the model’s solvability.