The system of driven dense colloid mixtures is studied in one-, two-, and three-dimensional geometries. We calculate the diffusion coefficients and mobilities for each particle type, including cross-terms, in a hydrodynamic limit, using a mean-field-type approximation. The set of nonlinear diffusion equations are then solved. In one dimension, analytical results are possible. We show that in mixtures, the “Brazil nut” phenomenon, or depletion of larger particles by force of smaller ones, appears quite generically. We calculate the ratchet current and quantify the capability of sorting particles according to their size. We also indicate that the “Brazil nut” effect lies behind the possibility of perfect separation, where large and big particles travel in strictly opposite direction.

• Received 22 December 2022
• Accepted 9 June 2023

DOI:https://doi.org/10.1103/PhysRevE.107.064606