Hydrodynamic approximations for driven dense colloidal mixtures in narrow pores

TL;DR

This paper investigates driven dense colloidal mixtures in various geometries, deriving hydrodynamic approximations to analyze particle diffusion, mobility, and separation phenomena like the 'Brazil nut' effect, with implications for particle sorting.

Contribution

It introduces a hydrodynamic mean-field approximation for driven dense colloids, providing analytical and numerical insights into diffusion, mobility, and size-based separation in confined geometries.

Findings

The 'Brazil nut' effect occurs generically in mixtures.

Analytical solutions are obtained in one dimension.

The study demonstrates the potential for perfect particle separation.

Abstract

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 non-linear 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.