  A colloidal particle placed in an inhomogeneous solution of smaller
non-adsorbing polymers will move towards regions of lower polymer
concentration, in order to reduce the free energy of the interface between the
surface of the particle and the solution. This phenomenon is known as
diffusiophoresis. Treating the polymer as penetrable hard spheres, as in the
Asakura-Oosawa model, a simple analytic expression for the diffusiophoretic
drift velocity can be obtained. In the context of drying films we show that
diffusiophoresis by this mechanism can lead to stratification under easily
accessible experimental conditions. By stratification we mean spontaneous
formation of a layer of polymer on top of a layer of the colloid. Transposed to
the case of binary colloidal mixtures, this offers an explanation for the
stratification observed recently in these systems [A. Fortini et al, Phys. Rev.
Lett. 116, 118301 (2016)]. Our results emphasise the importance of treating
solvent dynamics explicitly in these problems, and caution against the neglect
of hydrodynamic interactions or the use of implicit solvent models in which the
absence of solvent backflow results in an unbalanced osmotic force which gives
rise to large but unphysical effects.
