Stratification in drying films: diffusiophoresis driven by nanoparticles and their counterions

Recent experimental work has highlighted that electrolyte-driven diffusiophoresis is likely to be the most significant phoretic motion in a mixture of silica nanoparticles and relatively large latex particles, which are commonly used in coatings. In this work, this diffusiophoretic effect, powered by gradients in the nanoparticles and their stabilizing cations, is modelled in drying films. A continuum hydrodynamic model is derived, and the resulting partial differential equations solved numerically. An asymptotic solution is found for high evaporation rate. It is found that the final film structure is governed by the relative magnitudes of the diffusive and diffusiophoretic terms. Two methods are discovered to control the resulting stratification: (i) setting the surface charge on the particles, and (ii) setting the background salt concentration. Either of these can be used to select either small- or large-on-top stratification or a homogenous film. The diffusiophoretic term promotes small-on-top stratification, and so may account for experimental observations of accumulated small particles at the top surface of dried films.