Stratification in drying films – how a mixture of differently-sized particles arranges itself upon drying – is examined. Being able to control this would allow the design of coating formulations which self-assemble during drying to give a desired structure. Potential applications are across a range of industries, from a self-layering car paint, to a biocidal coating in which the biocide stratifies to the top surface, where it is required. Diffusiophoresis is the migration of particles along a concentration gradient of a different solute species. Diffusiophoresis can be caused by different mechanisms, two of which are investigated here: excluded volume and electrolyte-driven diffusiophoresis. A continuum hydrodynamic model is derived, and the resulting partial differential equations solved numerically. Asymptotic solutions are 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. 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. In the case of electrolyte-driven diffusiophoresis, two methods are discovered to control the resulting stratification: (i) setting the surface charge on the particles, and (ii) setting the background salt concentration.
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