Diffusion in evaporating solutions
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We present an analysis of the colloidal dynamics of particles in a mixture of two solvents subjected to evaporation. For simplicity, only one out of the two solvents is considered to be volatile. The evaporation generates a distribution of the solvent concentration in the system. As the particles selectively interact with the solvents, their migration becomes affected by a "chemotaxis" force, caused by the gradient in the solvation energy along the diffusion path. The net particle flux is the result of the interplay between the migration under the action of the chemotaxis and the bulk convection flow caused by the evaporation. The most unusual features of the particle migration occur when the particles have an affinity to the evaporating solvent. In this case, the particles may diffuse against the concentration gradient and form bands with increased particle concentration, i.e., undergo focusing. The resulting particle concentration patterns are strongly dependent on the geometry of the container in which the evaporation occurs. This model has important practical applications. It provides a framework for understanding and controlling the skin formation at the surface of evaporating colloidal suspensions, an effect that is briefly illustrated experimentally on the example of ink-jet printing. On a thermodynamic level, the model is also applicable to cases, in which the third component is molecularly dispersed, although a smaller magnitude of the effects is predicted.