Dynamical density functional theory for the evaporation of droplets of nanoparticle suspension

Abstract

We develop a lattice gas model for the drying of droplets of a nanoparticle suspension on a planar surface, using dynamical density functional theory (DDFT) to describe the time evolution of the solvent and nanoparticle density profiles. The DDFT assumes a diffusive dynamics but does not include the advective hydrodynamics of the solvent, so the model is relevant to highly viscous or near to equilibrium systems. Nonetheless, we see an equivalent of the coffee-ring stain effect, but in the present model it occurs for thermodynamic rather the fluid-mechanical reasons. The model incorporates the effect of phase separation and vertical density variations within the droplet and the consequence of these on the nanoparticle deposition pattern on the surface. We show how to include the effect of slip or no-slip at the surface and how this is related to the receding contact angle. We also determine how the equilibrium contact angle depends on the microscopic interaction parameters.

35 pages, 10 figures

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• Kinetic Monte Carlo and hydrodynamic modelling of droplet dynamics on surfaces, including evaporation and condensation
• Coexisting multiphase and interfacial behaviour of ouzo
• Dynamics of particle aggregation in dewetting films of complex liquids
• Stability of nanoparticle laden aerosol liquid droplets
• Timescales for stochastic barrier crossing: inferring the potential from nonequilibrium data
• Classical density functional theory for nanoparticle-laden droplets
• Interactions between droplets in immiscible liquid suspensions and the influence of surfactants
• Nonequilibrium statistics of barrier crossings with competing pathways