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

TL;DR

This paper develops a dynamical density functional theory model to simulate nanoparticle droplet evaporation, capturing phase separation and deposition patterns without fluid flow dynamics.

Contribution

It introduces a DDFT-based lattice gas model for nanoparticle suspension drying, emphasizing thermodynamic effects over hydrodynamics and linking contact angle to microscopic interactions.

Findings

Replicates coffee-ring effect thermodynamically

Shows phase separation influences nanoparticle deposition

Connects contact angle with microscopic parameters

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.