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.

Kinetic Monte Carlo and hydrodynamic modeling of droplet dynamics on surfaces, including evaporation and condensation

“…Ref. [35] -but the results presented here showing that the DFT is also accurate at some temperatures for describing the contact angle and the other related interfacial properties have not been performed before for a 2D model, to the best of our knowledge.…”

“…[24], or DFT can also be applied to develop coarse-grained mesoscopic theories such as those described in Refs. [33][34][35]. Thin-film equation based models are also widely used [2,[19][20][21][22] and if thermal fluctuations are important, these can also be incorporated, creating stochastic thin-film equation models [36,37].…”

Classical dynamical density functional theory: from fundamentals to applications

“…Moreover, DDFT for binary mixtures has been applied to model anisotropic pair correlations [286], bubble dynamics [451], chemical reactions [52,416,417,452], CO 2 dissolving in poly (lactic acid) melt [453], colloid-polymer mixtures [203], demixing on a sphere [454,455], derivation of a PFC model for binary mixtures [380,456], disease spreading [50,420], evaporating nanoparticle suspensions [457][458][459][460], field-driven demixing [306], instabilities in driven systems [324,325], particles switching between two states [461], pattern formation [462], polymer-particle suspensions [210], protein adsorption [463,464], sheared polymer nanocomposites [51], sedimentation [465], selectivity effects [201], solvation dynamics [466][467][468][469], stratification [188,339], surfactant mixtures [419], and the Brazil nut effect [294],…”

“…A simple finite-difference integration scheme for deterministic DDFT can be found in Ref. [460]. Discretization of deterministic DDFT is discussed in Ref.…”

“…DDFT models allow to analyze a variety of effects in the context of dewetting and evaporation, such as spinodal decomposition, nucleation, and fingering [457][458][459]. Moreover, a thermodynamic equivalent of the coffee-ring stain effect can be found [460]. A review is given by Ref.…”