Dynamical Density Functional Theory for the Evaporation of Droplets of Nanoparticle Suspension

Density Functional Theory Approach to Interpret Elastowetting of Hydrogels

Sessile hydrogel drops on rigid surfaces exhibit a wetting/contact morphology intermediate between liquid drops and glass spheres. Using density functional theory, we reveal the contact forces acting between a hydrogel and a rigid glass surface. We show that while transitioning from liquid-like to solid-like hydrogels, there exists a critical hydrogel elasticity that enables a switch from attractive-to-repulsive interaction with the underlying rigid glass surface. Our theoretical model is validated by experimental observations of sessile polyacrylamide hydrogels of varying elasticity on glass surfaces. Further, the proposed model successfully approaches Young's law in the pure liquid limit and work of adhesion in the glassy limit. Lastly, we show a modified contact angle relation, taking into account the hydrogel elasticity to explain the features of a distinct hydrogel foot.

Binding potential and wetting behavior of binary liquid mixtures on surfaces

We present a theory for the interfacial wetting phase behavior of binary liquid mixtures on rigid solid substrates, applicable to both miscible and immiscible mixtures. In particular, we calculate the binding potential as a function of the adsorptions, i.e., the excess amounts of each of the two liquids at the substrate. The binding potential fully describes the corresponding interfacial thermodynamics. Our approach is based on classical density functional theory. Binary liquid mixtures can exhibit complex bulk phase behavior, including both liquid-liquid and vapor-liquid phase separation, depending on the nature of the interactions among all the particles of the two different liquids, the temperature, and the chemical potentials. Here we show that the interplay between the bulk phase behavior of the mixture and the properties of the interactions with the substrate gives rise to a wide variety of interfacial phase behaviors, including mixing and demixing situations. We find situations where the final state is a coexistence of up to three different phases. We determine how the liquid density profiles close to the substrate change as the interaction parameters are varied and how these determine the form of the binding potential, which in certain cases can be a multivalued function of the adsorptions. We also present profiles for sessile droplets of both miscible and immiscible binary liquids.

Stability of nanoparticle laden aerosol liquid droplets

We develop a model for the thermodynamics and evaporation dynamics of aerosol droplets of a liquid, such as water, surrounded by gas. When the temperature and the chemical potential (or equivalently the humidity) are such that the vapor phase is in the thermodynamic equilibrium state, then, of course, droplets of the pure liquid evaporate over a relatively short time. However, if the droplets also contain nanoparticles or any other non-volatile solute, then the droplets can become thermodynamically stable. We show that the equilibrium droplet size depends strongly on the amount and solubility of the nanoparticles within, i.e., on the nature of the particle interactions with the liquid and, of course, also on the vapor temperature and chemical potential. We develop a simple thermodynamic model for such droplets and compare predictions with results from a lattice density functional theory that takes as input the same particle interaction properties, finding very good agreement. We also use dynamical density functional theory to study the evaporation/condensation dynamics of liquid from/to droplets as they equilibrate with the vapor, thereby demonstrating droplet stability.

Dynamic density functional theory for sedimentation processes on complex domains: Modelling, spectral elements, and control problems

Modelling of many real-world processes, such as drug delivery, wastewater treatment, and pharmaceutical production, requires accurate descriptions of the dynamics of hard particles confined in complicated domains. In particular, when modelling sedimentation processes or systems with driven flows, it is important to accurately capture volume exclusion effects. This work applies Dynamic Density Functional Theory to the evolution of a particle density under diffusion, external forces, particle-particle interaction, and volume exclusion. Using a spectral element framework, for the first time it is possible to include all of these effects in dynamic simulations on complex domains. Moreover, this allows one to apply complicated no-flux, and other non-local, non-linear, boundary conditions. The methodology is also extended to control problems, addressing questions of how to enhance production set-up in industrially-motivated processes. In this work the relevant models are introduced, numerical methods are discussed, and several example problems are solved to demonstrate the methods' versatility. It is shown that incorporating volume exclusion is crucial for simulation accuracy and we illustrate that the choice of boundary conditions significantly impacts the dynamics.

Evaporation in nano/molecular materials

Evaporation is a physical phenomenon with fundamental significance to both nature and technology ranging from plant transpiration to DNA engineering. Various analytical and empirical relationships have been proposed to characterize evaporation kinetics at macroscopic scales. However, theoretical models to describe the kinetics of evaporation from nano and sub-nanometer (molecular) confinements are absent. On the other hand, the fast advancements in technology concentrated on development of nano/molecular-scale devices demand appropriate models that can accurately predict physics of phase-change in these systems. A thorough understanding of the physics of evaporation in nano/molecular materials is, thus, of critical importance to develop the required models. This understanding is also crucial to explain the intriguing evaporation-related phenomena that only take place when the characteristic length of the system drops to several nanometers. Here, we comprehensively review the underlying physics of evaporation phenomenon and discuss the effects of nano/molecular confinement on evaporation. The role of liquid-wall interface-related phenomena including the effects of disjoining pressure and flow slippage on evaporation from nano/molecular confinements are discussed. Different driving forces that can induce evaporation in small confinements, such as heat transfer, pressure drop, cavitation and density fluctuations are elaborated. Hydrophobic confinement induced evaporation and its potential application for synthetic ion channels are discussed in detail. Evaporation of water as molecular clusters rather than isolated molecules is discussed. Despite the lack of experimental investigations on evaporation at nanoscale, there exist an extensive body of literature that have applied different simulation techniques to predict the phase change behavior of liquids in nanoconfinements. We infer that exploring the effect of electrostatic interactions and flow slippage to enhance evaporation from nanoconduits is an interesting topic for future endeavors. Further future studies could be devoted to developing nano/molecular channels with evaporation-based gating mechanism and utilization of 2D materials to tune energy barrier for evaporation leading to enhanced evaporation.

Evaporation Mass Flux: A Predictive Model and Experiments

Evaporation is a fundamental and core phenomenon in a broad range of disciplines including power generation and refrigeration systems, desalination, electronic/photonic cooling, aviation systems, and even biosciences. Despite its importance, the current theories on evaporation suffer from fitting coefficients with reported values varying in a few orders of magnitude. Lack of a sound model impedes simulation and prediction of characteristics of many systems in these disciplines. Here, we studied evaporation at a planar liquid-vapor interface through a custom-designed, controlled, and automated experimental setup. This experimental setup provides the ability to accurately probe thermodynamic properties in vapor, liquid, and close to the liquid-vapor interface. Through analysis of these thermodynamic properties in a wide range of evaporation mass fluxes, we cast a predictive model of evaporation based on nonequilibrium thermodynamics with no fitting parameters. In this model, only the interfacial temperatures of liquid and vapor phases along with the vapor pressure are needed to predict evaporation mass flux. The model was validated by the reported study of an independent research group. The developed model provides a foundation for all liquid-vapor phase change studies including energy, water, and biological systems.