Classical density functional theory for nanoparticle-laden droplets

Droplets of a pure fluid, such as water, in an open container surrounded by gas, are thermodynamically unstable and evaporate quickly. In a recent paper [Archer et al. J. Chem. Phys. {\bf 159}, 194403 (2023)] we employed lattice density functional theory (DFT) to demonstrate that nanoparticles or solutes dissolved in a liquid droplet can make it thermodynamically stable against evaporation. In this study, we extend our model by using continuum DFT, which allows for a more accurate description of the fluid and nanoparticle density distributions within the droplet and enables us to consider size ratios between nanoparticles and solvent particles up to 10:1. While the results of the continuum DFT agrees well with those of our earlier lattice DFT findings, our approach here allows us to refine our understanding of the stability and structure of nanoparticle laden droplets. This is particularly relevant in light of the recent global COVID-19 pandemic, which has underscored the critical role of aerosol particles in virus transmission. Understanding the stability and lifetime of these viron-laden aerosols is crucial for assessing their impact on airborne disease spread.

💡 Research Summary

This research presents a significant advancement in understanding the thermodynamic stability of nanoparticle-laden droplets through the application of Continuum Density Functional Theory (cDFT). Pure liquid droplets, such as water, are inherently unstable in open environments due to rapid evaporation. However, the presence of solutes or nanoparticles can stabilize these droplets against evaporation by altering the chemical potential and vapor pressure at the interface. Building upon previous lattice-based DFT models, this study introduces a more sophisticated continuum approach to provide a highly accurate description of fluid and nanoparticle density distributions.

The core methodology involves a dual-approach to particle interactions to overcome the limitations of discrete lattice models. To account for the hard-sphere (HS) repulsion and the excluded volume effects, the researchers employed Fundamental Measure Theory (FMT). To model the short-range attractive forces, a Square-Well (SW) potential was implemented using the Random Phase Approximation (RPA) within a mean-field framework. A major breakthrough of this study is the expansion of the size ratio between nanoparticles and solvent particles up to 10:1. This expansion is crucial because it allows the model to realistically simulate the physical characteristics of virus-sized particles within much smaller solvent droplets, a feat that was previously limited by the discrete nature of lattice-based models.

By assuming spherical symmetry, the study calculates the one-particle correlation function $c^{(1)}_i(r)$ to derive self-consistent density distributions $\rho_i(r)$. The results demonstrate that the continuum DFT approach aligns well with earlier lattice DFT findings while offering much-needed refinement in structural and stability analysis, particularly regarding how larger particles influence the internal density profiles.

The implications of this work extend far beyond theoretical physics into the realm of global public health. The stability and lifetime of virion-laden aerosols are critical factors in the transmission dynamics of airborne diseases, as demonstrated during the COVID-19 pandemic. By providing a precise mathematical framework to predict how nanoparticles influence the evaporation and longevity of droplets, this research offers essential tools for assessing the risks of aerosol-based disease spread and developing more effective containment strategies. Understanding the interplay between particle size, concentration, and thermodynamic stability is fundamental to modeling the environmental persistence of pathogens in the atmosphere.