Combined effects of evaporation, sedimentation and solute crystallization on the dynamics of aerosol size distributions on multiple length and time scales

TL;DR

By integrating sharp-interface, molecular-dynamics, and diffuse-interface modeling, the paper delivers a multi-scale analysis of aerosol drying and its implications for airborne infection risk. The sharp-interface framework provides an exact time-dependent droplet-size distribution and viral-load dependence on relative humidity $RH$, the MD analysis quantifies the interfacial water reflection coefficient $p_{ref}$ and its dependence on velocity and incidence, and the diffuse-interface CH/AC model generalizes evaporation to include solute crystallization and crust formation within a thermodynamically consistent PDE system. The findings show that increasing humidity suppresses long-time airborne virions, while crust formation can slow or halt evaporation, emphasizing the need to incorporate interface physics when assessing infection risk. Together, these results offer a coherent, scalable toolkit for predicting aerosol behavior and informing public-health guidance across environmental conditions.

Abstract

We investigate three aspects of aerosol-mediated air-borne viral infection mechanisms on different length and time scales. First, we address the evolution of the size distribution of a non-interacting ensemble of droplets that are subject to evaporation and sedimentation using a sharp droplet-air interface model. From the exact solution of the evolution equation we derive the viral load in the air and show that it depends sensitively on the relative humidity. Secondly, from Molecular Dynamics simulations we extract the molecular reflection coefficient of single water molecules from the air-water interface. This parameter determines the water condensation and evaporation rate at a liquid droplet surface and therefore the evaporation rate of aqueous droplets. We find the reflection of water to be negligible at room temperature but to rise significantly at elevated temperatures and for grazing incidence angles. Thirdly, we derive a thermodynamically consistent three-dimensional diffuse-interface model for solute-containing droplets that is formulated as a three-phase Cahn-Hilliard/Allen-Cahn system. By numerically solving the coupled system of equations, we explore representative scenarios that show that this model reproduces and generalizes features of the sharp-interface model. These interconnected studies on the dynamics of aerosol droplet evaporation are relevant in order to quantitatively assess the airborne infection risk under varying environmental conditions.

Figures (12)

• Figure 1: Fraction of suspended virions $\phi_\mathrm{s}(t)$ as a function of time $t / \tau$ for different relative humidities $RH$, using initial droplet distributions given by (a) a normal distribution, \ref{['eq:gaussian']}, and (b) a log-normal distribution, \ref{['eq:lognormal']}. The characteristic time scale $\tau$ is given by $\tau = R_0^2 / \theta$.
• Figure 2: (a) Simulation snapshot. The angle of incidence $\beta$ is defined as the angle between the initial velocity vector (black arrow) and the surface normal of the water slab (black dotted line). (b) Molecular reflection coefficient $p_\mathrm{ref}$ as a function of the velocity of the impinging water molecule. The histogram combines data from all three sets of simulations with different initial velocity distributions. Average velocities according to $\sqrt{k_\mathrm{B} T / m_\mathrm{w}}$ for $T = \unit[300]{K}$ (red), $\unit[1200]{K}$ (green), and $\unit[4800]{K}$ (purple) are indicated by vertical dashed lines. (c) Molecular reflection coefficient $p_\mathrm{ref}$ as a function of the angle of incidence $\beta$ of the impinging water molecule for initial velocities drawn from a Maxwell-Boltzmann distribution at $\unit[300]{K}$. (d) Same as (c) but for initial velocities drawn from a Maxwell-Boltzmann distribution at $\unit[1200]{K}$. (e) Same as (c) but for initial velocities drawn from a Maxwell-Boltzmann distribution at $\unit[4800]{K}$. Error bars in all panels indicate the standard error given by \ref{['eq:error']}.
• Figure 3: (a) Potential $W(\varphi)$ from \ref{['choice-W']} for $\Lambda=100$ (solid, blue) compared to standard quartic $18\varphi^2(1-\varphi)^2$ (dotted, gray) and (b) energy landscape $(\Psi-\min\Psi)$ with $\lambda=10$, $\beta=-10$, $\Lambda=100$, $\gamma_\ell=\gamma_c=1/8$, $\gamma_v=2$, $\varepsilon=0.2$, $s_\mathrm{sat}=0.3$ for a homogeneous solution (no gradients) without vapor $\varphi_v=0$, i.e., $\varphi_c=1-\varphi_\ell$ with isolines and negative gradient vector field.
• Figure 4: Solute concentration $s(t,r)$ and phase fields $\varphi_i(t,r)$ for $i=\{\ell,c,v\}$ as a function of time $t$ and radius $r$ for different parameters for Example (a) with $\lambda=1$, $\beta=-1$, $\bar{s}^0=10^{-2}$, where the droplet completely evaporates. The dotted red curve indicates the function $R(t)= (R_0^{1/\alpha}-Ct)^\alpha$ for $\alpha=0.3$.
• Figure 5: Energy $\mathcal{E}$ and different contributions to the dissipation $\mathcal{D}^*$ for the Example (a) shown in \ref{['fig:examples_cryst_a']} and \ref{['fig:examples_cryst_a1']} (left) with the mobilities from \ref{['tab:params']} and (right) with the reduced liquid mobilities $m_{\ell i}=10^{-3}$ for $i\in\{\ell,v,c\}$.