Stability of respiratory-like droplets under evaporation

Recent studies have shown that enveloped viruses contained in airborne respiratory droplets lose infectability fastest at intermediate ambient relative humidities $H_r$. However, the precise physicochemical mechanisms that generate such least-favorable conditions for the virus are not fully understood yet. Studying the evaporation dynamics of respiratory-like droplets in air experimentally and analytically, we reveal that at high $H_r$, the salt dissolved in respiratory drops inhibits their evaporation indefinitely. Conversely, at low $H_r$ the drop evaporates leaving a porous solid residue, inside which virions may remain dormant for long times. We conclude that the optimal relative humidity for minimal infectability should coincide with droplets containing the maximum concentration of salt for longest periods of time.

Figure 1

Experimental images of evaporating droplets semilevitating on top of the superhydrophobic substrate. Time evolves increasing from the leftmost column $t=0$ to the rightmost $t=t_f$, where $t_f$ corresponds to the final evaporation time of a water droplet of approximately 3 $\mu \mathrm{l}$ at 80% RH for the first and second rows. Notably, while the water droplet completely evaporates (first row), the model respiratory droplet (second row) remains stable indefinitely. A model respiratory droplet evaporating at a relative humidity below the deliquescence limit (third row) leaves a solid but hollow residue, with a structure that depends on the relative amount of solutes initially dissolved and the evaporation process.

Figure 2

(a) We show experimental curves of the droplet volume, as $V{\left(t\right)}^{2/3}-V_0^{2/3}$ (in ${\mathrm{mm}}^2$), against time (in seconds) for a wide range of humidities. The colormap on the left indicates the relative humidity of each experiment [also in panels (b, c)]. Composition of droplets is denoted by symbols (see the top legend). Additionally we show data for pure water droplets at three different relative humidities. For humidities smaller than $H_{\mathrm{r}}=0.75$, the experimental curves end when the drop has dissolved completely. (b) Normalized droplet volume, ${(V\left(t\right)/V_0)}^{2/3}$, against a dimensionless time $\tilde{t}=t/t_d$ with $t_d$ being a diffusive evaporative timescale [27]. Using the normalization, which is independent of the droplet content, all experiments for $H_{\mathrm{r}}⩾0.75$ overlap. We furthermore plot two asymptotic limits of the evaporation process: the gray line denotes the linear model of volume reduction for pure water droplets. The dash-dotted green line indicates the prediction for the stable volume, based on the initial sodium chloride concentration in the droplets and the saturation concentration. (c) Comparison between experimental data and analytical model. The graph shows the normalized droplet volume ${(V/V_0)}^{2/3}$ with $V_0=V(t=0)$, against the normalized time $\tilde{t}$, as also shown in Fig. 2 of the main manuscript. As denoted in the legend, experimental data is shown with symbols, the analytical model with a line. The symbols for the experimental data were chosen in accordance with the other plots in this study. We present an example corresponding to a relative humidity 0.81. The model yields very good agreement with the experimental data for all the relative humidities explored, and in both limiting regimes: the diffusion-limited evaporation regime and the final stable volume.

Figure 3

(a) Time evolution, computed using our model, of the mass concentration of NaCl in a droplet with initial radius $R_0=0.7$ mm containing only this salt, for three different humidities. In those cases where the droplet dissolves completely, the diamond markers indicate the final evaporation time. The horizontal dashed line marks the salt saturation value: mass salt fraction 26%. (b) Concentration of sodium chloride in solution in stable liquid droplets. The mass of sodium chloride is computed based on the initial concentration in solution. The concentration $c_{\text{NaCl},\text{stable}}$ denotes the mass of sodium chloride per unit volume in the stable drop. The red line in this plot corresponds to the saturation concentration at ${20}^{\circ }\mathrm{C}$: 313 g/l. Note that this concentration is given as mass per volume of solution in a stable drop. The yellow line denotes the analytical model, discussed in the text. The droplets tend to stabilize at lower salt concentrations as the relative humidity increases.

Figure 4

Scanning electron micrographs taken from the remains of dried droplets containing (a) sodium chloride (initial droplet volume 3.5 $\mu \mathrm{l}$), (b) sodium chloride and mucin (initial droplet volume 1.4 $\mu \mathrm{l}$), and (c, d) sodium chloride, mucin and surfactant (respiratory-like droplets with initial volume 1.6 and 2.2 $\mu \mathrm{l},$ respectively). All scale bars correspond to 100 $\mu \mathrm{m}$. The micrographs are taken facing the superhydrophobic substrate [25, 27] where the droplets are deposited.