Shrinking of Rapidly Evaporating Water Microdroplets Reveals their Extreme Supercooling

The fast evaporative cooling of micrometer-sized water droplets in a vacuum offers the appealing possibility to investigate supercooled water—below the melting point but still a liquid—at temperatures far beyond the state of the art. However, it is challenging to obtain a reliable value of the droplet temperature under such extreme experimental conditions. Here, the observation of morphology-dependent resonances in the Raman scattering from a train of perfectly uniform water droplets allows us to measure the variation in droplet size resulting from evaporative mass losses with an absolute precision of better than 0.2%. This finding proves crucial to an unambiguous determination of the droplet temperature. In particular, we find that a fraction of water droplets with an initial diameter of $6379\pm 12\mathrm{nm}$ remain liquid down to $230.6\pm 0.6\mathrm{K}$. Our results question temperature estimates reported recently for larger supercooled water droplets and provide valuable information on the hydrogen-bond network in liquid water in the hard-to-access deeply supercooled regime.

Figure 1

Stroboscopic image of the liquid water jet emerging from a $3.2\pm 0.1\text{−}\mu \mathrm{m}$-diameter glass capillary nozzle. The jet was illuminated by $\approx 8$-ns-long fluorescent light pulses and imaged on a $2048\times 2048$ CCD camera equipped with a $12\times$ objective at the working distance of 86 mm. The jet breakup was triggered by an external excitation at the frequency of 966 kHz to produce a periodic stream of uniform water droplets.

Figure 2

Normalized and two-point baseline-corrected Raman spectra measured as a function of the distance from the nozzle, indicated by labels in both panels. The thick black solid curve is a fit to the experimental spectrum at $z=0.9\mathrm{mm}$ by assuming five Gaussian functions for the $\mathrm{O}─\mathrm{H}$ stretching band (shown as thin solid lines) and five additional Gaussian peaks for the resonances (shown as filled curves).

Figure 3

Droplet diameter and temperature as a function of the distance from the nozzle, i.e., travel time $t=z/v$ (upper $x$ axis). (a) Droplet diameter determined from the Raman shifts of the resonance peaks by the iterative approach described in the main text and based on Eq. (4) (filled symbols). The error bars represent standard deviations obtained by an error propagation analysis. The thick solid curve is a fit to the data points based on the Knudsen model of evaporative cooling. The light-shaded region indicates the 68% confidence interval for the model parameters $D_0$ and $v$, whose standard deviations were obtained by least-squares fits to independent synthetic data sets sampled from the experimental data points [26]. (b) The thick solid curve is the calculated volume-averaged droplet temperature corresponding to the fit shown in (a). The temperature uncertainty is represented by the line thickness. The open circles represent the droplet temperature obtained from the analysis of the shape of the Raman $\mathrm{O}─\mathrm{H}$ stretching bands shown in Fig. 4. The error bars are smaller than the symbol size.

Figure 4

Fundamental $\mathrm{O}─\mathrm{H}$ stretching bands obtained by subtracting the contribution of the resonances from the Raman spectra in Fig. 2. For clarity, only the bands up to $z=25.4\mathrm{mm}$ are shown. The inset shows the calibration data (filled circles) plotted as the inverse of the temperature against the natural logarithm of the ratio of the integrated band intensities $I_{<\mathrm{\Delta }{\nu }^{*}}$ and $I_{>\mathrm{\Delta }{\nu }^{*}}$ below and above $\mathrm{\Delta }{\nu }^{*}=3360{\mathrm{cm}}^{-1}$, respectively. The solid line is a linear fit that was extrapolated to the supercooled region in order to determine the droplet temperature from the bands in the main figure.