Abstract

Ice multiplication processes are known to be responsible for the higher concentration of ice particles versus ice nucleating particles in clouds, but the exact secondary ice formation mechanisms remain to be quantified. Recent in-cloud observations and modeling studies have suggested the importance of secondary ice production upon shattering of freezing drizzle droplets. In one of our previous studies, four categories of secondary ice formation during freezing of supercooled droplets have been identified: breakup, cracking, jetting, and bubble bursts. In this work, we extend the study to include pure water and an aqueous solution of analog sea salt drizzle droplets moving at terminal velocity with respect to the surrounding cold humid air. We observe an enhancement in the droplet shattering probability as compared to the stagnant air conditions used in the previous study. Under free-fall conditions, bubble bursts are the most common secondary ice production mode in sea salt drizzle droplets, while droplet fragmentation controls the secondary ice production in pure water droplets.

1. Introduction

Precipitation, cloud lifetime, and optical properties of mixed-phase clouds are strongly dependent on the presence of ice particles and their interaction with water vapor, liquid droplets, and aerosol particles. However, the microphysical processes that govern the evolution of the ice phase are not well understood and remain a source of uncertainty in numerical weather prediction models (Korolev et al. 2017) as well as in climate simulations (Boucher et al. 2013; Vergara-Temprado et al. 2018). In-cloud observations often show glaciation rates and ice number concentrations that cannot be explained by primary ice formation mechanisms (e.g., Koenig 1963; Mossop et al. 1970; Hobbs and Rangno 1985; Fridlind and Ackerman 2018). Several ice multiplication mechanisms have been proposed to explain the discrepancy between ice crystal number concentration and ice nucleating particle concentration. These are rime splintering (Hallett and Mossop 1974), ice–ice collisions (Vardiman 1978), sublimation fragmentation (Oraltay and Hallett 1989), and the shattering of freezing drizzle droplets (Langham and Mason 1958). The relative contributions of these mechanisms to secondary ice production (SIP) in clouds remain unclear (Field et al. 2017). The Hallett–Mossop process received considerable attention, as it can explain high numbers of secondary ice particles within a limited range of cloud conditions. However, aircraft measurements (e.g., Hobbs and Rangno 1990; Korolev et al. 2020) have demonstrated that high ice number concentrations are also observed when the conditions required for the Hallett–Mossop mechanism are not fulfilled.

Supercooled water droplets freeze in two stages (Pruppacher and Klett 1997). When ice nucleation is initiated, ice dendrites start spreading through the volume of supercooled droplet, a process accompanied by release of the latent heat of fusion. The latent heat cannot be released to the environment within the time span of the first freezing step, which proceeds on a millisecond time scale, but heats the droplet to the melting point of ice. Therefore, only a fraction of ≈ΔT/80 of the droplet’s mass is converted to ice in the first freezing step, with ΔT being the supercooling temperature of the droplet (K) (Pruppacher and Klett 1997). To convert the remaining water to ice during the second freezing step, latent heat is released to the surrounding air through the droplet’s surface, resulting in the formation of an ice shell around the droplet. As ice is less dense than supercooled water, the inward growth of this ice shell exerts pressure onto the interior and the outer shell of the droplet. Depending on ice shell mechanical stability, the pressure can be released in different ways, one of them being the violent fragmentation of the freezing droplet. Evidence for shattering of freezing drizzle droplets in clouds has been earlier provided by Knight and Knight (1974), who found hemispherical fragments of frozen droplets preserved as hailstone embryos. Recently, images of fragments of shattered frozen drizzle droplets have been taken during the in-cloud aircraft-based measurements by Korolev et al. (2020).

Modeling studies by Phillips et al. (2018) suggested that ice crystal number concentration in deep convective clouds could be quantitatively reproduced only by including droplet freeze shattering into the feedback mechanism. The results of Sullivan et al. (2018) indicate that droplet breakup upon freezing is an important secondary ice production mechanism if the ice nucleating aerosol particles are limited in numbers and certain temperature and updraft velocity are reached. Lawson et al. (2015) suggested that fragmentation of freezing droplets contributes to ice enhancement in strong tropical cumulus updraft cores, where the Hallett–Mossop criteria are not met. The results of Qu et al. (2020) hint that freeze-shattering SIP dominates over other SIP mechanisms during the initial stage of formation of deep convective clouds.

Several laboratory studies on the shattering of freezing drops have been conducted in the last century (e.g., Mason and Maybank 1960; Brownscombe and Thorndike 1968; Takahashi and Yamashita 1970; Pruppacher and Schlamp 1975; Kolomeychuk et al. 1975). The experimental methods of that time allowed merely indirect observations of the shattering events. Nowadays, detailed observations of the very fast fragmentation of freezing water droplets are possible due to the advance of high-speed video microscopy. Recently, we have reported on the secondary ice production upon freezing of drizzle droplets by levitating individual water droplets in an electrodynamic balance (EDB; Lauber et al. 2018). In particular, we have confirmed that larger droplets (on the order of 300 μm in diameter) would shatter more often than the small ones (100 μm), and have quantified the fragmentation probability in the temperature range from −5° to −30°C. We have also reported several other potential SIP mechanisms associated with freezing of water drops: cracking, jetting, and bubble bursting (Lauber et al. 2018). However, in the experiments reported in Lauber et al. (2018), the freezing droplets were levitated in stagnant air whereas in real clouds, they fall with terminal velocity relative to the surrounding air. In this study we report on the effects of introducing a flow of cold moist air at terminal velocity on the rates of the potential SIP events.

2. Experiment

As in our previous study (Lauber et al. 2018), we observe freezing of supercooled water droplets of 300 μm in diameter that are levitated in an EDB (Hoffmann et al. 2013). In the setup used here, the single water droplets are exposed to a laminar flow of cold moist air, thus mimicking the free-fall of a drizzle droplet at its terminal velocity. To achieve this, the gas flow through the trap chamber is adjusted until the vertical dc voltage across the EDB is reduced to zero to ascertain that the weight of the droplet is balanced by the drag force of the flow. For a droplet of 300 μm in diameter this condition corresponds to a settling velocity of 1.2 m s−1. Ice nucleation in the droplet is initiated by introducing an LN2-cooled metal pin into the airflow creating a stream of fine ice particles (<5 μm) colliding with the supercooled droplet. The freezing of the droplet and associated SIP events are observed with a high-speed video camera (Phantom V710, Vision Research) equipped with long working distance objective lens. The video sequences of the freezing events have been recorded at a frame rate of 22 000 fps. Afterward, the video records were scrutinized for various SIP events, such as breakups, crackings, bubble bursts, and jettings as introduced in Lauber et al. (2018). The secondary particles could be identified visually if their size exceeded 5 μm and if they were visible at least on two consecutive frames of the record. The unambiguous identification of secondary particle phase (liquid or frozen) was possible only for the fragments produced during droplet shattering. We therefore report only the total apparent number of frozen secondary particles produced during droplet shattering. Contrary to our previous study, the recoils due to mass ejection or charge loss could not be used to detect the visually unidentified SIP events, as the nonspherical frozen droplets would invariably spin and tumble in the airflow.

In total, more than 700 droplets within 10 temperature intervals ranging from −1° to −30°C have been examined. All experiments have been conducted at standard pressure but the flow humidity and droplet composition have been varied. The experimental conditions and the number of observed droplets are summarized in Table 1:

  • Case 1: Pure water droplets in moist airflow

  • Case 2: Pure water droplets in dry airflow

  • Case 3: Aqueous solution of sea salt analog (SSA) droplets in moist airflow

In the “dry” airflow experiments, the dewpoint temperature of the airflow was −30°C. The humidity of the airflow in the experiments with moist airflow corresponds to ice saturation at flow temperature. In all experiments, CHROMASOLV Plus water (Honeywell Riedel-de Haën) was used. For experiments with SSA droplets, 2.9 mg L−1 Instant Ocean (Spectrum Brands) was added to simulate the salt concentration in drizzle droplets formed by coalescence of cloud droplets condensed on sea salt aerosol particles. This concentration is lower than in the previous study (100–2000 mg L−1) and within the salinity range for drizzle droplets of 1–41 mg L−1 observed by Turner (1955).

Table 1.

Summary of the experimental conditions and obtained results for the three experimental cases of this study. The bottom section labeled “Maximum frequency of SIP events” represents the highest observed frequency of an event (e.g., jetting) over the sampled temperature intervals. Uncertainties in the droplet size and in the observed number of secondary ice particles corresponds to the 95% confidence interval assuming normally distributed values. Multiple ejections or repeated cracking of the same droplet are not considered. The uncertainties in the maximum frequency were estimated assuming binomial distribution and correspond to the 95% confidence interval.

Summary of the experimental conditions and obtained results for the three experimental cases of this study. The bottom section labeled “Maximum frequency of SIP events” represents the highest observed frequency of an event (e.g., jetting) over the sampled temperature intervals. Uncertainties in the droplet size and in the observed number of secondary ice particles corresponds to the 95% confidence interval assuming normally distributed values. Multiple ejections or repeated cracking of the same droplet are not considered. The uncertainties in the maximum frequency were estimated assuming binomial distribution and correspond to the 95% confidence interval.
Summary of the experimental conditions and obtained results for the three experimental cases of this study. The bottom section labeled “Maximum frequency of SIP events” represents the highest observed frequency of an event (e.g., jetting) over the sampled temperature intervals. Uncertainties in the droplet size and in the observed number of secondary ice particles corresponds to the 95% confidence interval assuming normally distributed values. Multiple ejections or repeated cracking of the same droplet are not considered. The uncertainties in the maximum frequency were estimated assuming binomial distribution and correspond to the 95% confidence interval.

3. Results

The secondary ice production events observed during the freezing process were classified into the secondary ice production categories defined in Lauber et al. (2018). These are breakup, cracking, jetting, surface bubble burst and spicular bubble burst. Breakup (Fig. 1) is the splitting of the freezing droplet into two large parts, while sometimes ejecting a smaller ice particle as well. On rare occasions, we have observed droplets shattering into three or more parts. Breakups can be further subcategorized into complete and incomplete breakups. During incomplete breakups, the water bridging the two halves freezes, holding them together and thus preventing the production of large secondary ice particles. When the breakup does not lead to shattering and the halves seal back together, the event is termed cracking (Fig. 2). Jetting (Fig. 3) is the sudden ejection of liquid from the freezing droplet. Both cracking and jetting do not result in a sufficient reduction of the internal pressure to terminate the pressure buildup, as a freezing droplet can exhibit cracking and/or jetting once or twice and still break up at a later stage of freezing. Ejection can also be observed during bubble bursts occurring either at the tip of a spicule (Fig. 4) or directly on the droplet’s surface (Fig. 5).

Fig. 1.

Breakup of a droplet into two large hemispheres while ejecting a small ice particle. Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Fig. 1.

Breakup of a droplet into two large hemispheres while ejecting a small ice particle. Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Fig. 2.

Cracking expressed by first splitting of the freezing droplet and then closing and sealing together of the two hemispheres. As in this sequence, cracking is often accompanied by the encapsulation of an air bubble inside the freezing droplet. Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Fig. 2.

Cracking expressed by first splitting of the freezing droplet and then closing and sealing together of the two hemispheres. As in this sequence, cracking is often accompanied by the encapsulation of an air bubble inside the freezing droplet. Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Fig. 3.

Frame sequence of a jetting droplet. As shown in the last frame, the jet is diverging into small splashes. Whether the ejected matter is entirely liquid or carries ice particles with it could not be determined in this study and will be investigated in upcoming studies. Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Fig. 3.

Frame sequence of a jetting droplet. As shown in the last frame, the jet is diverging into small splashes. Whether the ejected matter is entirely liquid or carries ice particles with it could not be determined in this study and will be investigated in upcoming studies. Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Fig. 4.

Frame sequence of two consecutive spicular bubble bursts. The first bubble burst is accompanied by an ejection of matter. In total eight spicular bubble bursts could be observed during the freezing of this droplet, two of the bursts included clearly visible ejections. The phase of the ejection is unknown at this point and is subject to future studies. Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Fig. 4.

Frame sequence of two consecutive spicular bubble bursts. The first bubble burst is accompanied by an ejection of matter. In total eight spicular bubble bursts could be observed during the freezing of this droplet, two of the bursts included clearly visible ejections. The phase of the ejection is unknown at this point and is subject to future studies. Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Fig. 5.

Frame sequence of five consecutive surface bubble bursts in one freezing event. As water is pushed out of the freezing droplet through channels in the ice shell, small bubbles appear on the droplet surface, merging into larger bubbles that eventually burst. In total, nine bubble bursts at multiple locations on the surface were observed during the freezing of this droplet. After the last bubble bursting event in this droplet, an ice rim is seen to be left at the site of bubble burst (last frame). Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Fig. 5.

Frame sequence of five consecutive surface bubble bursts in one freezing event. As water is pushed out of the freezing droplet through channels in the ice shell, small bubbles appear on the droplet surface, merging into larger bubbles that eventually burst. In total, nine bubble bursts at multiple locations on the surface were observed during the freezing of this droplet. After the last bubble bursting event in this droplet, an ice rim is seen to be left at the site of bubble burst (last frame). Video footage of this droplet can be accessed online (via https://doi.org/10.5445/IR/1000117652).

Frequency of secondary ice production events

Table 1 and Figs. 6a–c summarize the frequencies of occurrence of the SIP events according to our classification. On the whole, the frequency of SIP events is higher for droplets freezing in airflow (Figs. 6a–c) compared to droplets freezing in stagnant air (previous study; Fig. 6d). For pure water droplets, the peak at around −11° to −12°C rises from 36% in stagnant air to 69% in dry airflow and up to 100% in moist airflow. In contrast to the stagnant air experiments, bubble bursts play only a minor role in secondary ice production in pure water droplets freezing in free-fall. While single surface bubble bursts were occasionally observed in dry and moist airflow, spicular bubble bursts remained absent in both experiments. In experiments with SSA droplets in moist airflow (Fig. 6b), the frequency of SIP events reaches 46% without showing a pronounced maximum in temperature. Unlike in the experiments with pure water droplets, surface and spicular bubble bursts may play a significant role for secondary ice production in SSA droplets, as in some droplets up to ten consecutive bubble bursting events per freezing SSA droplet were observed. On average, 1.1 jetting events per jetting droplet were observed in cases 1 to 3.

Fig. 6.

Frequency of splitting and ejection events for (a) case 1: pure water droplets in moist airflow; (b) case 3: SSA droplets freezing in moist airflow; (c) case 2: pure water droplets freezing in dry airflow; and (d) pure water droplets freezing in stagnant air (previous study; Lauber et al. 2018).

Fig. 6.

Frequency of splitting and ejection events for (a) case 1: pure water droplets in moist airflow; (b) case 3: SSA droplets freezing in moist airflow; (c) case 2: pure water droplets freezing in dry airflow; and (d) pure water droplets freezing in stagnant air (previous study; Lauber et al. 2018).

The frequency of occurrence for complete breakups (Fig. 7) of pure water droplets reaches a maximum of 45% in moist airflow, of 26% in dry airflow, and of 3% for droplets freezing in stagnant air (previous study; Fig. 7). The complete breakup frequency for SSA droplets in moist airflow varies between 4% and 15%, depending on freezing temperature. The average number of visually detectable secondary ice fragments produced during complete breakups is 2.4 ± 0.1 in each experiment (cases 1 to 3). Due to the limited number of observations we do not report this number for various temperature ranges separately. Note that we only count the ice fragments where the ice phase identification of the secondary particles was unambiguous.

Fig. 7.

Comparison of the complete breakup frequency for case 1: pure water droplets freezing in moist airflow; case 2: pure water droplets freezing in dry airflow; case 3: SSA droplets freezing in moist airflow; and pure water droplets freezing in stagnant air (Lauber et al. 2018). The uncertainty on the complete breakup frequency corresponds to the 95% confidence interval, assuming a binomial distribution. Lines connect the data points belonging to a single set of measurements and are not meant as an interpolation and therefore not to be interpreted as indicating the temperature dependence.

Fig. 7.

Comparison of the complete breakup frequency for case 1: pure water droplets freezing in moist airflow; case 2: pure water droplets freezing in dry airflow; case 3: SSA droplets freezing in moist airflow; and pure water droplets freezing in stagnant air (Lauber et al. 2018). The uncertainty on the complete breakup frequency corresponds to the 95% confidence interval, assuming a binomial distribution. Lines connect the data points belonging to a single set of measurements and are not meant as an interpolation and therefore not to be interpreted as indicating the temperature dependence.

4. Discussion

Apparently, flow conditions strongly influence the freezing regime of a supercooled drizzle droplet. The shattering frequency and other SIP mechanisms can be clearly distinguished between freezing in stagnant air, dry airflow, and moist airflow. Below we discuss the effect of flow in more detail.

a. Enhancement of breakup frequency in airflow

As shown in Fig. 7, the complete breakup frequency for droplets freezing in airflow is increased by an order in magnitude compared to droplets freezing in stagnant air. An earlier study by Dye and Hobbs (1968) hints to a coupling between the shattering probability and the growth rate of ice shell enclosing the freezing drop. The growth of the ice shell is coupled to the release rate of latent heat of fusion. As discussed in Dye and Hobbs (1968) and Johnson and Hallett (1968), the rate of latent heat release to the environment is enhanced by ventilation. For droplets freezing in stagnant air, the rate of latent heat release is limited by the rate of heat and mass transfer through natural convection and evaporation. Droplets freezing in airflow additionally experience forced convection, resulting in a more efficient transport of latent heat to the environment. This increases the rate of ice shell growth. In this study, droplets freezing in airflow were observed to complete the freezing process in half of the time needed by droplets freezing in stagnant air under otherwise identical conditions. For example, droplets freezing at −12.7°C in stagnant air were completely frozen after 4.2 s, while the freezing of droplets in airflow took 1.8 s at the same temperature. Dye and Hobbs (1968) hypothesize that at faster freezing rates the ice shell has less time to adapt to the increasing mechanical stresses that results in a higher fragmentation frequency.

b. Number of secondary ice particles

During complete breakups, 2.4 ± 0.1 visually detectable secondary ice particles have been observed in each case (cases 1 to 3). Particles smaller than the threshold of visual detection (5 μm), or potentially liquid particles (as recognized by their spherical shape) were not counted. Therefore, the number of 2.4 ± 0.1 secondary ice particles per complete breakup must be understood as the lower limit for the total number of secondary particles produced during freezing. The actual number of secondary ice particles produced during breakup might well be significantly higher than the value of 2.4 ± 0.1 reported here, since particles smaller than 5 μm could not be quantified. The number of secondary ice particles produced during bubble bursts, cracking, and jetting could not be assessed in this study. Note also that the number of secondary ice particles reported in this study is only valid for freezing drizzle droplets with the size of ~300 μm in diameter, as the breakup frequency and the number of secondary ice particles increases with droplet size (Takahashi and Yamashita 1969; Kolomeychuk et al. 1975; Lauber et al. 2018).

Due to the limitations of visual detection, the numbers of secondary ice particles ejected during crackings and bubble bursts are not reported here. The frequency of bubble bursts reported in this study is a lower estimate, as an area that exhibits bubble bursts on the droplet’s surface is facing the observer for only a limited time span as the droplet is rotating in airflow. Thus, not all bubble bursts could be detected. The phase of the SI particles ejected during jettings and bubble bursts could not be identified in this study. The detection of particles smaller than 5 μm and the distinction between the liquid and ice phase of matter ejected during jetting or bubble bursts will be subject of future experiments involving a dedicated ice particle counter.

The high-purity water (CHROMASOLV Plus) used in this study is not representative for cloud water composition, as cloud water is a solution of organic and inorganic material (Brantner et al. 1994; Deguillaume et al. 2014; van Pinxteren et al. 2016). As shown in this study, sea salt solution droplets show a reduction in the breakup frequency compared to pure water droplets but a higher frequency of bubble bursts. Other dissolved salts may influence the SIP rate of freezing droplets in a similar way. On the other hand, solid inclusions such as mineral dust aerosols suspended in the droplet act toward enhancing the breakup frequency (Lauber et al. 2018).

All experiments in this and in our previous study (Lauber et al. 2018) have been conducted at atmospheric pressure. Earlier experiments by Johnson and Hallett (1968) show an increase in droplet breakup frequency for decreasing air pressure, which they attribute to a higher rate of latent heat release to the surrounding air at lower pressures. The extreme case of pressure effect was recently demonstrated in experiments of Wildeman et al. (2017), where droplets freezing in the atmosphere of water vapor at ice saturation (ambient pressure of approximately 100 Pa at −20°C) violently exploded during freezing, producing hundreds of ice fragments.

The nature of the airflow in this study is considered to be laminar. Phillips et al. (2018) suggest that flow turbulence in natural clouds could boost the tumbling and spinning motion of the freezing droplet. The rotation of the droplet normal to the direction of airflow is crucial for the formation of an ice shell that is uniform in strength and would allow sufficient pressure buildup prior to shattering (Dye and Hobbs 1968; Johnson and Hallett 1968; Kolomeychuk et al. 1975). The uniform formation of the ice shell is driven by the transport of latent heat to the environment being uniformly distributed around the droplet’s surface. Without droplet rotation the heat exchange has a local minimum at the airflow’s stagnation point and a maximum where the airflow is the strongest at the droplets surface. This imbalance prevents the formation of an ice shell with uniform thickness and pressure may be relieved through weak spots without violent fragmentation and the production of secondary ice particles. It is worth mentioning that in this study droplets were observed to rotate or tumble in airflow, thus cooling more uniformly in contrast to our previous study in stagnant air where droplets were oriented in the electric field with their longest axis in vertical direction.

At present, additional efforts are needed to investigate the frequency of occurrence of the various SIP events according to our classification as a function of droplet size, ambient air pressure, presence of soluble and solid inclusions, and concentration of dissolved gasses. Before a reliable parameterization can be formulated, the number of secondary ice particles produced during breakup, cracking, jetting, and bubble bursts needs to be determined. This will be addressed in the forthcoming experiments.

5. Conclusions

In this study we have investigated the freezing of drizzle droplets in free-fall conditions and observed a higher potential secondary ice production frequency compared to our previous study conducted in stagnant air. The breakup frequency is an order of magnitude higher for droplets freezing in airflow compared to droplets freezing in stagnant air (Fig. 7).

In experiments with pure water droplets, mechanisms associated with intense internal pressure buildup as jetting, cracking and breakup dominate the secondary ice production. If droplets contain sea salt, the formation of brine channels in the ice shell reduces effective pressure buildup and promotes bubble bursts, that are potentially accompanied by ejection of small secondary ice particles. While jetting, cracking and breakup can occur in combination in the same droplet, the combination of bubble bursts with the three other mechanisms were not observed.

The results of this experiment indicate that the frequency of droplet breakup crucially depends on the rate of latent heat release, supporting earlier findings by Dye and Hobbs (1968) and Johnson and Hallett (1968). This conclusion is also supported by the observation that the total freezing time for drizzle droplets in free-fall is reduced by factor of 2 as compared to freezing in stagnant air.

Acknowledgments

The authors acknowledge financial support of German Research Foundation (DFG) under Grant KI 1997/1-1, as well as support by the Helmholtz Association under Atmosphere and Climate Programme (ATMO).

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