Droplet heterogeneous nucleation in a rapid expansion aerosol chamber Open Access

One of the largest remaining uncertainties in climate projections involves the impact of aerosols on the optical properties of clouds.¹ Aerosols are particles suspended in the atmosphere that can serve as cloud condensation nuclei (CCN) upon which water vapor can condense to form cloud droplets. Understanding the influence of different seeding aerosols on aerosol activation (i.e., water droplet nucleation), droplet growth, and evaporation is essential for accurate predictions of cloud behavior and resulting impacts on the environment.^2–4 

The relevant physical scales for warm clouds composed of liquid droplets span several orders of magnitude, ranging from nano-scale aerosol particles [$O$(10 nm)], to micro-scale droplets [$O$(10 μm)], to small-scale turbulent fluctuations [$O$(cm)], to meso-scale turbulent processes such as cloud top entrainment [$O$(1–10 m)], and to large-scale convective patterns [$O$(1–10 km)]. The nucleation of cloud droplets and their subsequent growth dynamics lead to specific concentrations and size distributions of droplets, depending on the seeding aerosol number density and composition, and the thermodynamic conditions of the surrounding environment (e.g., water vapor concentration, temperature, and pressure), which are themselves modulated by the surrounding turbulent flow.^5–7 These factors determine whether cloud droplets remain stable for extended periods of time or rain out and also govern the optical interactions of the droplets with sunlight and terrestrial radiation.^4,8

Beyond the challenges of droplet nucleation in warm turbulent clouds, higher latitude low level clouds can be mixed-phase, containing both crystalline ice and liquid water droplets,^9,10 which add further complexity to aerosol nucleation microphysics. At higher altitudes, cirrus clouds and contrails are formed purely of ice particles. The conditions under which ice-nucleating particles form and the size and shape of atmospheric ice crystals are particularly sensitive to the size and chemical composition of seeding aerosol nuclei.^9,11,12 There are also many open questions regarding the sensitivity of ice formation to thermodynamic conditions and the interplay between homogeneous freezing and various modes of heterogeneous freezing on seeding aerosol.^9,11

Despite decades of laboratory efforts, observational field studies, remote sensing, and modeling work, fundamental questions remain regarding the nucleation and growth of droplets and ice on aerosols. These processes play a critical role in atmospheric science, through their influence on cloud processes, weather patterns, and radiative balance of Earth’s atmosphere,¹ and are central to proposed climate mitigation strategies such as marine cloud brightening¹³ and cirrus cloud thinning.¹⁴ 

Highly controlled laboratory conditions provide a path forward to gain physical insights into the mechanisms responsible for ice and droplet nucleation on seeding aerosols and subsequent growth under various thermodynamical conditions. While experimental cloud chambers have been instrumental in developing the understanding of cloud microphysics and informing parameterizations implemented in large-scale models,^4,15–18 only a few chambers are still in operation.¹⁹ As discussed by Shaw et al.,¹⁹ there is a significant need for a renewed effort of experimental studies into cloud and aerosol microphysics in controlled environments (i.e., well-constrained boundary conditions, thermodynamical properties, seeding aerosol ensembles, and turbulence conditions). The ideal cloud chamber experiment should include diagnostics capable of detecting multiscale dynamics directly within the flow, including droplet and ice particle size and spatial distributions as well as water vapor content. The ability to isolate specific processes is essential, as is a high degree of repeatability, in order to make detailed comparisons between experiments and modeling frameworks.

Cloud chambers can operate through different working principles, two configurations being expansion (Wilson-type) chambers and turbulent convection chambers. To give two relevant examples, the Aerosol Interaction and Dynamics in the Atmosphere (AIDA) expansion chamber at the Karlsruhe Institute of Technology (KIT)²⁰ and the turbulent Π cloud chamber at Michigan Technological University (MTU)^6,21 have contributed to recent scientific discoveries on aerosol cloud microphysics.

The AIDA facility is a large volume (84 m³) expansion chamber capable of studying droplet and ice growth over a range of thermodynamic conditions.²⁰ The large chamber size brings certain operational challenges and motivated KIT to develop a smaller (0.02 m³) vessel, AIDAm, housed inside AIDA. AIDAm is used to study the long-term physical and chemical aging of aerosols under relevant atmospheric thermodynamic conditions and to measure the impact of aging on aerosol ice-nucleating properties.²² The Portable Ice Nucleation Experiment (PINE) chamber²³ is another expansion chamber led by KIT, designed as a plug and play facility. PINE is capable of minute-to-hour-long observations of ice-nucleating particles by controlling the wall temperatures and thereby creating the necessary thermodynamic conditions for ice growth. PINE’s small volume (0.01 m³) and portable design permits its deployment in field sites²⁴ allowing for monitoring ice nucleation on aerosols in various atmospheric backgrounds. Small-scale expansion chambers in various other locations have also been used to study heterogeneous gas-to-liquid phase transitions for various particles and vapors, including investigations into droplet heterogeneous nucleation in microgravity²⁵ and heterogeneous nucleation of water vapor²⁶ and water–n-propanol²⁷ mixtures on silver nanoparticles.

In an alternative mode of operation, the Π chamber at MTU uses Rayleigh–Bénard turbulent convection conditions to study aerosol–cloud interactions, cloud formation, and turbulence coupling.^6,21 Elegantly, specific humidity and temperature boundary conditions may be chosen to reach supersaturation inside the chamber, leading to droplet heterogeneous nucleation. The Π chamber is meter-scale (volume of 3.14 m³) and operates in a statistically stationary state with a continuous injection of aerosols to compensate for sedimentation and wall loss. Studies of droplet formation and dynamics over minutes to days have been performed, with a focus on droplet–turbulence interactions. Major efforts have analyzed preferential sampling,²⁸ the heterogeneous spatial distribution of cloud droplets,²⁹ and the effect of fluctuating saturation fields in turbulent clouds.⁶ 

Following a recent community workshop, Shaw et al.¹⁹ laid out a list of lingering open questions in cloud microphysics and the experimental scales needed to address them. While a very tall convection chamber is required for some questions—including rain formation and processes at the cloud boundary where gradients are sharp—meter-scale chambers are sufficient to attack key questions on aerosol activation, droplet formation and growth, and ice formation and growth. Small centimeter-scale chambers have been used in single-particle growth studies and have revealed a diversity of ice growth behaviors that may be impossible to directly observe in a large AIDA-scale chamber.^30–32 Intermediate-scale cloud chambers are more suitable to measure the diversity of ice growth within a population of particles. Smaller facilities also have the advantages of easier logistics and faster experimental repetition rates, making them possible to sweep a wider range of conditions in a fixed amount of lab time. The facility we introduce in this paper has been specifically designed to target such questions.

Here, we present a new intermediate-scale cloud-chamber facility: the rapid expansion aerosol chamber (REACh). REACh consists of two vacuum chambers: a 0.14 m³ aerosol chamber, where seeding aerosols are introduced and measurements are conducted, and the expansion chamber, into which the aerosol chamber can be vented to create the necessary conditions for droplet (or ice) nucleation. Crucially, our setup allows for a very fast repetition rate, with a typical expansion experiment taking only ∼30 min to set up and run. We can survey a wide range of aerosol, flow, and thermodynamic conditions in just a few days. Such fast experimental turnaround times can be intractable in larger chambers. This facility also includes the possibility to introduce turbulent flow during the expansion—inspired from particles in turbulence studies^5,33,34—so that droplet and ice nucleation and growth can be studied in a fluctuating environment.

The REACh facility emphasizes a suite of high-frequency, accurate diagnostic methods to monitor droplet growth and thermodynamical conditions throughout each expansion experiment. Detailed quantification of droplet properties is enabled by the use of phase Doppler anemometry (PDA), high-speed in-line holography,^35–37 and temporally resolved measurements of the chamber temperature and pressure. An infrared absorption spectroscopy system to measure the saturation ratio has also been implemented and will be presented in a follow-up paper. Such real-time measurements are essential to advance the understanding of cloud microphysics. Nucleation diagnostics are often made post-hoc, e.g., by extracting samples from the chamber and running subsequent analyses. Such methods result in the loss of timescale information needed to constrain particle and cloud growth models. Our more ideal diagnostics track the size distribution and number densities of dry aerosols and droplets together with temperature and liquid vapor content³⁸ and the spatial and temporal fluctuations of these fields.

In this paper, we demonstrate the capabilities of the REACh facility for the parametric studies of the heterogeneous nucleation and growth of liquid droplets. In particular, we consider water droplet nucleation on pre-existing aerosol intentionally introduced into the chamber and the subsequent growth of these liquid droplets. We refer to this process hereafter as “water droplet nucleation (on an aerosol)” for brevity. We do not consider the formation of particles/drops directly from the vapor phase in the present work. The kinetics of droplet nucleation and growth are not typically considered in atmospheric models, yet these processes are highly relevant to the atmospheric behavior of large aerosol particles (e.g., sea-salt) that might be used in hygroscopic cloud seeding or marine cloud brightening.

Here, we make use of time-synchronized, highly temporally resolved measurements to probe the dynamics of the droplet growth for a variety of initial conditions, including saturation ratio, seeding aerosol concentration, and air mixing. We perform experiments that can go beyond classic atmospheric conditions in terms of particle concentration, level of supersaturation ratio, timescale of expansion, and intensity of turbulence, which can also help models avoid the extrapolation of parameters when at the edge of typical, or extreme, atmospheric conditions. We carry out these extensive parameter sweeps with the goal to gain insights into cloud microphysics and eventually inform more accurate theoretical models.

Here, we illustrate the capabilities of our rapid-expansion-cloud-chamber on the heterogeneous nucleation of liquid droplets. We make use of time-synchronized, highly temporally resolved measurements to probe the dynamics of the droplet growth for a variety of initial conditions, including saturation ratio, seeding aerosol concentration, and air mixing.

The remainder of this paper is organized as follows: We describe the operating principle of the facility, experimental procedures, measurement instrumentation, and facility characterization in Sec. II. We illustrate the capabilities of the system by characterizing the thermodynamics and associated droplet heterogeneous nucleation and growth in various aerosol concentration regimes in Sec. III, with dense regimes of droplets characterized by PDA and dilute regimes characterized by holography. We examine how droplet lifetimes, mean diameters, and concentrations vary as a function of initial saturation ratio and aerosol concentration. We provide conclusions and a future outlook in Sec. IV.

Figure 1 shows a schematic of the REACh facility. Engineering drawings are included in the supplementary material. Both the aerosol-nucleation and expansion chambers, as well as various control devices and diagnostics, are depicted. The facility consists of two cylindrical vacuum-sealed stainless steel (grade 304L) chambers separated by a solenoid valve, which is typically closed. The primary aerosol-nucleation chamber is where all the experimental measurements are conducted and where most of the scientific instrumentation is located. The expansion chamber is approximately equal in volume to the aerosol-nucleation chamber. We vent the contents of the aerosol-nucleation chamber into the expansion chamber to increase the saturation ratio via adiabatic expansion and cooling, thus creating conditions for droplet nucleation.

The aerosol-nucleation chamber is 50.8 cm in diameter and 49.5 cm in height with a volume of $V≈0.14$ m³. The volume is slightly greater than that of a cylinder due to the presence of the viewports. A vacuum-sealed access lid is located on top of the chamber, allowing easy access to the main compartment. The chamber features six 13.5 cm (5.32 in.) diameter borosilicate glass viewports positioned along its circumference to provide optical access. In addition, measurement and control devices are attached to several 20.3 cm (8 in.) and 6.99 cm (2.75 in.) access ports positioned around the circumference of the aerosol-nucleation chamber and on the top lid. The chamber walls are equipped with cooling channels, which are not used in the present work, but will permit us to explore lower-temperature conditions in the future. Three 82 mm diameter fans (CUI Devices, model CFM-9225V-130-340) are mounted onto the walls of the aerosol-nucleation chamber to enhance mixing inside the chamber. The fans are offset by 120° around the circumference of the chamber, positioned near the top and pointing toward the chamber center.

We produce a cloud of liquid droplets in the aerosol-nucleation chamber using the following procedure. First, the aerosol-nucleation chamber is prepared with the desired initial saturation ratio, S₀, and the concentration of seeding aerosols, C₀ (see Sec. II B). At the same time, the expansion chamber is evacuated to pressures as low as 2.6 × 10⁻⁵ bar using a Roots vacuum pump (Leybold ECODRY 40 plus). Fully pumping down the expansion chamber results in a maximum pressure drop in the aerosol-nucleation chamber of Δp = 0.54 bar upon venting; this is the condition used for the majority of experimental runs reported in this paper. As described in Sec. III A, we can also work with a smaller pressure drop by only partially evacuating the expansion chamber.

An experiment is initiated when the solenoid valve connecting the two chambers is opened rapidly (∼20 ms opening time), causing gas to flow out of the aerosol-nucleation chamber in ∼0.5 s. Note that the rate of expansion can be controlled via the solenoid valve, although we do not explore this degree of freedom in the present experiments. Changing expansion timescales would also need to be associated with wall temperature control. This expansion drops the aerosol-nucleation chamber pressure and is accompanied by a drop in temperature and a corresponding increase in saturation ratio (see the next paragraph). At this point, water droplets may begin to form in the aerosol-nucleation chamber. Nucleation can, in principle, occur either via heterogeneous nucleation on seeding aerosols or via homogeneous nucleation, depending on the initial conditions. Expansion experiments can be performed with fans off (hereafter referred to as the unforced mixing case) or with the fans running (referred to as the forced mixing case) to evaluate the influence of mixing on droplet formation. Note that for all experiments in this paper, we do not observe or have direct evidence that the fans act as droplet impactors, thereby reducing the concentration of droplets in the chamber. We also note that in the current work, the rapid expansions we perform (0.54 bar pressure drops in 0.5 s) correspond to effective vertical velocities much faster than atmospheric processes. Our experiment design is not aimed to replicate the atmospheric vertical velocity but instead to obtain highly repeatable conditions, under which droplet nucleation and growth on reasonable experimental timescales are studied and a wide range of aerosol and thermodynamic parameters are probed.

One of the key metrics that governs droplet nucleation in humid air is the saturation ratio, defined as S = e/e*(T), where e is the partial pressure of water vapor and e*(T) is the saturation water vapor pressure at temperature T. S is related to the relative humidity (RH) by S = RH/100. A large range of maximum supersaturations (S − 1) can be achieved during our expansion experiments depending on the initial conditions and pressure drop.

The following data are collected for each expansion experiment: initial temperature, pressure, and saturation ratio; initial aerosol concentration; time-resolved pressure and temperature drop; and time-resolved droplet diameter, number, vertical, and horizontal speed distributions.

The aerosol-nucleation chamber pressure, temperature, and saturation ratio are monitored using the following sensors:

• Three pressure sensors (Keller Preciseline)—two in the aerosol-nucleation chamber and one in the expansion chamber—are used to measure the changes in pressure that occur during an expansion. These sensors feature a sampling rate of 250 Hz and equivalent response times.

• One thermocouple temperature sensor (Type T, 44 AWG, Omega Engineering Inc.) is hung in the center of the aerosol-nucleation chamber to measure the temperature throughout each expansion. The response time of the thermocouple is on the order of 10 ms. A cold junction compensation held at 20 °C (National Instruments SCB-68A) is applied to the thermocouple. Note that in some of the data presented here, the cold junction compensation of 20 °C was applied in post-processing. Note that the thermocouple wire is very fine and thus may move in the presence of turbulence.

• Six relative humidity sensors (Sensirion SEK-SHT35)—four near the bottom of the aerosol-nucleation chamber and two in the expansion chamber—are used to record relative humidity. The response time of these sensors is on the order of 2 s, so they are only used to record humidity before and after the expansion.

In addition to the above, we record the partial pressure of water inside the aerosol-nucleation chamber using infrared laser absorption spectroscopy.^38,39 While we do not report the results of these measurements here, we mention this technique here for completeness.

The instrumentation used to record aerosol and droplet statistics is described in Secs. II C and II D.

We prepare for an expansion experiment by initializing the aerosol-nucleation chamber. The most important parameters to control are the initial saturation ratio, S₀, and the concentration of dry seeding aerosol particles, C₀. It can take 20–35 min to prepare the chamber, depending on conditions.

First, we thoroughly clean both chambers of aerosols from any previous experiments. The cleaning procedure is as follows: the inside of both chambers is dusted off with compressed air, and then, the inside surfaces are cleaned with isopropyl alcohol and lint-free wipes. Finally, the chambers are sealed and evacuated, and the valve connecting the two chambers is closed. Following cleaning, the aerosol-nucleation chamber is filled with pure nitrogen (N₂). Next, we pass pure N₂ through a bubbler filled with ultrapure water from a Milli-Q, creating a mixture of water vapor and droplets suspended in the N₂ carrier gas. The bubbler is equipped with an electrically heated, feedback-controlled thermal jacket capable of reaching 100 °C, although this system was not used in the present experiments. The bubbler can also be used to produce vapors other than water, but only water vapor is used in the present experiments. The resulting water/N₂ mixture passes through a two-stage compressed gas filter to remove any droplets or particles with diameters above d > 5 μm, resulting in a stream of humid air. This humid air is injected into the aerosol-nucleation chamber at a flow rate of 10 standard liters per minute (SLPM) using a mass flow controller (Alicat Scientific) until the desired S₀ is reached.

Next, we set the concentration of dry seeding aerosol particles, C₀, in the aerosol-nucleation chamber. Aerosols are injected using a two-stage powder dispersion system, similar to those described by Sullivan et al.⁴⁰ and Huynh and McNeill.⁴¹ A schematic of the aerosol injection system is shown in the top left of Fig. 1(a). The system consists of two 2 L Erlenmeyer flasks connected in series with the first flask connected to an N₂ source and the second to the aerosol-nucleation chamber. Aerosol powder of known composition is placed in the first flask along with a Teflon-coated stir bar. The flask is placed on a stir plate set to continuously stir the powder. A mass flow controller (Alicat Scientific) is used to inject dry N₂ into the first flask at a flow rate of 0.4 to 5 SLPM. The N₂ entrains aerosol particles from the first flask in the flow, then passes into the second flask, and eventually passes into the aerosol-nucleation chamber. Sharp turns are introduced into the tubing and inside the second flask to trap large particles, thereby enhancing the selection of small particles. During the initial preparation of the aerosol-nucleation chamber, the fans mounted inside the chamber are kept on to assist with the mixing of humid air and seeding particles.

For all experiments described in this paper, the aerosol-nucleation chamber is seeded with calcium carbonate particles (CaCO₃, 99% pure, American Elements Inc., nominal size of 100 nm). We choose CaCO₃ to demonstrate the capabilities and simple usage of the chamber and associated instrumentation. In future experiments, other seeding aerosols relevant to cloud microphysics (e.g., mineral dust, sea salt, and soot) will be explored to assess the role of hygroscopicity in cloud droplet nucleation.⁴² 

Two separate measurement systems are used to characterize the seeding aerosols. We use a scanning mobility particle sizer (SMPS) to record size distributions and a condensation particle counter (CPC) to record concentrations.

The SMPS (TSI) is used to characterize the diameter distribution of the dry CaCO₃ particles injected into the chamber, measuring particle sizes between 10 nm and 1 μm. Our SMPS configuration includes an advanced aerosol neutralizer (TSI model 3088), an electrostatic classifier (TSI model 3082), a differential mobility analyzer (TSI model 3081), and a condensation particle counter (TSI model 3752). Figure 2 shows the probability density function (PDF) of the CaCO₃ particle diameter as measured with the SMPS. This distribution is centered around $d̄=$ 316 nm with a standard deviation of 257 nm. The difference between the nominal 100 nm particle diameters and the measured diameters is likely due to the coagulation of the aerosols during their preparation and seeding. The PDF is insensitive to the N₂ flow rate used in the powder dispersion system.

We use a separate CPC (TSI model 3007) to measure the concentrations of aerosols up to 10⁵ #/cm³ with an accuracy of ±20%. The CPC is sensitive to particles larger than 10 nm in diameter. We use the CPC to sample air from the aerosol-nucleation chamber during the preparation of the experiment to confirm that room aerosols inside the aerosol-nucleation chamber are removed down to a base concentration of 1–2 #/cm³. We also use the CPC to record the CaCO₃ concentration after chamber initialization, just prior to triggering an expansion.

We characterize the droplets that appear during an expansion using a phase Doppler anemometry (PDA) system (a Dantec Inc. flow explorer, a HiDense FiberPDA optical receiver, and a burst spectrum analyzer). In its present configuration, our PDA system can record droplet diameter distributions between 1 and 50 μm as well as horizontal and vertical droplet velocity distributions. The flow explorer consists of two lasers with wavelengths of 532 and 561 nm. Each beam is split into two; the resulting four beams intersect at a measurement region of ∼0.013 mm³ in volume and with a projected area of A = 0.119 × 0.1196 mm². The measurement volume is located close to the center of the aerosol-nucleation chamber, ∼26.7 cm from the bottom of the chamber and 15.5 cm from the walls. Horizontal and vertical droplet speeds as well as diameters are recorded for all droplets that pass through the measurement volume with a sampling rate of up to 1 MHz. Detected droplets with diameters smaller than 1 μm are removed from the dataset as they are below the measurement accuracy threshold.

In addition, we use cinematic inline holography to measure droplet statistics, including size, number, concentration, and speed. A detailed description of this system is provided by Erinin et al.³⁶ We use this technique in Sec. III D to report on the temporal evolution of droplet diameters and concentration during an expansion. In these experiments, the system is recording at a frame rate of 600 Hz and has a spatial resolution of 1.41 μm with an ability to measure droplets with diameters down to about 6 μm.

The PDA system is designed to operate in relatively dense spray and provides statistics at a single point in space. In contrast, holography probes droplet concentration, size, and speed over an extended path length and operates at low droplet concentrations. Holography is especially suited to measurements of ice particles,⁴³ which often nucleate in low concentrations and form nonspherical shapes. In the present paper, we use PDA for experiments with large pressure drops and seeding aerosol concentrations from 10² to 10⁵ #/cm³, yielding droplet concentrations of similar orders of magnitude. We use holography for experiments with lower aerosol concentrations (1–100 #/cm³) carried out closer to the onset of droplet nucleation. Note that PDA has a much smaller measurement volume than the holography system. Holography can, therefore, record a larger number of individual droplets than PDA despite operating in a less dense cloud.

We now present the characterization of the REACh facility in terms of thermodynamic conditions and flow and then demonstrate its capabilities to analyze droplet heterogeneous nucleation for a range of initial aerosol concentration and saturation conditions. Table I details the experimental conditions for all results presented in this paper.

In Secs. III A and III B, we characterize the thermodynamic and flow conditions during expansion experiments for a range of pressure drops and initial saturation ratios, with both forced and unforced mixing. We compare the minimum temperature reached during each expansion to dry and moist adiabatic theories.

In Secs. III C and III D, we present an analysis of conditions where droplets are formed in the presence of seeding CaCO₃ aerosols, for various initial saturation ratios, aerosol concentrations, and mixing conditions. We leverage both PDA (Sec. III C) and holography (Sec. III D) to probe high and low ranges of aerosol and droplet concentration, respectively. In Sec. III C, we present PDA data from experiments over a range of S₀ conditions, sweeping the concentration of seeding CaCO₃ particles from 100 to 10⁵ #/cm³. The same datasets are collected for both unforced and forced mixing conditions. For all experiments in Sec. III C, the initial temperature and pressure are 20 °C and 1 bar, respectively, and the pressure drop is always Δp = 0.54 bar. In Sec. III D, we demonstrate the use of holography to track time-resolve droplet growth. This experiment is performed for a small seeding aerosol concentration, and we consider a lower pressure drop (Δp = 0.36 bar) relatively close to the onset of droplet heterogeneous nucleation.

Here, we describe the measurements of thermodynamic properties inside the chamber throughout an expansion and compare these results with theoretical predictions. Figure 3 shows the changing pressure and temperature during an expansion with an initial saturation ratio of S₀ = 0.7 and an initial CaCO₃ particle concentration of C₀ = 1.8 × 10⁵ #/cm³. Such large particle concentrations, while not typical of the atmosphere, allow condensation to keep up with supersaturation generation during experiments with large pressure drops, keeping the supersaturation ratio close to unity. As described in Sec. II A, fans are installed inside the chamber to enhance the mixing of humid air and aerosols and can be left on during an expansion. We show results for experimental runs with both fans off (unforced mixing, red curves) and fans on (forced mixing, blue curves).

In both the unforced and forced mixing cases, the rapid pressure decrease lasts ∼1 s [Fig. 3(a)] and is accompanied by a decrease in temperature [Fig. 3(b)]. In all experiments, the initial temperature is that of the room, 20 °C. Shortly after the expansion, the temperature reaches a minimum and then subsequently increases as the air returns to thermal equilibrium via heat conduction through the chamber walls. In the unforced mixing case, the minimum temperature reached in the center of the chamber is 3 °C colder than in the forced mixing case and persists for ∼3 s. The air then thermalizes over the following ∼30 s fluctuating by ±5 °C, likely due to large-scale convective air currents inside the chamber. By contrast, this thermalization process lasts only ∼15 s in the forced mixing case as the fans enhance the thermal conduction of heat through the air–wall boundary.

In both experiments shown in Fig. 3, a sudden temperature increase is observed during the thermalization process, occurring $∼17$ s after the expansion is triggered in the unforced mixing case and after $∼6$ s in the forced mixing case. These times correspond approximately to the cloud lifetime, τ_f, which we define as the length of time over which cloud droplets are present and detectable after an expansion. Measurements of the cloud lifetime are discussed in more detail in Sec. III C 2. Eventually, the cloud of droplets evaporates; thermalization can then accelerate afterward, as the heat flux from the chamber walls goes entirely toward sensible heating (raising the temperature), rather than providing latent heat for droplet evaporation. This process explains the sudden changes observed in temperature as the chamber returns to thermal equilibrium.

The minimum temperature reached in the aerosol-nucleation chamber during an expansion, T_min, is a key thermodynamic variable and is an important determining factor for the total condensed water in an expansion. In Fig. 4, we report T_min for a series of pressure drops with Δp = p_f − p₀ ranging from 0.02 to 0.54 bar. Figure 4 shows results for both the dry expansion case with S₀ = 0 and minimal seeding aerosols and the moist expansion case with S₀ = 0.5 and C₀ = 2000 #/cm³. In both cases, T_min decreases as Δp increases.

The maximum possible saturation ratio S_max reached during an expansion can be estimated from the pressure drop and the dry adiabatic minimum temperature according to S_max = e/e*(T_min). Assuming an adiabatic expansion,¹⁷ the water vapor pressure is estimated as e = e₀ × (p_f/p₀), where e₀ is the initial water vapor pressure set by S₀, p₀ is the initial total chamber pressure, and p_f is the final chamber pressure after expansion. Assuming S₀ = 0.3, for the highest pressure drop Δp = 0.54 bar, we obtain S_max values as high as 10, while Δp = 0.42 bar yields S_max ≈ 4 and Δp = 0.23 bar yields S_max ≈ 1. We note that the highest S_max values are not actually reached in the chamber as water vapor is lost through condensation on seeding aerosols. We rather indicate that the available pressure drops create conditions highly conducive to droplet nucleation and growth.

Most of our expansion experiments are carried out in a humid environment, where Eq. (1) is no longer valid. In order to validate the thermodynamics of moist expansions, we must modify to Eq. (1) to account for humidity. Determining T_f as a function of p_f for humid air with 0 < S₀ < 1 requires two ingredients. First, we must determine the temperature T_sat and pressure p_sat at which the expanding humid chamber air initially reaches saturation (S = 1), and second, we must generalize Eq. (1) for saturated air.

We note that because S might exceed 1 in the chamber, T_sat will be an upper bound of the minimal temperature, while T_min obtained from the dry adiabat will be a lower bound.

Figure 4 shows the comparison of the measured values of T_min with those predicted by Eq. (10) for a representative humid expansion (teal trace and markers). We observe a good agreement between data and theory for pressure drops up to Δp = 0.45 bar.

T_min calculated from the dry adiabatic expansion is the lower temperature limit if no condensation occurs. Since the process of condensation releases energy, we expect the temperature to remain above that bound. Our thermodynamic model for drop formation assumes that S ≲ 1 (i.e., enough vapor condenses to maintain equilibrium), but in instances where S > 1, the temperature will be lower than what is predicted by Eq. (10). We, therefore, consider the dry adiabat as a conservative uncertainty estimate of the lowest possible temperature.

Finally, we characterize how the expansion thermodynamics are impacted by the presence of various concentrations of seeding aerosols. Figure 5 shows the time evolution of temperature during expansions with different aerosol concentrations, C₀. These experiments are carried out with unforced mixing, an initial saturation ratio of S₀ = 0.3, and the maximum pressure drop of Δp = 0.54 bar. The dependence of T_min on C₀ is found to be very weak, with variations of at most 0.5 °C. After the expansion, for times t > 2.5 s, random temperature fluctuations are observed, which vary from run to run. We note that this insensitivity of T_min to C₀ is likely due to the relatively large aerosol concentrations used here, which keep S close to 1 despite the large pressure drop.

We now characterize mixing inside the aerosol-nucleation chamber by comparing droplet velocity statistics acquired with phase Doppler anemometry for unforced and forced mixing conditions. Velocity distributions and statistics are collected over the full time of the expansion experiment.

Figure 6 shows representative horizontal (V) and vertical (W) velocity PDFs for both mixing cases with S₀ = 0.7 and C₀ = 8 × 10⁴ #/cm³. In the unforced mixing case [Fig. 6(a)], the droplets feature horizontal and vertical velocity distributions that are not centered about zero and do not have clearly defined shapes due to the limited statistics. In the forced mixing case [Fig. 6(b)], a random turbulent flow is induced by the motion of the fans. Both V and W have peaks at $∼0.2$ m/s. The V and W distributions display absolute values nearly an order of magnitude larger in the forced mixing case than in the unforced mixing case. Velocity distributions are similar across various C₀, S₀, and Δp conditions tested.

We define the mean droplet speed as $Ū=V2+W2̄$⁠, where V and W are the measured velocities by PDA and the overline indicates the average over drops passing through the sensor over time. We define a characteristic fluctuating velocity as $U=σV2+σW2$⁠, where σ represents the standard deviation. The mean droplet speed under forced mixing is $Ūforced=0.8$ m/s and under unforced mixing is $Ūunforced=0.1$ m/s, with variations of less than 0.1 and 0.01 m/s across conditions, respectively. The characteristic velocity fluctuations $(U)$ are very similar than the means so that either can be used as characteristic velocity in the rest of this paper.

We now characterize droplet heterogeneous nucleation as a function of initial aerosol concentration and saturation ratio. We perform a parameter sweep over 46 conditions while tracking the size and number of droplets formed throughout the expansion. All experiments described herein are performed at the maximum pressure drop (Δp = 0.54 bar).

We start by discussing the droplet nucleation and subsequent growth for a typical expansion experiment. Figure 7 shows the time evolution of the thermodynamic chamber parameters alongside droplet statistics measured with PDA from the time the pressure drop is initiated (t = 0 s) to the point where most droplets have disappeared (t ≈ 8 s). These data are from a single representative expansion with S₀ = 0.7 and C₀ = 1.8 × 10⁵ #/cm³ under forced mixing conditions. As discussed in Sec. III A, the sharp drop in pressure [Fig. 7(a)] triggers a rapid temperature decrease [Fig. 7(b)]. The drop in temperature causes a sudden increase in saturation ratio, which initiates the nucleation of water droplets.

Figure 7(c) plots the time evolution of N, the number of droplets detected per 0.17 s time interval, beginning shortly after the expansion occurs. N increases until time τ_m, as marked with black vertical lines in Figs. 7(c)–7(f). The cloud lifetime, τ_f, is the point after which very few droplets are detected as marked with a red vertical bar in Figs. 7(c)–7(f).

The temporal evolution of the mean droplet speed, $Ū$ (see Sec. III B), is shown Fig. 7(d). Over the time window 0 < t < τ_m, the mean droplet speed is found to increase from ∼0.2 to 1.1 m/s. The increase in velocity is related to the large-scale flow that occurs in the chamber during the expansion. For t > τ_m, this increased mean droplet speed is sustained for several seconds after which it decreases as t approaches τ_f and the cloud dissipates.

The time evolution of the mean droplet diameter, $d̄$⁠, is shown in Fig. 7(e). During the initial stages of droplet growth, $d̄$ increases from $∼1$ μm at t = 0 s to $∼4$ μm at t = 0.5 s and then stays nearly constant until t approaches τ_f.

The swarm plot in Fig. 7(f) illustrates each detected droplet as a point. This plot captures the evolution of both the droplet number in the vertical width of the swarm and the droplet diameter, as indicated by the color of each point. After t > τ_f, most droplets have evaporated.

A notable feature of the data shown in Fig. 7 is that the droplet diameter $d̄$ is fairly constant between τ_m and τ_f, while droplets are evaporating and N is decreasing. This is consistent with the “inhomogeneous mixing” paradigm,^47,48 where the time it takes for thermodynamic cloud properties (such as temperature) to homogenize is much longer than the time it takes for droplets to equilibrate with their local environment. In this paradigm, heat transferred from the chamber walls completely evaporates the droplets only in nearby pockets of air, rather than rapidly mixing throughout the volume and partially evaporating droplets throughout. This leads to little change in $d̄$ but a change in the average N passing through the PDA detection volume. These results support recent reports, suggesting that inhomogeneous mixing is a rather ubiquitous phenomenon in cloudy air masses.^7,37,49

We now examine the cloud lifetime, τ_f, as a function of the initial saturation ratio, initial aerosol concentration, and mixing conditions. Figure 8 shows several swarm plots illustrating the time-dependent number and size distribution of droplets for various initial aerosol concentrations, C₀. For the smaller values of C₀ tested, characterization becomes challenging as very few droplets are measured. An initial saturation ratio of S₀ = 0.7 is used for all experiments reported in Fig. 8.

In the unforced mixing cases shown in Fig. 8(a), the droplet number gradually grows to a maximum around τ_m = 5–6 s, as marked with black horizontal bars, and decays to nearly zero by τ_f = 10–15 s, as marked with red horizontal bars. In the forced mixing cases in Fig. 8(b), the peak droplet numbers are instead reached at τ_m = 2–3 s, while droplets disappear by τ_f = 6 s. The droplet cloud lives less than half as long under forced mixing as under unforced mixing; again, the fans speed the thermalization process. As in Fig. 7, droplet diameters are observed to be fairly constant in time, while the droplet number decreases between τ_m and τ_f, again indicative of inhomogeneous mixing.

Figure 9(a) shows the extracted τ_m and τ_f timescales as a function of C₀ from the same experimental datasets reported in Fig. 8. τ_m and τ_f appear to be independent of C₀. The only notable trend is that all timescales are shorter with forced mixing, as we have already noted. Meanwhile, Fig. 9(b) shows τ_m and τ_f as a function of S₀. Both τ_m and τ_f increase as S₀ increases. As we will see in Sec. III C 3, a higher initial water content facilitates the growth of droplets to larger average diameters, which then persist for a longer period of time before evaporating.

We now analyze the total number of nucleated droplets and their mean sizes as functions of initial aerosol concentration and saturation ratio. We explored calculating the total number of droplets by integrating N over either 0 < t < τ_m or 0 < t < τ_f. Both methods give similar trends as functions of C₀ and S₀. The mean droplet diameter $d̄$ is also nearly identical when evaluated over both time windows. We, therefore, define N_tot as the total number of droplets detected by PDA over 0 < t < τ_f and $d̄$ as the mean droplet diameter averaged over the same window as counting more droplets yields better statistics.

Figure 10(a) shows the dependence of the total droplet number, N_tot, on C₀ and S₀ for both unforced and forced mixing. As C₀ increases, N_tot increases; this trend remains consistent across all S₀ and mixing conditions. N_tot is also observed to increase with S₀. The relationship between N_tot and S₀ is related to the longer droplet cloud lifetime [see Fig. 9(b)].

Figure 10(b) plots the dependence of the mean droplet diameter, $d̄$⁠, on C₀ and S₀ for both unforced and forced mixing. $d̄$ consistently decreases with increasing C₀ and increases with increasing S₀.

Figures 10(c) and 10(d) highlight how N_tot and $d̄$ compare between unforced and forced mixing for S₀ = 0.5. $d̄$ is not significantly affected by the mixing conditions for any value of C₀. Meanwhile, N_tot, which quantifies the number of droplets that pass through the measurement plane, is consistently larger under forced conditions than under unforced conditions. This can be attributed to the difference in characteristic mixing velocity—either the mean droplet speed $Ū$ or the fluctuating velocity $U$⁠, see Sec. III B—between the two mixing conditions. The dependence of N_tot on mixing is, therefore, due to enhanced flow in the forced mixing case, which causes more particles to pass through the measurement volume per unit time. In fact, when N_tot is normalized by $Ū$⁠, the data collected under forced and unforced conditions collapse; see Fig. 11.

Prior to an expansion, the water vapor concentration is set by S₀, which determines the mass of liquid vapor available for condensation. The pressure drop during the expansion, Δp, determines changes in temperature and the partial pressure of water vapor during the expansion. These factors combine to control changes in S and lead to an estimated maximum S_max above 3 or 4 for a typical expansion experiment. As such, it is reasonable to assume that all seeding aerosols will be activated and nucleate droplets during an expansion, causing C_drop to track directly with C₀.

Figure 11 shows a plot of C_drop calculated from Eq. (13) as a function of C₀ for all initial S₀ and mixing conditions. Error bars on measurements of C_drop derive from uncertainties in τ_f and $Urms$⁠. At intermediate concentrations (4 × 10³ #/cm³ < C₀ < 8 × 10⁴ #/cm³), C_drop falls close to the gray dashed line, which has a slope of C_drop/C₀ = 1, suggesting that every solid aerosol in the chamber nucleates a droplet during the expansion.

The curves of C_drop do deviate from this 1:1 line for both low and high values of C₀. Deviations at lower aerosol concentrations (C₀ < 4 × 10³ #/cm³) could be related to larger PDA measurement errors at lower particle counts, as well as related uncertainties in estimating the cloud lifetime (see Fig. 8). At high aerosol concentrations (C₀ > 8 × 10⁴ #/cm³), the concentration of droplets observed undershoots the concentration of seeding aerosols, i.e., not all aerosol particles are activated. This suggests that for high C₀, rapid water condensation onto numerous, easily activated particles keeps the actual S in the chamber very close to 1, preventing the activation of less efficient condensation nuclei in the aerosol distribution. Experimental uncertainties could also be partly responsible for C_drop < C₀ at high C₀: PDA is only sensitive to droplets larger than 1 μm, so if smaller droplets are present, they would be missed by this analysis. Indeed (as detailed further below), when more droplets are formed, they are smaller on average, due to conservation of mass. Results with and without forced mixing are similar, suggesting that the fans do not act as droplet impactors or induce significant loss of droplets.

We can qualitatively compare the droplet size scaling with C₀ to the work of Shaw et al.⁵⁰ in the context of Π chamber experiments. The Π chamber operates under statistically steady-state conditions, with a constant aerosol injection rate of $ṅinj$⁠, compensated by wall loss and sedimentation. The mean droplet size $d̄$ is then related to the rate of droplet nucleation, which is assumed to be proportional to the injection rate, yielding $d̄∝ṅinj−1/3$⁠. In our REACh chamber, the expansion is a transient phenomenon. However, if we assume $ṅinj∝C0$⁠, our scaling argument for the droplet size with aerosol concentration given in Eq. (15) and our data (Fig. 10) agree with the steady state results of Shaw et al.⁵⁰ We also note that the range of aerosol and droplet concentrations explored in the Π chamber^51,52 ranges from 2 to 2.2 10⁴ #/cm³, with a significant overlap with the experimental conditions presented here. This point of comparison provides confidence that our ability to rapidly probe a range of experimental conditions with the REACh facility can provide useful physical insights into cloud microphysics.

Finally, we demonstrate the capabilities of holography for tracking droplet nucleation and growth. Our holographic system has the advantage of being able to probe a much larger measurement volume than PDA. Holography measurements average over a path length spanning the chamber and can, therefore, access more dilute regimes, closer to nucleation threshold and more relevant to the droplet concentrations observed in actual clouds. It is important to note that thanks to the large sampling volume (8.44 cm³), the holographic system measures more individual droplets than PDA and achieves better statistics, allowing us to track the droplet size distribution in time.

In Fig. 12, we report the temporal evolution of the droplet size distribution tracked with holography for a single expansion. Figure 12(b) plots the number of drops detected, Fig. 12(c) plots the mean droplet diameter, and Fig. 12(d) shows the droplet size distribution. The experiment is performed with an initial saturation ratio of S₀ = 0.3, an initial aerosol concentration of C₀ = 71 #/cm³, and a pressure drop of Δp = 0.36 bar under unforced mixing conditions. The minimum temperature reached is close to −16 °C [Fig. 12(a)]. This combination of Δp and S₀ is chosen to be relatively close to the threshold of droplet nucleation, while we work with a low concentration of seeding aerosols to avoid excessively high droplet concentrations that can obscure the holographic data.

The first droplets are detected by holography ∼1 s after the temperature drop. In a first regime, occurring 1–2.5 s after expansion, we observe a rapid increase in the number of droplets detected in the measurement volume up to 10⁴ per time bin [Fig. 12(b)], together with an increase in the mean droplet diameter up to 20 μm [Figs. 12(c) and 12(d)]. The mean droplet diameter appears to grow as $t$⁠, consistent with diffusive growth. We note that droplets larger than 20–25 μm are most likely to grow through collisions and coalescence instead of diffusive growth; see the discussion by Poydenot and Andreotti.⁸ After 2–3 s, the droplet number plateaus before slowly decreasing, while the mean diameter continues to increase until t ∼ 6 s. The concentration of liquid droplets is calculated by dividing the number of measured droplets by the holography measurement volume (8.44 cm³). The maximum droplet concentration is ∼22 ± 2.1#/cm³ and is reached at t = 2.0 s, during the first droplet growth regime. The maximum droplet concentration is on the same order of magnitude as the concentration of seeding aerosols.

These findings highlight our ability to directly measure the growth of droplets during an expansion using holography in dilute regimes. We note that the absolute number of droplets detected here is much higher than when using PDA in Sec. III C 3 because of the much larger detection volume, while the actual droplet concentration is smaller. Overall, our combined use of PDA and holography allows us to probe droplet nucleation and growth over a wide range of conditions.

We have presented a new experimental rapid expansion cloud chamber facility designed to study processes relevant to aerosols and cloud microphysics. The experimental principle of our facility is that of an expansion chamber but with the addition of state-of-the-art real-time diagnostics and the ability to induce turbulent flows. The experimental facility comprises two vacuum-sealed chambers, which are capable of reproducing an adiabatic-like expansion, where the gas from the aerosol-nucleation chamber is allowed to expand into the evacuated expansion chamber, causing a sudden increase in saturation ratio. We demonstrate precise control over the initial conditions of the expansion, including the initial saturation ratio, S₀, seeding aerosol concentration, C₀, and air mixing conditions.

Our facility design allows us to achieve a high repetition rate of experiments to probe a wide range of conditions and ample optical access to perform high frequency real-time measurements. This report represents an initial demonstration of these capabilities. First, we characterize the chamber thermodynamics, finding the minimum temperature during the expansion in good agreement with theoretical predictions for both dry and moist conditions. We then present a discussion of droplet nucleation and growth in the presence of seeding aerosol particles for a range of experimental parameters. We characterize the total droplet number and mean droplet diameter throughout expansions. We observe the classic competition between the number of droplets and droplet size for a fixed amount of water vapor; the more the seeding aerosol, the more the droplets are observed and the smaller they are on average. The droplet concentration is shown to scale linearly with the initial aerosol concentration, while the mean droplet size decreases with seeding aerosol concentration. Simple scaling laws based on thermodynamic principles can describe these trends. Finally, we demonstrate the ability to characterize droplet growth under conditions near the onset of nucleation using inline holography.

The key advantage of the REACh facility is our high experimental repetition rate and our use of high-speed measurement techniques that enable us to conduct systematic parametric studies more efficiently than larger facilities. Future studies will involve detailed investigations of the interplay of homogeneous and heterogeneous droplet nucleation. We are also implementing high-speed infrared absorption measurements to directly measure the changing water vapor concentration (and therefore saturation ratio) throughout each expansion, coincident with holography measurements. We will also consider the role of turbulent mixing of different intensities and anisotropies. Finally, the chamber walls are equipped with a cooling system, which will permit us to explore lower-temperature conditions and the nucleation and growth of ice crystals in future work.

The supplementary material includes engineering drawings of the aerosol chamber and the expansion chamber.

This work was supported by a seed grant from the Simons Foundation (Award No. 1019423) and Princeton University internal funds from the Princeton Catalysis Initiative and the High Meadows Environmental Institute’s Climate and Energy Grand Challenge Award granted to L.D. and M.L.W. We thank Clare Singer for performing the internal review of this manuscript for NOAA-GFDL.

The authors have no conflicts to disclose.

Martin A. Erinin: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Cole R. Sagan: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Writing – review & editing (equal). Ilian Ahmed: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Gwenore F. Pokrifka: Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Nadir Jeevanjee: Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Marissa L. Weichman: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Luc Deike: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

All data used in preparing this work are available upon request.