The injection head is composed of two parts – the droplets and the AP injection. The upper part is used to inject the droplets while the APs are injected in the second part about 10 cm below. This distance is required to measure the droplet size through the two facing windows (see Sect. 2.4.1) but also to let droplets decelerate and reach their terminal velocity.

The droplet train is injected through a housing made with a 3D printer set at the top of the droplet injector (see Fig. 3). This housing has been constructed to precisely place the droplet generator and the electrostatic inductor together. Indeed, the electrostatic inductor has to keep the same position relative to the droplet generator to prevent changes in the electric field Eind, which in turn can disturb the droplet charge and stop the neutralisation (detailed in Sect. 2.4.2).

The APs are injected from the sides of the entire circumference through a flat torus inlet. This injection principle is based on the CLINCH experiment (CoLlision Ice Nucleation CHamber, Ladino et al., 2011), which ensures a laminar flow and a great spatial APs mixture in the collision chamber's inlet.

The CE is calculated from the AP mass collected by the droplets during an experiment and the average AP mass concentration in the collision chamber. To obtain these quantities, the droplet train must be separated from the interstitial APs (which were not collected).

The system developed to separate the droplet train from the AP flow is presented in Fig. 4. It is composed of a converging portion (from 5 to 3 cm in diameter) where a gutter is inserted to prevent the water condensed on the wall from entering to the In-CASE chamber bottom. The APs are directly vacuumed toward a HEPA filter (see Fig. 2) at the upper part of the separator through four outlets while the droplets – containing collected APs – are impacted into a cup at the separator's lower part.

To prevent AP pollution in the droplet impaction cup, a counterflow is injected below the In-CASE chamber and passes through the droplet impaction cup from nine holes set on its entire circumference. Since the counterflow is injected at the laboratory temperature, and the AP downward flow is colder, Argon – denser than the air – was selected to avoid any Rayleigh–Taylor instability (Sharp, 1983).

Argon is injected at 0.4 L min-1. The diameter of the nine holes is 4 mm, and the top of the droplet impaction cup is 2.5 cm. Thus, the upward Argon flow is injected at 5.9 and 1.4 cm s-1, through the nine holes and the top of the impaction cup, respectively. Because the droplet velocity is about 25 cm s-1 (for the 50 µm droplet radius studied) and the AP terminal velocity is less than 10-3 cm s-1, APs cannot settle into the impaction cup, whereas droplets are impacted without undue disruption.

The droplet and AP separation were verified with two tests. First, In-CASE was run under standard experimental conditions except no droplets were generated. After 5 h of experiment, a spectrometry analysis was performed in the droplet impaction cup, and no fluorescein was detected. Thus, no AP had settled on the droplet impaction cup during the experiment.

The second test was to ensure that droplets were collected by the impaction cup. Then, In-CASE was again run like a typical experiment except the flow passing through the In-CASE chamber was clean air without any AP. Droplets were tracked by adding sodium fluorescein salt in the water supplying the piezoelectric injector. Since the concentration of sodium fluorescein salt in the water, the droplet generation frequency, the droplet size and the experiment time were known, the goal was to verify if the expected fluorescein mass in the droplets and the actual measured fluorescein mass were equal. After 5 h (=450 000 injected droplets), a discrepancy of 2 % between expected and measured fluorescein mass was obtained. Therefore, all droplets are considered impacted in the impaction cup.

Finally, this indicates that the AP mass detected in the droplet impaction cup after the experiment effectively results from collection by drops in the In-CASE collision chamber and not from contamination from other sources.

The collision chamber is a 1 m stainless steel cylinder with an inner diameter of 5 cm (see Fig. 5). The collision chamber's temperature is controlled through a coolant which spirally circulates outside the chamber, from the bottom to the top of the collision chamber. The pressure (Pair), temperature (Tair) and relative humidity (RH) are measured at the top and the bottom by sensors. To clean the chamber, water or compressed dried air is injected via a purge. Three sampling points are available but were not used for these experiments.

The temperature and the relative humidity discrepancies between top and bottom were respectively less than 1 ∘C and 4 % in all the CE measurements – the mean values are then considered for both parameters.

All the experiments were conducted at atmospheric pressure. To get comparable CE measurements, the temperature has been set to 0.58±0.50 ∘C – as constant as possible between experiments. Three levels of relative humidity (RH) were considered – 71.1 %, 82.4 % and 93.5 %. To increase the relative humidity at a given collision chamber temperature, the temperature of the pure water in the humidifier (Fig. 2) was increased. The relative humidity level of 71.1 % was obtained by completely removing the humidifier to get the driest AP flow possible at the collision chamber's inlet. At lab temperature (about 22 ∘C), the relative humidity of the dry AP flow ranged from 10 % to 20 % at the In-CASE chamber inlet.

Note that the AP flow before the injection head is also thermally set to inject APs with the same temperature as in the collision chamber.

The change in droplet radius due to evaporation in the collision chamber is calculated according to the Sect. 13.2 of Pruppacher and Klett (1997). The corresponding terminal velocity (UA,∞≈25 cm s-1) is computed from Beard (1976). The residence time of the droplet in the chamber (≈4 s) is computed considering these two changes. Since the droplet radius only decreases around 3 % by evaporation with the lower relative humidity considered in the experiments (71.1 %), the droplet evaporation in the collision chamber is neglected.

The APs are composed of pure sodium fluorescein salt, which is a high hygroscopic chemical compound. The APs inside the collision chamber then grow to reach their equilibrium size with the relative humidity (RH). In order to evaluate the increase in size by humidification, the AP growth factor (GroF) measured in Quérel et al. (2014) was considered. The growth factor is defined as the ratio of the size of the wet AP over the size of the dry AP. Since their data are limited to relative humidity levels below 90 %, the kappa theory described in Petters and Kreidenweis (2007) is used to extrapolate to the required values. To fit the measurements of Quérel et al. (2014) with the kappa theory, only their data with a relative humidity level less than 85 % were considered. Figure 6 shows the AP growth factor related to the relative humidity for a kappa value of 0.23 and two extreme values of 0.2 and 0.27 – fitting to the sodium fluorescein salt hygroscopicity.

Thus, for relative humidity levels of 71.1 %, 82.4 % and 93.5 % studied here, a dry AP radius of 50 nm selected by the differential mobility analyser (DMA) grows with a growth factor (GroF) of 1.16, 1.27 and 1.57, respectively. Consequently, the CEs measured are applied for size of respectively 58.0, 63.5 and 78.5 nm AP radii.

Note that the AP density is not the one of sodium fluorescein salt (ρfluorescein=1580 kg m-3) since APs contain water. Indeed, the water density (ρwater) should be considered in the AP density (ρAP) calculation. At a given relative humidity (RH), the AP density inside the chamber is then deduced by Eq. (1): 1ρAPRH=ρfluorescein+ρwater×GroFRH3-1GroFRH3.

Since the relative humidity after the dryer (see Fig. 2) ranges from 10 % to 20 %, the AP growth factor is less than 1.02 (see Fig. 6) in the DMA. APs are then considered dry when exiting the DMA.

The droplet generator used for these experiments is a piezoelectric injector provided by Microfab – the MJ-ABL-01 model with an internal diameter of 150 µm. This model has been used for its stability over time, since the experiments can last up to 5 h. This piezoelectric injector generates droplets – at a given frequency – above their terminal velocity. The distance between two following droplets reduces when droplets fall away from the injector's nozzle since the droplet velocity decreases (see Fig. 8, left). It was emphasised during ex situ experiments that droplet generation frequencies greater than 25 Hz induce droplet coalescence since the inter-droplet space becomes too short to prevent droplets from aerodynamically disturbing each other. This agrees with Ardon-Dryer et al. (2015), who observed droplet coalescence for droplet generation frequency larger than 30 Hz operating a similar piezoelectric injector. Thus, droplets were generated at 25 Hz in all experiments presented in this current paper.

The droplet generator is placed at the top of the In-CASE collision chamber, within an injection head (see Fig. 3). A few times during an experiment, droplet pictures are recorded by optical shadowgraphy through two facing windows in the injection head (see Fig. 3). A circle Hough transform is then applied to evaluate the droplet radii in the recorded pictures. An example is given in Fig. 8 (right) for a 49.7 µm droplet radius. Note that the size distributions of the droplets generated by the piezoelectric injector are considered monodispersed since the droplet size dispersion is very low (σ∼1 %).

It is well know that the piezoelectric droplet generator produces highly electrically charged droplets. With a similar device, Ardon-Dryer et al. (2015) measured up to 104 elementary charges on the generated droplets. Since this paper focused only on the relative humidity influence, the droplets, as well as APs, must be neutralised.

To do so, an electrostatic inductor was built following Reischl et al. (1977). Two parallel metal plates are placed at the droplet generator's nozzle – this is the electrostatic inductor shown in Fig. 9 (labelled 1, left). One plate is connected to a potential (Vind) while the other is connected to the neutral potential – as presented in Fig. 9 – in order to induce an electric field (Eind∼102–103 V m-1). Sodium chloride is added to the pure water that feeds the piezoelectric injector. According to the generated electric field polarity, the system can selectively attract negative or positive ions toward the nozzle where the droplet is formed. If Vind is positive, the negative chloride ions (Cl-) migrate toward the nozzle and the positive sodium ions (Na+) are repulsed from the nozzle and inversely if the potential is negative. Following the electric field amplitude – through Vind – the ion quantity can be set. This system can conclusively control the droplet charge. Note that the sodium chloride concentration has no effect on the principle of induction used here since the ion number is large enough for the entire experiment period (Reischl et al., 1977) – 3.3 g L-1 has been considered.

To evaluate the droplet charge and then neutralise the droplets, an ex situ experiment has been conducted where the droplet train passed through a capacitor (labelled 2, Fig. 9, left). One capacitor's plate is connected to the neutral, whereas the other is connected to a high potential (Vcap) – inducing an electric field (Ecap∼105–106 V m-1). A Faraday cage surrounding the capacitor and a plate maintained at a neutral potential are set in order to prevent the electric field at the capacitor (Ecap) from disturbing the electric field at the inductor (Eind), which could change the droplet charge. Finally, the potential Vind which electrically neutralises the droplet is found by selecting for the Vind value which minimises the droplet train deflection.

Actually, this system can also be used to precisely evaluated the electric charges on the droplets (for both polarities); this method is applied and presented in Dépée et al. (2021).

Note that the droplet charge induced by the piezoelectric injector has been calculated to -8400 elementary charges – in line with Ardon-Dryer et al. (2015) using a similar generator. Moreover, after the droplet neutralisation, an uncertainty of 600 elementary charges was estimated.

The first AP radius uncertainty is related to the AP selection by the DMA. Nevertheless, this uncertainty has been neglected since the spectral bandwidth of the DMA is quite small compared to the AP radius uncertainty addressed below.

Indeed, the only significant AP radius uncertainty results from the effective AP radius inside the In-CASE collision chamber due to the hygroscopicity of the APs. For the relative humidity levels studied (71.1 %, 82.4 % or 93.5 %), the extreme relative humidity levels measured in all experiments are considered – for 71.1 %, the minimum and maximum values are 69.2 % and 73.4 %, respectively. As a reminder, the kappa value is assumed from the Quérel et al. (2014) data and ranges from 0.2 to 0.27 (see Fig. 6). The low uncertainty for the AP radius is then evaluated by considering the minimum growth factor (GroF) in Fig. 6 for the lower level of relative humidity measured and the lower kappa value determined – respectively 69.2 % and 0.2. Similarly, for the same example (RH = 71.1 %), the high uncertainty for the AP radius is estimated by evaluating the maximum growth factor – for the maximum level of relative humidity observed and the maximum kappa value assumed – respectively 73.4 % and 0.27. In this example, for a dry AP radius of 50 nm selected by the DMA, its wet radius in the In-CASE collision chamber is likely to be 58 nm (GroF = 1.16), ranging from 56.5 nm (GroF = 1.13) to 60 nm (GroF = 1.20) resulting from the respective low and high uncertainties.

Since the method of CE evaluation differs in the presence of multiple charged APs, the uncertainty calculation is also different depending on the situations. The method is described in Appendix B.

When there are no multiple charged APs in the AP flow, the CE is directly estimated through Eq. (3), which can be rewritten as Eq. (7): 7CE(a,A,RH)=mAP,dπA+GroF(RH)×a2×Nd×Heff×Cm,AP≈mAP,dπA2×Nd×Heff×Cm,AP, where Nd is the number of injected droplets during the experiment. The relative CE uncertainty (uCE) is then evaluated according to Lira (2002) and summarised by Eq. (8), 8uCE=uA2+uHeff2+uNd2+umAP,d2+uCm,AP2, with the following.

The relative uncertainty related to the droplet radius measurement (uA), which is the ratio between the standard deviation and the mean droplet radius on 200 pictures obtained by optical shadowgraphy. This relative uncertainty is about 1 %.