The NaCl particles were generated by means of an atomizer (TSI 3075, TSI Inc., St. Paul, Minnesota, USA) atomizing an aqueous solution of 1 g NaCl L⁻¹ of double de-ionized water. The resulting aerosol was dried in a diffusion dryer to a RH lower than 20 %, i.e., a RH well below the ERH of NaCl particles, which is between 43 % and 45 % for the investigated particle size range .

Downstream of the dryer, the particles are charged by means of a neutralizer. A differential mobility analyzer (DMA; , type “Vienna medium”) is used to select a narrow particle size fraction. Inside the DMA, a further drying occurred as the RH of the DMA sheath air was always ≤ 5 %. For the experiments, we selected a mobility diameter of Dp_mob = 400 nm in order to be able to detect dry, solid particles optically by means of a Promo 2000 with a welas 2300 aerosol spectrometer (Palas GmbH, Karlsruhe, Germany) inside LACIS-T as well as to minimize the number of larger, doubly charged particles being present. As it turns out, their proportion in relation to the total number of selected particles is less than 1 %; i.e., doubly charged particles do not affect our results. Note that a particle shape factor has to be considered when converting the mobility diameter to a mass equivalent diameter because of the non-spherical shape of solid NaCl particles. This factor is 1.08 for NaCl particles according to, e.g., . Earlier measurements with the laminar flow tube LACIS confirm that this shape factor is valid for NaCl particles in the selected size range. In consequence, Dp_mob = 400 nm corresponds to a mass equivalent diameter of Dp_me = 370 nm.

The number concentration of the selected particles was determined utilizing a condensational particle counter (CPC; TSI 3010, TSI Inc., St. Paul, Minnesota, USA) and was kept at about 1000 cm⁻³ by means of a dilution system upstream of the DMA. The dilution system consists of a bypass, a filter, and two valves for adjustment of the flows. All flows, i.e., aerosol flow, DMA sheath, and excess airflow, as well as the CPC sample flow, were controlled by mass flow controllers (Brooks Instrument GmbH, Dresden, Germany) and checked with a bubble flow meter (Gilian^® Gilibrator™, Sensidyne Inc., Clearwater, Florida, USA) on a daily basis.

For the experiments, three different types of pre-conditioning were applied concerning the NaCl particles which were fed into LACIS-T:  

Case i. The particles were left dry (i.e., RH ≤ 5 %); therefore solid NaCl particles entered the measurement section of LACIS-T. This setup was only used to determine the optical size distribution of solid NaCl particles (see Sect. 4.2), as dry particle injection into LACIS-T reduces the mean RH in the mixing zone of the measurement section significantly (see Appendix ).

LACIS-T is a unique turbulent moist-air wind tunnel which has been established to study cloud physical processes, in general, and cloud microphysics–turbulence interactions, in particular. LACIS-T can be operated under a wide range of well-characterized and reproducible initial and boundary conditions resembling atmospheric warm, mixed-phase and cold clouds. The design, functionality, and capabilities of the setup are described in detail in , and only a brief description will be given here.

LACIS-T is a closed-loop wind tunnel of Göttingen type (Fig. ). The unique characteristic of LACIS-T is that it features two parallel flow branches, in which two particle-free airflows, “A” and “B”, can be separately conditioned and controlled with respect to volume flow rate (through the radial blowers and valves, up to 6000 L min⁻¹ each), water vapor content in terms of a dew-point temperature (through the humidification system, dew-point temperature range -40 °C < Td < 25 °C, with an accuracy of 0.1 K), and temperature (through the heat exchangers, temperature range -40 °C < T < 25 °C, with an accuracy of 0.05 K). These two airflows pass passive square-mesh grids through which defined turbulence is induced. They then enter the measurement section, at the entrance of which the particle-free airflows are combined and turbulently mixed. The measurement section is of cuboid shape with the dimensions of 200 cm × 80 cm × 20 cm. The aerosol particles are introduced into the mixing zone of the two turbulent particle-free airflows. This mixing zone provides an ideal environment for studying the influence of the turbulent fluctuations on aerosol and cloud microphysical processes. Downstream of the measurement section, the flow is directed towards an adsorption dehumidifying system where it is dried and heated. Afterwards, the flow is split up into the two branches, cleaned by particle filters, and the whole cycle starts again.

In this study, the flow rate was set to 4300 L min⁻¹ for each particle-free airflow, leading to a mean flow velocity of 1.35 m s⁻¹ in the measurement section. Turbulence conditions inside the measurement section are determined by means of hot-wire anemometry (Dantec Dynamics Inc., Skovlunde, Denmark) and LESs and are very similar to those described in . For example, the eddy turnover time τmix, which is a measure for the turbulent mixing timescale, is between τmix = 0.1–0.7 s. It increases due to the decaying turbulence inside the measurement section and is given as τmix = lT2/ε(1/3) e.g.,. The quantity ε represents the energy dissipation rate, while lT denotes the Taylor microscale. In the context of atmospheric conditions, the Taylor microscale is frequently considered to be the appropriate mixing length scale .

We use isothermal conditions in this study; i.e., the temperature in both particle-free airflows was identical, set to TA = TB = 15 °C and monitored via PT100 temperature sensors (1/10 class B, DIN EN 60751, accuracy of ±(0.0300°C+0.0005×T)). The dew-point temperature was set individually in each particle-free airflow and monitored by means of two dew-point mirrors (DPMs; model 973 by MBW Calibration AG, accuracy of ≤ ±0.1 K; reproducibility of ≤ ±0.05 K), sampling air in each flow branch between the heat exchanger and turbulence grid. Due to the individual settings of the dew-point temperatures, and thus the individual RH values in each flow branch, various RH mixing conditions could be established. That means different mean RH values, and different strengths of RH fluctuations, could be set in the mixing region (see Fig. a as an example for a specific set of RH conditions in branch A and B). In general, the larger the difference between RH_A and RH_B, the larger the strength of the RH fluctuations. However, no direct measurement of dew-point temperature fluctuations and consequently RH fluctuations is available so far. The strengths of the fluctuations are determined by means of LESs, which are described in Sect. 4.1.

Finally, particle size distributions are determined optically via a Promo 2000 with a welas 2300 aerosol spectrometer (Palas GmbH, Karlsruhe, Germany). The welas 2300 sensor is placed inside the measurement section with a 15 cm long stainless-steel tube (5 mm inner diameter) on top of its own inlet tube. This additional long tube ensures particle extraction and detection from the flow field, which is only very weakly influenced by the body of the welas 2300, which disturbs the flow field in its closer vicinity. Please note that the distance of the tip of this stainless-steel tube relative to the aerosol inlet of LACIS-T, called “z”, is used as a reference in the later data description.

In the first set of experiments, the welas 2300 is placed at a fixed position inside the measurement section, leading to a fixed residence time of the particles until the detection occurs. The inlet tube is placed at z = 30 cm below the aerosol inlet of LACIS-T. In the second set of experiments, the position of the tube together with the welas 2300 is varied, leading to different mean residence times of the particles.

At first, the simulations are employed to determine the RH experienced by the particles, as well as to ascertain the impact of the particles themselves on the RH field within the mixing region inside the measurement section. This is presented exemplarily for the setting of RH_A = 60 % and RH_B = 85 %, leading to a mean RH of 72.5 % along the center line. About 78 000 monodisperse NaCl particles with a mass equivalent diameter of Dp_me = 370 nm are tracked inside the measurement section. The NaCl particles are pre-conditioned according to Case (ii); i.e., the aerosol is injected with RH = 70.2 % (as introduced in Sect. 2.1). In Fig. a, a snapshot of the instantaneous RH field in the symmetry plane is shown, including the respective particles deliquescing and growing along the inverse vertical axis. The dashed line represents the center line, where the strongest mixing occurs, as well as where the particles are detected further downstream. As the particles shown move through the channel, statistics are calculated at distinct horizontal planes over time; i.e., data from particles that pass a given horizontal plane are stored and analyzed later on.

As mentioned, the RH of the introduced aerosol is slightly lower than the mean RH along the center line of the measurement section. This influences the RH field along the center line, which is illustrated in Fig. b in terms of the median RH (RH_med), the mean RH (RH_mean) and the standard deviation of the RH (σRH). First of all, it can be seen that generally RH_med and RH_mean fall together. Secondly, RH_mean is observed to be slightly lower close to the location of aerosol injection. However, it increases on the very first centimeters and then reaches a constant value of 72.5 % at a height of approximately z = 15 cm. Additionally, σRH demonstrates an increase within the initial 15 cm, subsequently reaching a constant value of 4.9 %. Consequently, the data obtained for z ≥ 15 cm will be employed for the subsequent data interpretation. As an example, the RH experienced by particles near the center line when passing the horizontal plane at z = 30 cm is shown as normalized frequencies in Fig. c, and the obtained RH distribution has a Gaussian shape.

Note that there is an influence of the SGS motions on the simulated fluctuations and consequently σRH. Based on currently ongoing work and in accordance with a study performed by , we estimate the contributions from these SGS fluctuations to the total fluctuations to be max ±0.04 × σRH, which represents the uncertainty of the determined σRH values.

In order to be able to determine the fraction of deliquesced particles, first the size distributions of both dry and deliquesced particles, as well as those of a mixture of both, need to be considered. Therefore, in a first set of experiments, different RH conditions are adjusted in order to obtain and interpret the corresponding size distributions. The corresponding RH_mean values at the center line are calculated from the RH values of the individual particle-free airflows. In general, it turns out from repeated measurements of temperature and dew-point temperature inside the tunnel that there is an absolute uncertainty in RH_mean of up to 0.6 %. The width of the RH distribution which is given in terms of σRH is obtained from the LES. For this first set of experiments, the welas 2300 position was fixed, with its inlet being placed at z = 30 cm leading to a mean residence time of the particles before detection of approx. 0.22 s as the mean velocity is 1.35 m s⁻¹. Figure  shows the results of four different experiments for the conditions given in Table .

No distinct difference in the obtained particle size distributions is observed for experiments (1) and (2). During experiment (2), the particles most likely start to take up water molecules, leading to a thin liquid shell surrounding the particles; however, particles are still non-deliquesced under these humid conditions. This is in agreement with observations obtained by and for single NaCl particles.

Experiment (3) shows a clear increase in particle size compared to experiments (1) and (2). In this case, the NaCl particles are fully deliquesced. The mean particle diameter determined optically agrees with the diameter calculated with the Köhler equation for this RH_mean.

Finally, experiment (4) results in two modes. The first mode fits with the one for solid NaCl particles, while the second mode fits with the one obtained for the deliquesced particles. That means we observe both solid and deliquesced particles at the same time. In other words, the humidity fluctuations lead to particle deliquescence although RH_mean is smaller than the DRH, which is about 75.5 % at 15°C Chap. 10.2.2, pp. 453–454. By fitting both modes with two lognormal distributions (see Fig. ), the solid and deliquesced particle fractions can be determined, which in the example are 0.57 and 0.43, respectively.

To systematically quantify this effect, such experiments have been performed for various thermodynamic and flow conditions, as well as particle residence time (i.e., welas 2300 sensor positions).

First of all, the influence of RH fluctuations on the deliquesced particle fraction was determined for a fixed welas 2300 position, i.e. a fixed mean residence time. For this, the welas 2300 inlet was placed again at z = 30 cm. RH_mean was varied between 71.6 % and 78.1 %, i.e., from below to above the DRH of the investigated NaCl particles, and σRH was set between 0 % and 9.5 %. A few studies exist e.g., that show σRH values in the range of 1 % to 4.6 %, depending on the environmental conditions. It means that our measurements cover this range of observed strengths of RH fluctuations.

The obtained deliquesced particle fractions fdel are depicted in Fig.  as a function of σRH for four different RH_mean values.

Generally, it becomes obvious that the humidity fluctuations have a strong influence on the fraction of deliquesced particles. Particle deliquescence can be observed although RH_mean < DRH. Furthermore, we detect an increase in the deliquesced particle fraction with increasing σRH as long as RH_mean < DRH. In this case, an increasing σRH increases the probability that solid NaCl particles are in a RH field with RH values higher than the DRH. The slope of fdel flattens for RH_mean, which is close to the DRH, and becomes negative for RH_mean > DRH as now the increasing σRH increases the probability that solid NaCl particles experience a RH field with RH values lower than the DRH and therefore do not deliquesce. In other words, in this case, not all particles deliquesce although RH_mean > DRH.

Secondly, the influence of RH fluctuations on the deliquesced particle fraction was determined as a function of mean particle residence time tres in a fluctuating RH field. This was achieved by changing the position of the welas 2300. The purpose of this type of experiment is as follows. Particles once deliquesced will not recrystallize/effloresce at the DRH. They would do so at the ERH, which is between 43 % and 45 % for NaCl particles of the investigated size range . However, in our experiments, even for the broadest RH distributions, we do not reach this ERH. That means if solid NaCl particles are inserted into fluctuating RH fields, the residence time in this field might influence the number and fraction of deliquesced particles.

Figure  shows a series of normalized particle size distributions for RH_mean = 75.9 % and σRH = 4.9 %, with different tres inside the measurement section. It can be seen that the deliquesced particle mode of the distributions (right mode) increases with increasing tres, while the solid particle mode (left mode) decreases. In other words, more particles deliquesce with increasing tres due to the hysteresis effect.

Measurements as presented in Fig.  have been carried out for other sets of RH_mean and σRH values. The respective results are summarized in Fig. . Here, the fraction of deliquesced particles fdel is depicted as a function of tres (logarithmic scale) inside the fluctuating RH environment. In the left plot, RH_mean is fixed, and σRH is varied. In the right plot, it is vice versa. The key findings are that the fraction of deliquesced particles increases with increasing tres for all investigated cases. For fixed RH_mean, the slope of the three curves looks very similar, pointing towards an approximately exponential relationship between fdel and tres, with the curves shifting upwards to higher values of fdel as σRH increases. When looking at the curves for fixed σRH it can be observed that the slopes become flatter with increasing RH_mean, as a greater proportion of the particles is already deliquesced at the lowest measured residence times. Consequently, fewer solid particles are available for deliquescence.

In summary, it can be said that the combination of turbulent RH fluctuations and hysteresis in aerosol particle deliquescence and efflorescence has a significant impact on the fraction of deliquesced particles over time. The time required for all NaCl particles to deliquesce depends on both the mean RH and the strength of the fluctuations, or in other words, the proportion of deliquesced particles is dependent on RH_mean, σRH, and residence time.

Finally, we simulated the deliquescence of the NaCl particles in the turbulent RH field by running LESs in OpenFOAM. In general, the time dependence of fdel can also be identified in the model results. However, the simulations appear to overestimate the observed deliquesced particle fractions, which might be caused by our assumption of a constant timescale for the deliquescence process itself. A detailed discussion about this discrepancy and its possible reasoning is given in Appendix . Nevertheless it is important to point out that this discrepancy between measurement and simulation does not invalidate the experimental observations and central statements. Furthermore, it motivates us to investigate the suitability of different theories in the future (more details given in Appendix ).