Direct observation of vapor saturation and droplet growth inside the CPC is not feasible. To support the interpretation of experimental measurements, we employed numerical simulations. These simulations were conducted using COMSOL Multiphysics^®, a three-dimensional computational fluid dynamic simulation program (CFD).

A two-dimensional axisymmetric model of the saturator and condenser stages was developed, with geometries chosen to closely reflect the actual instrument. Within the saturator, a metal rod of radius 0.2cm is located at the centerline. It is assumed that this metal rod also has the saturator temperature Tsat. An additional insulator stage was simulated between the saturator and condenser stage. The overall flow rate was set to 0.6L min⁻¹, as specified for the CPC. Simulations were carried out under various pressure and internal temperature conditions. Temperature-dependent properties of the working fluids, including surface tension, density, vapor pressure, and gas-phase diffusion coefficient, were obtained from Yaw’s Handbook for both DMSO and butanol . Atmospheric pressure effects were considered by modifying the diffusion coefficient of the working fluid in air and the carrier gas density, as lower pressure decreases gas density and proportionally increases the diffusion coefficient .

The model couples laminar flow, heat transfer in fluids, and convective-diffusion modules to compute the temperature, velocity, and vapor concentration fields in the CPC. These fields are then passed to MATLAB for the calculation of the subsequent droplet growth inside the condenser . The minimum particle size that can be activated for condensation growth is given by the Kelvin equation, where σ is the surface tension, R the molar gas constant, T the temperature, S the supersaturation ratio, and νm the molar volume: 1Dp,Kelvin=4σνmRTln⁡S Due to the spatial variation of temperature, surface tension and saturation ratio, Dp,Kelvin also varies at different locations of the condenser. When the required supersaturation ratio is reached for a specific radial position and particle size Dp,Kelvin according to Eq. (), droplet growth computation is initialized and solved using MATLAB’s ode15s solver. This solver is designed to handle stiff differential equations and differential-algebraic equations (DAEs) with a variable-order integration method. A more in-depth description of the particle growth rate can be found in . Concentration-dependent effects, such as vapor depletion and condensational heating, are not considered in the simulation, as they become significant only at high particle number concentrations . Vapor depletion refers to the uptake of working fluid vapor by particles, while condensational heating arises from the release of latent heat during condensation, which increases the local temperature and reduces the supersaturation. A more detailed description of the model can be found in .

Accurate interpretation of Faraday Cup Electrometer (FCE) measurements requires correction of the raw data for instrumental offsets and pressure-dependent flow variations. The electrical offset of the FCE arises from small background currents within the electrometer circuitry or leakage currents in the measurement system. Offsets of a few femtoamperes (fA) are commonly observed and can be comparable in magnitude to the aerosol-induced signal, especially under conditions of low particle concentration . Consequently, regular baseline measurements with particle-free air must be performed to determine and subtract the offset current from the recorded data. Proper correction for this offset is essential to ensure the accuracy of the derived charge fluxes and to avoid systematic bias in the aerosol charge or concentration estimates. Furthermore, corrections to the electrometer flow rates were made to account for the corresponding conditions of reduced pressure.

When using a diffusion charger together with a DMA and an FCE as the reference instrument, it is important to account for the presence of multiple charged particles exiting the DMA. A particle carrying n charges will be detected n times by the FCE, whereas the CPC will register it only once. To correct for this discrepancy in counting rates, the procedure described by was applied. This method incorporates the actual particle size distribution to properly account for the contribution of multiple charged particles.

The FCE instrument was not calibrated immediately prior to the measurements. According to the manufacturer, the calibration factor typically does not exceed 2 %, indicating only a minor contribution to overall measurement uncertainty. Moreover, because we normalise our efficiency curves using the linearity of concentration signal (see Sect. ), any systematic offset associated with the FCE calibration factor is effectively incorporated into this normalisation procedure. As a result, the absence of an externally applied FCE calibration factor is not expected to influence the interpretation of our results, especially the cutoff diameters.

The Sky-CPC 5411 provides an internal diagnostic of droplet growth. Aerosol particles enter the instrument, undergo condensational growth to droplets in the condenser, and are subsequently detected optically. This growth process is evaluated by the instrument using two fixed signal thresholds.

In the following, we refer to the particle number concentrations c0 and c1, which the instrument derives from two fixed manufacturer-defined voltage thresholds in order to distinguish different levels of droplet growth based on the scattered-light signal. These thresholds are Uth(c0)=0.5V and Uth(c1)=1.2V, respectively.

The lower threshold Uth(c0) represents the minimum signal required for a grown droplet to be detected above the noise level. The corresponding concentration c0 therefore includes all aerosol particles that have grown into optically detectable droplets. The higher threshold Uth(c1) requires a stronger scattered-light signal and is only exceeded by droplets that have grown to larger sizes. The concentration c1 thus represents the subset of detected droplets that produce a higher optical signal. By design, the instrument reports the c1 concentration as the particle number concentration.

The ratio c1/c0, hereafter referred to as the indicative droplet growth ratio, provides a diagnostic of the growth efficiency, i.e. the fraction of optically detected droplets that reach the higher signal regime within each 1 s measurement interval. Values of c1/c0<1 indicate that a fraction of grown droplets does not reach the higher detection threshold.

As illustrated in Fig. , the DMSO droplet diameters corresponding to the c0 and c1 thresholds are approximately 2.5 and 4.6 µm, respectively, with smaller droplets not being counted. These values were derived by from signal measurements of latex test particles combined with a model of scattered-light intensity for the GRIMM measuring cell. Since these thresholds were originally defined by the manufacturer for operation with butanol, an adjustment is required when using DMSO. This is due to the lower vapor pressure of DMSO, which reduces the available vapor for condensational particle growth. Ideally, this adjustment would be implemented in the instrument hardware through a redefinition of the voltage thresholds for DMSO operation. As a practical workaround in this study, we use the c0 count as the particle number concentration.

The linearity of the concentration signal of a CPC describes how its measured response varies with changes in total particle number concentration relative to a reference instrument. Calibration is necessary due to the specific configuration and instrumentation used in this study. The measurement shown in Fig.  was performed using the experimental setup described in Sect.  and illustrated in Fig. . A single DMA scan cycle was conducted, covering particle diameters from 140nm down to 2.5nm, producing monodisperse aerosol populations at each step. The reference number concentration for each size was determined using the FCE, which measures particle charge to provide an accurate, traceable count. The linear relationships between the concentrations measured by both CPCs and the FCE is characterised by the slope K0. The black dashed line represents the 1:1 relationship, while the shaded gray area indicates a ±10% deviation. Filled squares correspond to the coincidence-corrected concentrations of the B-CPC, and circles denote the coincidence-corrected and c0-adjusted concentrations of the DMSO-CPC. Both datasets are plotted against the fully corrected FCE concentration. The slope obtained for the B-CPC is K0=0.886, which agrees well with the slope of the DMSO-CPC, for which K0=0.866. The slope of each linear fit is subsequently used to correct the data, ensuring comparability of the D50 cutoff diameters across all measurements by normalising the efficiency curves to unity (see Sect. ).

In order to ascertain the performance of a CPC, the counting efficiency curve with respect to a reference instrument is utilised. The calculation of the particle-size-dependent counting efficiency η is derived from the ratio of the corrected number concentration of particles detected by the CPC (NCPC) to the corrected number concentration measured by the reference instrument, in this case the electrometer (NFCE): 2η(Dp)=NCPCNFCE Figure  presents representative counting efficiency curves for the Sky-CPC 5411 operated with butanol and DMSO. The efficiency curves are parameterized by an exponential fit function introduced by : 3ηfit(Dp)=A1-exp⁡(B-Dp)(C-B)ln⁡2 From the efficiency curves, two characteristic parameters can be determined. First, the asymptotic maximum counting efficiency ηmax. It represents the plateau region where the counting efficiency remains constant as the particle diameter increases. Second, the cutoff diameters, D50 and D90, which correspond to the particle diameters at which 50% or 90% of the particles are counted relative to the reference.

To validate the experimentally quantified final droplet size in the condenser (Sects.  and ), model simulations of the saturation ratio and droplet growth were conducted. The temperature and vapor pressure fields were simulated for the Sky-CPC 5411 operated with butanol and DMSO, as described in Sect. . From the results, the calculation of the saturation ratio S was performed, which are presented as contour plots in Fig.  for the pressure stages of 1000, 500, 250 hPa and for a temperature setting of Tsat=40°C and Tcon=10°C. Figure  only shows the condenser section of the CPC, starting at 110mm from the instrument inlet. The preceding parts, including the saturator (0–100mm) and the 10mm insulating section, are not shown, as the focus is on supersaturation within the condenser and the droplet growth at its outlet. The simulations were performed for all pressure stages and temperature settings of the experimental results (see Sect.  and ), but for clarity only those conditions are provided.

Figure  shows that both working fluids produce nearly identical saturation profiles inside the condenser when operated under identical conditions. This consistency holds across all simulated temperature and pressure settings. A key feature of the profiles is the region of maximum saturation ratio Smax, which determines the smallest particles that can be activated. The position of Smax depends on pressure: at 1000hPa, it occurs near the end of the condenser, while at lower pressures it shifts progressively toward the center. This trend agrees with previous simulation studies and can be attributed to the pressure dependence of the Reynolds number Re in the heat and mass transfer equations . The CPCs were operated at constant volumetric flow. As diffusivity increases with decreasing pressure, heat and mass transport within the condenser become more efficient. As a result, the supersaturation maximum shifts toward the inlet of the condenser, effectively increasing the usable length of the condenser and the residence time available for particle activation and droplet growth under reduced-pressure conditions.

Furthermore, the magnitude of Smax varies with pressure, being lowest at 1000hPa and highest at 500hPa. The low supersaturation observed at 1000hPa may be attributed to the limited dimensions of the condenser. Owing to its short length, the system does not allow sufficient residence time for the maximum supersaturation to be reached. Furthermore, the longer mean free path at lower pressures enhances diffusion away from the liquid surface, leading to higher saturation ratios. At the lowest pressure stage (250hPa), however, the supersaturation decreases again due to the reduced number of vapor molecules available.

The final droplet sizes resulting from the simulated saturation profiles were calculated for all temperature and pressure settings. The results are shown in Fig.  for both working fluids. Consistent with the lower saturation vapor pressure of DMSO compared to butanol, droplets in the B-CPC exhibit approximately four times greater growth than those in the DMSO-CPC, although the overall behaviour remains similar. The pressure-dependent droplet growth follows the same trend as the saturation profiles: the smallest growth occurs at 1000hPa, reaches a maximum at 500hPa, and decreases slightly at 250hPa. This pattern is observed for both working fluids across all temperature settings. Comparison of the different temperature conditions confirms two main trends derived from the experimental results. First, a larger temperature difference between the saturator and condenser ΔT leads to enhanced droplet growth. Second, for the same ΔT, a higher saturation temperature Tsat also promotes greater droplet growth. This is consistent with previous studies, where similar behaviour was observed .

However, the simulated absolute final droplet sizes do not match the measured droplet sizes discussed in Sect. . While the c1/c0 values suggest insufficient droplet growth for DMSO under most conditions (see Table ), the simulated final droplet diameters exceed 8µm for all conditions. Two potential explanations can be proposed for this discrepancy. First, the simulations assume a perfectly wetted wick and account solely for condensation processes. Because the freezing point of DMSO is 18°C, sublimation of the vapor may occur, which is not captured by the simulations. Second, we were limited to using estimated condenser dimensions as input for the numerical calculations in our study. demonstrated that the condenser diameter strongly affects droplet growth, with larger diameters yielding larger droplets. Also, their simulations similarly over-predicted droplet sizes compared to their experimental measurements. Accordingly, we may overestimated the Sky-CPC’s geometric dimensions, leading to larger simulated droplet sizes. Nevertheless, the overall trends and the comparison between working fluids, temperature settings, and other studies support the validity of the results.

With the experimental setup described in Sect.  the counting efficiencies for two Sky-CPCs 5411 were determined at four different pressures of 1000, 700, 500 and 250hPa. One CPC was operated with butanol as working fluid (B-CPC), the other with DMSO (DMSO-CPC). The chosen temperature setting for the DMSO-CPC corresponds to the setting where it was found to perform best, especially regarding its c1/c0 ratio which indicates sufficient particle growth. The saturator temperature of the DMSO-CPC was 40°C, the temperature at the condenser 5°C. The saturator temperature of the B-CPC was 36°C, the temperature at the condenser 10°C as intended by the manufacturer. The obtained counting efficiency curves are shown in Fig. . The y axis error bars indicate the standard deviation of the counting efficiency mean values and the vertical dashed lines represent the calculated D50 cutoff diameters.

The asymptotic maximum counting efficiency ηmax is normalised to unity due to the applied calibration (see Sect. ). Consequently, it is not possible to directly evaluate the dependence of ηmax on pressure. However, to assess this dependence, the slope correction parameters, K0, can be compared, while the D50 cutoff diameters remain directly comparable across different measurement conditions. Figure  shows a slight shift in the D50 towards larger particle diameters, which is associated with a less steep slope as the pressure decreases. This shift is negligible, as it moves the cutoff from D50(1000hPa)=4.9nm to D50(250hPa)=6.2nm and lies within the uncertainty of the experiment. Figure  shows the K0 values plotted against the temperature difference and the different pressures are denoted by the different markers. Due to the imprecise sheath flow control within the electrometer, these K0 values cannot be treated as absolute values, but rather as a relative indicator on how the asymptotic maximum counting efficiency depends on pressure. As demonstrated in Fig. , there is a minor dependence of K0 on pressure for both CPCs, with reduced values as the pressure decreases. The asymptotic maximum counting efficiency, ηmax, decreases by about 14% as K0‾ drops from 0.88 at 1000hPa to 0.75 at 250hPa.

A key finding from the pressure-dependence measurements is the close agreement between the B-CPC and the DMSO-CPC, consistent with the observations from . Furthermore, these results align with experimental data for a CPC operated with isopropyl alcohol reported by . Earlier studies consistently report a critical low-pressure point at which the CPC counting efficiency drops sharply . As no such sharp drop was observed in our measurements, it is likely that the critical pressure for the Sky-CPC 5411 was not reached for either working fluid. Moreover, the pressure independence of D50 was confirmed for other CPC temperature settings (see Sect. ).

The counting efficiencies of the two Sky-CPCs 5411 (B-CPC and DMSO-CPC) were measured at five different internal temperature settings, as described in Sect. . The saturator and condenser temperatures are fixed values set via the CPCs' software, allowing investigation of both the temperature difference between saturator and condenser and the absolute temperatures of each component. The chosen settings cover a temperature difference range of 25–35°C, with saturator temperatures varying between 35 and 40°C. Of particular interest is the setting Tsat=40°C and Tcon=15°C, since the freezing point of DMSO is 18°C. With the condenser temperature close to the freezing point, potential differences in droplet growth – whether forming solid crystals or droplets – could be observed .

Figure  shows the counting efficiency curves of different temperature settings for the DMSO-CPC at ambient pressure of approximately 1000hPa. As before, the y axis error bars indicate the standard deviation of the counting efficiency mean values and the vertical dashed lines represent the calculated D50 cutoff diameters. It is evident that the temperature settings of the CPC have an impact on the D50, with a higher temperature difference leading to lower D50 cutoff diameters. This finding is in good agreement with other studies and can simply be explained by higher supersaturations achieved in the condenser . Especially the reduced saturator temperature of Tsat=35°C seems to lead to a more pronounced shift towards larger particle diameters than the temperature difference itself. This finding was also reported by , who conducted a simulation study in which they varied the temperatures of the saturator and condenser of a water-based CPC, while maintaining the temperature difference constant.

The temperature setting of interest, with a condenser temperature near the freezing point of DMSO, does not show a significant difference compared to the other efficiency curves at the same saturator temperature. Consequently, it remains unclear whether droplet growth is unaffected or if the particle phase has no influence on the detection process.

In analogy to the pressure dependence, the asymptotic maximum counting efficiency ηmax was investigated using the calibration parameter K0. As shown in Fig. , K0, and consequently ηmax, exhibits no significant temperature dependence for either CPC within the range of tested temperature differences. Previous studies that examined even smaller temperature differences, however, reported a decrease in the maximum counting efficiency as the temperature difference becomes very small .

Figure  shows the combined dependencies of the averaged D50 cutoff diameters for both CPCs based on repeated measurements. The CPC operated with butanol exhibits only minor variations in D50 across all temperature settings and pressures, with an average value of D50Butanol‾=(5.6±0.5)nm. This result agrees well with the value of D50=(5.5±1.5)nm reported by , measured under identical conditions for both butanol and DMSO.

In contrast, the CPC operated with DMSO shows larger variations in D50 with changing temperature differences and pressures. Compared to the findings of , our measurements indicate a higher variability, with D50DMSO‾=(6.6±2.2)nm across all conditions. The temperature setting of Tsat=35°C and Tcon=10°C, in particular, results in notably larger cutoff diameters. This can be explained by the corresponding c1/c0 ratios, which fall below 0.1 under these conditions, indicating insufficient particle growth. When considering only temperature settings with c1/c0>0.2, the mean value reduces to D50DMSO‾=(5.8±0.9)nm, which is consistent with the result obtained using the B-CPC.

The highest temperature difference of ΔT=35°C could not be applied to the B-CPC, as homogeneous nucleation of butanol was observed under this condition. Figure  shows the uncorrected counts of both CPCs and the FCE. In this measurement, both CPCs were operated at Tsat=40°C and Tcon=5°C. For smaller particle diameters, the number concentration recorded by the B-CPC does not decrease to zero, indicating the occurrence of homogeneous nucleation of butanol. This observation is consistent with the findings of , who reported homogeneous nucleation in a different model CPC at ΔT=39°C.

At this point, it should be emphasized that the DMSO-CPC is capable of achieving results comparable to those of the B-CPC under appropriate conditions, where the c0 adjustment is justified. Further adaptations and optimisation steps aimed at improving the performance of the DMSO-CPC are discussed in Sect. .

Long-term experiments were conducted to quantify the consumption of the working fluid. The B-CPC was operated at temperatures of Tsat=36°C and Tcon=10°C, as intended by the manufacturer. The DMSO-CPC was operated at temperatures of Tsat=40°C and Tcon=5°C, were it was found to perform best. The CPC was completely dry at the beginning of the experiment and a well known amount of working fluid was filled in the supply bottle. The CPC was considered to be dry again as soon as the liquid level warning was displayed even though the CPC was still operating for several hours after the initial warning. The consumption of DMSO was calculated to be in the range of 2–3mLd-1, whereas that of butanol was determined to be 96mLd-1.

Furthermore, ambient air measurements were conducted over several days. It was observed that the DMSO-CPC did not exhibit any complications and functioned in a stable manner. Moreover, throughout the duration of the present study, the CPC operated with DMSO was utilised for a period of several months, encompassing all experiments conducted.

DMSO is soluble in water. The usage of a mixture of DMSO and water as working fluid brings two important advantages. First, the freezing point of DMSO of +18°C can be adjusted to less than -100°C by adding defined amounts of water . Second, defined amounts of water also increase the flash point of DMSO from 98°C to temperatures above 140°C, as can be seen in Fig.  in the Appendix. It depicts the pressure-dependent flash points calculated according to , using the experimental mole fraction data for DMSO and H2O reported by . Consequently, employing a DMSO–H2O mixture as the working fluid enables CPC operation under extreme conditions, such as low pressures encountered during aircraft measurements or low temperatures in polar environments.

Furthermore, as the CPC measures ambient air, water is always present in the system. This lowers the effective freezing point of DMSO, such that operation at condenser temperatures below 18°C is not expected to result in freezing or ice buildup on the condenser walls, even during extended operation. This is supported by our observations, as continuous liquid drainage was observed in the DMSO-CPC throughout operation.

Figure  shows the results of an ambient air measurement at the campus of Forschungszentrum Jülich (Germany), which is located within a forest area. During this measurement the CPC was operated with a mixture of 90% DMSO and 10% water. To test the performance and duration of operation of the DMSO–H2O–CPC, there was no automatic refilling. Panel (a) shows the c1/c0 ratio over time. Panel (b) depicts the number concentration measured by both CPCs, where the DMSO-H2O data is adjusted to the c0 threshold (see Sect. ). The results show a decreasing c1/c0-ratio over time, indicating that the wick inside the CPC becomes drier and the saturation for particle activation decreases. Nevertheless, the c0 number concentration of the DMSO–H2O–CPC is in good agreement with the B-CPC, which was operated as intended by the manufacturer. This experiment demonstrates that the DMSO–H2O–CPC can operate accurately for at least 72 h without requiring maintenance. Nevertheless, the option of automatic refilling further enhances its suitability, making the DMSO–H2O–CPC ideal for deployment at remote measurement stations in challenging environments. Panel (c) depicts the correlation between the B-CPC and the DMSO–H2O–CPC during this ambient air experiment. The slope of the linear correlation is 1.0046±0.0001 (R2>0.99, number of data points n=253769), indicating that the measurements made using DMSO-H2O as working fluid are not distinguishable from the measurements performed with butanol.

In order to investigate the dependence of the CPCs on the chemical composition of the aerosol, we conducted systematic measurements using three types of aerosol particles: sodium chloride (NaCl), ammonium sulfate ((NH4)2SO4; AS), and soot. These seed types represent a range of hygroscopic properties and atmospheric relevance. The soot particles were generated using an inverted flame soot generator (see Sect. ), producing a size distribution with a CMD around 140nm. Due to this relatively large CMD, we are primarily sensitive to the left-hand side of the distribution, limiting the observable size range for these particles in the CPC, which could lead to a greater uncertainty of the resulting D50 cutoff diameters for soot particles.

Measurements were performed at two pressures, 1000 and 700hPa. For each pressure level, the CPC was operated at three different temperature settings, corresponding to a range of temperature differences between the saturator and condenser from 35-25°C. This range allows to systematically probe the influence of supersaturation on particle activation and detection efficiency. The resulting data provide insight into how the CPC responds to particles of varying composition and size under different environmental and operational conditions. The resulting D50 cutoff diameters are listed in Table  for both CPCs.

It is evident from the data presented that there is no significant difference in the D50 cutoff diameter between the B-CPC and the DMSO-CPC at 700hPa. At ambient pressures of approximately 1000hPa the performance of the DMSO-CPC is highly depending on the temperature difference between saturator and condenser. While the cutoff diameters from the DMSO-CPC for ΔT=35°C and ΔT=30°C are comparable to the ones from the B-CPC, the D50 diameters at ΔT=25°C are shifted towards larger diameters for the DMSO-CPC. The only exception is soot, where also at ΔT=30°C a larger D50 is observed with the DMSO-CPC. Overall, however, and particularly at the highest temperature difference, the results obtained using the CPC with DMSO are comparable to those obtained using the B-CPC. This indicates that both working fluids exhibit a similar dependence on the chemical composition of the aerosol if operated under reasonable temperature settings.

To improve the indicative droplet growth ratios c1/c0 under identical conditions and thus reduce the signal-to-noise ratio, the laser power for particle detection was increased. While the standard laser current of the Sky-CPC 5411 in the tested unit is approximately 24mA, a maximum current of 28mA was examined. At ambient pressure, this adjustment resulted in a fully stable c1/c0 ratio and improved linearity with respect to the reference instrument, up to concentrations of 8×104 particles cm-3. Furthermore, reducing the flow rate from the manufacturer-specified 0.6 to 0.3 L min⁻¹ enhanced linearity even further, enabling measurements exceeding 105particlescm-3. This indicates that the lower flow rate allows sufficient time for particle growth.

In Sect. , the lowest c1/c0 ratios were observed at Tsat=35°C and Tcon=10°C at 250hPa, as shown in Fig. a. This panel displays c1/c0 ratios as a function of total aerosol surface area concentration. Panel (b) shows results obtained under identical conditions but with increased laser power. The ratios rise dramatically – by nearly two orders of magnitude – yielding an average D50 cutoff diameter of (7.9±0.2)nm. In comparison, the lower laser power resulted in D50=(12.1±1.4)nm, nearly twice as large. This finding supports the hypothesis discussed in Sect.  that low c1/c0 ratios lead to unrepresentative D50 values with increased uncertainty.