Caffeine, citric acid, and dextran were chosen as analytes for this study. Caffeine was chosen because it is currently the standard default sample used in Agilent ELSDs as it is used for calibration. Dextran was chosen to represent a large-molecular-weight water-soluble polymer as the ELSD is often used to analyse molecules of this type. Citric acid was chosen as a non-volatile non-cyclical small molecule alternative to caffeine. The properties of caffeine and citric acid are summarised below in Table . The properties of the variety of dextran used in this study are unknown to precise values as they have not been tabulated by the manufacturer or in the literature for such large-molecular-weight chains.

Solutions of aqueous caffeine (obtained from Alfa Aesar, Thermo Fisher Scientific), dextran (Mw = 450 000–650 000 g mol⁻¹; Scientific Laboratory Supplies Ltd.), and citric acid (Alfa Aesar, Thermo Fisher Scientific) were prepared using distilled water (Merck Life Science UK Ltd.) at concentrations of 0.125, 0.25, 0.5, and 1 g L⁻¹. After mixing, all solutions were sonicated in a water bath held at 25 °C for 10 min to ensure total dissolution.

The ELSD (1290 Infinity II, Agilent Technologies) was operated at a steady-state liquid feeding rate, with the dissolved analyte in the mobile phase, instead of the more conventional analyte pulse injections from a liquid chromatography column. Steady-state operation is necessary to allow particle collection for SEM imaging and particle sizing experiments, which require significantly longer timescales than that of a pulsed injection. The ELSD was operated at a constant nebuliser temperature of 25 °C, an evaporator temperature of 25 °C.

In order to understand the process of droplet evaporation within the flow passages of the ELSD, measurements are required of the particle distribution upstream of the ELSD, i.e. the initial droplet size distribution produced from the nebuliser (Fig. ). For the present experiments, the nebuliser was operated at a constant volumetric liquid flow rate of 0.5 mL min⁻¹ controlled by a syringe pump (Aladdin; SyringeONE AL-1000) and a constant volumetric nitrogen gas flow rate of 0.4 L min⁻¹ controlled by a mass flow controller (Alicat Scientific).

Upstream particle sizing experiments aim to characterise the droplet size distribution for a given solvent, water, in the case of the aqueous solutions used in later experiments. However, accurately capturing the droplet distribution is particularly challenging due to rapid evaporation of the water solvent. This makes it difficult to obtain in situ measurements that span the full size range of interest. As a result, multiple complementary techniques are employed to assess the true droplet size distribution as discussed below.

A phase Doppler particle analyser (PDPA; DANTEC Dynamics DopplerPower DPSS laser 2 × 1 W 488/515 nm) was initially used to characterise the droplet size distribution emitted by the nebuliser. The transmitting probe uses a 500 mm focal length lens and one photodetector. The receiving probe contains a 310 mm focal length lens, an aperture mask, and three photodetectors. The receiving probe was angled 20° off-axis from the forward-scattering direction to allow first-order refraction to dominate the received light. The spatial resolution of the sampling region is of the order of 0.2 mm based on the pinhole aperture used. The settings were arranged to sample the smallest possible diameter corresponding to the index of refraction of the fluids considered (water, dioctyl sebacate (DOS)). This rapid and localised detection minimises the influence of evaporative losses on the measured droplet size distribution. However, as an optical technique, the PDPA has a lower detection limit of approximately 2 µm, below which droplets cannot be reliably sized . Consequently, a significant fraction of smaller droplets may fall below the detection threshold and remain unmeasured. To address this limitation, a second instrument was employed to cover the measurement gap between 200 nm and 2 µm. An aerodynamic aerosol classifier (AAC; Cambustion Ltd.) was used in conjunction with a condensation particle counter (CPC; TSI Instruments Ltd., model 3752) to measure the aerodynamic particle size distribution . The latter setup requires sampling and cannot realise spatially resolved measurements, but it is capable of detecting smaller particles (≤ 2 µm). Additionally, droplets that are still evaporating cannot be reliably classified, owing to the long convective timescales involved in sampling lines. A comparison of the capabilities of both instrumentations is provided in Table .

Preliminary measurements with the PDPA determined that the size peak from the nebuliser lies around the micrometre range. To bridge the measurement gap and approximate the full droplet size distribution, a compromise was achieved by combining PDPA measurements with those from the AAC-CPC system. A series of experiments were conducted using both the PDPA and the AAC/CPC in a size range where both are feasible using a non-evaporating liquid, namely dioctyl sebacate (DOS), a low-vapour-pressure oil (the vapour pressure of DOS is 2.6 × 10⁻⁴ Pa at room temperature and pressure, offering negligible evaporation rate ). The solvent properties for both DOS and water are shown in Table .

Figure  shows flow diagrams of the three sets of experiments used to obtain number distribution functions of the original spray.

Spray PDPA. The PDPA sampling volume is taken within the spray plume at a distance of 1 mm from the tip of the nebuliser along the centreline. The reference droplet size concentration distribution is labelled nP,s(dp), where dp is the droplet diameter.

In the well-mixed AAC experiment, the flow configuration incorporated a liquid trap to eliminate the largest droplets, which is required for preventing the flooding of the instrument, in accordance with the experimental setup for aerosol generation used by . Furthermore, this configuration required the inclusion of an additional diluting flow and a vent to accommodate the required sampling flow rate of the CPC at 1.5 L min⁻¹ relative to the atomiser flow of 0.4 L min⁻¹. The AAC was operated with a sheath flow of 15 L min⁻¹ and a sample flow of 1.5 L min⁻¹, corresponding to a resolution (defined as the ratio of particle size to the minimum resolvable size difference) of 10. Under these conditions, the AAC is capable of classifying aerodynamic particle sizes in the range of 200–6000 nm. The transfer function of the AAC has been extensively characterised using DOS droplets up to approximately 5 µm in diameter , and these characterisations were applied in the present study to deconvolve the measured concentrations and to recover the underlying particle size distribution.

For the well-mixed non-evaporative experiment (i.e. experiments 2 and 3 using DOS), particle losses across the liquid trap and transfer tube are attributed to gravitational settling and are adjusted for as outlined in the Appendix. Experimental data from setups 2 and 3 are related via a transfer function, as explained below.

We make the assumption that the particle size distribution from the well-mixed PDPA experiment, nP,m(dp), should equal that of the well-mixed AAC experiment, nA,m(dp), above a threshold size (> 2 µm). However, the values need to be corrected owing to a systematic difference, namely that PDPA measurements measure the passage of droplets at a local sampling volume of the order of a cubic millimetre, whereas the AAC measurements involve sampling the mean integrated total particle number in the flow.

We assume that the differences can be adjusted by a constant factor C, assumed not to be biased across the size distribution, times a transfer function which accounts for the diameter-dependent loss, fL(dp). The factor C is obtained by error minimisation across the size distribution obtained with the two measurement methods.

From the comparison between the well-mixed PDPA and well-mixed AAC experiments it is possible to calculate the loss function associated with the PDPA, fL, which characterises the diameter dependent signal loss, as given by the following: 1nP,m(dp)=1CfL(dp)nA,m(dp). The ratio of the two distributions is calculated as a function of diameter, between 0<dp<2 µm, where that fL asymptotes to unity for sizes near 2 µm. A final transfer function, fT, is associated with the losses in the tubes which feed the aerosol into the AAC, which is obtained experimentally by taking the ratio of number density distribution measured using the spray PDPA, nP,s(dp), to the well-mixed PDPA experiments: 2nP,s(dp)=fT(dp)nP,m(dp). It is assumed that all atomised solvents produce a log-normal droplet number distribution: 3ndp=Ndpσ2πexp⁡-ln⁡dp-μ22σ2, where N is the total concentration of droplets. Log-normal distributions are controlled by the parameters μ and σ, which are analogous to the distribution mode and width, respectively, in logarithmic space. We assume that the mode of the distribution, ln⁡μ, is obtained from the measurements below 2 µm using the best fit to the distribution nA,m. We also make the assumption that the value of σ does not vary between distributions using different atomising liquids as its value primarily depends on the atomiser geometry . The value of σ is determined from the best fit to nP,s using values above 2 µm.

In this description, we have so far only considered experiments using a non-evaporating liquid so that we could use appropriate instrumentation (AAC-CPC) to measure the expected droplet distribution nP,m. However, the liquids used in the ELSD (water, alcohols) have different properties compared to DOS regarding atomisation. In order to relate the present measurements to those of different fluids, we sought experiments and correlations produced in nebulisers with similar geometry, covering a range of compounds . After an analysis of the gas and liquid flow rates over which the experiments were validated, we selected the experiments and correlations by . Their measurements obtained log-normal distributions for twin-fluid concentric pneumatic nebulisers, similar to the one used in the ELSD for this study, for a range of compounds whose physical properties are well within the range of industrially relevant solvents, as shown in Table . A full discussion of these considerations is available in the thesis by . The correlations used are for the Sauter mean diameter (SMD, D32) as a function of characteristic flow non-dimensional numbers. The SMD is related to the log-normal parameters μ and σ via the following : 4D32=exp⁡μ+32σ2.

The function linking the D32 of the initial droplet distribution to the solvent properties and operating conditions, as expressed in the original work, is as follows : 5D32DL=C11+mrbGDL1/2ρLρGRebG1/41WeDL1+C2DLbG1/6RebGρL/ρG1/12WeDL1/6Oh2/3, where DL is the liquid orifice diameter; bG is the gas jet thickness (here taken as the thickness of the atomiser gas annulus); and ρL and ρG are densities of the liquid and gas, respectively. ReG is the gas-phase Reynolds number based on the atomiser gas annulus; WeDL is the Weber number based on the liquid properties and nozzle diameter; Oh is the Ohnesorge number; and C1 and C2 are experimentally determined constants with values of 1.734 and 1.0, respectively. The variable mr is the ratio of liquid to gas mass flow.

The Reynolds number RebG=ρGUbbG/μG is based on the thickness of the gas annulus and the corresponding gas velocity Ub and dynamic gas viscosity μG. The Weber number is based on the liquid properties of density ρL and surface tension σL, WeDL=ρLULDL/σL, where the liquid velocity is based on the area defined by the jet diameter DL. Finally, the Ohnesorge number is also based on the liquid properties and jet diameter, Oh=μL/ρLσLDL.

The final step is to obtain the actual number concentrations in the flow (coming from the atomiser centreline) for the particular operating conditions. These are obtained by imposing the conservation of liquid volumetric flow rate for the droplets, starting from the droplet size concentration distribution nP,s, which is assumed to remain self-similar for different fluids: 6QL=ϕQG∫0∞nP,s(dp)π6dp3d(dp), where QL and QG are the measured volumetric flow rates of liquid and gas delivered to the injector at reference conditions, the integral obtained corresponds to the total liquid mass per unit volume of gas, and the correction factor ϕ is applied to obtain the final estimated input droplet number distribution of the mixture of solvent and dilute analyte delivered by the nebuliser at section (1).

The previous section detailed the steps taken to obtain the particle size distributions at the upstream end of the flow network, which acts as an input to the overall model (i.e. (1) in Fig. ). In order to verify the accuracy of a model, it is also necessary to obtain particle size distributions at the outlet of the ELSD (i.e. corresponding to the outlet of (4) in Fig. ).

The measurements are made using a scanning mobility particle sizer (SMPS, TSI Instruments Ltd.). The SMPS comprises two pieces of aerosol instrumentation in series: a differential mobility analyser (DMA) and a CPC. The outlet of the ELSD was connected via non-particle-generating, conductive rubber tubing to the inlet of the SMPS as shown in Fig. . All SMPS experiments in this study used TSI-made DMAs (electrostatic classifier models 3080 and 3082 and a model 3081 long column) and CPCs (models 3752 and 3776). The SMPS was operated with a negative polarity such that positively charged particles were selected, with an aerosol flow of 1.5 L min⁻¹ and a sheath flow of 15 L min⁻¹. Experiments were obtained over 90 s scans across the explored size range of 8 to 232 nm. Each set of experimental conditions was repeated three times to ensure reproducibility; the reported results show the average of these three runs for each case.

Samples were collected from the ELSD outlet for SEM analysis on carbon TEM grids (EM Resolutions, Holey Carbon Film, Cu, 300 mesh, 4–6 nm, UL, hole diameters ranging from 0.25 to 5 µm) for 3 min using an ELSD gas flow of 2 L min⁻¹. The samples were coated in platinum to ensure that the organic samples were electrically conductive enough to be visible in the SEM before being analysed on a TESCAN MIRA3 FEG-SEM at 5 kV.

The results of the particle size distribution measurements obtained as described in Sect.  from the PDPA and AAC experiments using DOS are shown in Fig. . PDPA measurements are collected over 120 s, and averages over three repeats are produced, with negligible variation between measurements. Likewise, well-mixed AAC measurements were collected as an average of three scans, with variability of 5.2 nm (0.6 %) on the modes.

The green line for the well-mixed AAC measurements shows a log-normal mode around 450 nm, which is adopted as the mode for the final original spray distribution. The orange line for well-mixed PDPA, nP,m shows good agreement with the well-mixed AAC green nA,m line once scaled by a best-fit factor fL(dP)/C. The spray PDPA blue line is scaled by the same factor fL(dP)/C. The ratio of the blue signal (spray PDPA) and orange signal (well-mixed PDPA) reflects the losses within the liquid trap and tube via fT. The values determined for fT and fL as a function of diameter are shown in Fig. . The best-fit log-normal curve for the final total spray concentration curve nP,s(dp) is shown as the dashed black line log-normal curve in Fig. . The procedure can be summarised as using the mode determined by the AAC measurements and the value of σ determined by the spray PDPA measurements.

Once the mode and σ for the DOS distribution are determined, the correlation in Eq. () was used to determine the expected value of D32 and, thus, an updated value of μ, assuming that σ remains constant and that the total volume flow rate is conserved, as expressed in Eq. (). The original distribution for DOS and the final result for the expected droplet number distribution for water from the nebuliser are shown in Fig. .

The initial size distribution of water droplets is approximated using the same liquid and gas volumetric flow rates as in the DOS case. As a result, by conservation of volume, a larger peak droplet diameter corresponds to a lower peak number concentration compared to DOS. This difference in peak diameter is due to the higher surface tension of water relative to DOS. An increased surface tension would lead to more energy being required to break the liquid jet into droplets, resulting in larger droplets overall.

Measurements of particle concentrations as a function of size emerging from the evaporator section were made using an SMPS and are shown in Fig.  for caffeine, dextran, and citric acid diluted in water at concentrations from 0.125 to 1 g L⁻¹. Analytes with different volatilities and bulk densities were selected to understand whether different particle size distributions are produced. Their properties are shown in Table , with the lowest volatility associated with citric acid, followed by caffeine. The volatility of dextran is not known, although its molecular weight is highest compared to the other two compounds.

The lowest overall concentrations and smallest mean diameters are associated with citric acid, which has lower volatility and higher effective density relative to caffeine. Although there is little information about dextran properties, measurements show very little systematic difference between the number distributions compared to caffeine. This may indicate similar effective densities upon drying.

As expected, the peak numbers increase with the concentration but not linearly across the range. For all cases, the mode of the distribution increases with concentration. One can also observe that the distribution is not quite log-normal or symmetric but rather skewed towards larger sizes. This is indicative of a distribution which has gone through a size-dependent impingement via a cut-off diameter. This can be attributed to the effects of the Y junction and the diffuser cartridge (sections 2 and 3 in Fig. ) on the aerosol. Further evidence is presented in the parallel study modelling the ELSD signal response, which demonstrates that a collection efficiency curve for the two aforementioned impingement points leads to such a skewed distribution ().

From the measurements and adjustments discussed for the nebulised droplet distribution, a number concentration peak at a diameter value of 550 nm and a peak width of σ = 1.08 are estimated for the reconstructed initial distribution of water (Fig. ). An estimate of the dried-particle size for a droplet of initial diameter d0 and of analyte mass concentration c in the liquid can be made by assuming that the mass ma of the analyte not captured by the impingement is conserved after all solvent water has evaporated, leaving a final spherical droplet diameter df with known bulk density ρb: 7ma=π6d03c=π6df3ρb. The estimated diameter df obtained can be thought of as a lower bound for the dried-particle diameter as the bulk density may differ from that of the dried particle, particularly as the dried-particle diameter may differ from that of a sphere. Assuming that we can compare the peak of the distributions, we can compare the mode of the initial droplet distribution with the mode of the SMPS distribution: 8df=d0cρb1/3. Substituting the values for effective density for the bulk density values given in Tables  and and using the mode diameters from the peaks of Fig.  as representative for an analyte concentration of 1 g L⁻¹ yields final mode diameters of 46 and 52 nm for citric acid and caffeine, respectively (the density of dextran is uncertain, and so this is not calculated). The resulting values should be compared to the measured modes of 35 and 65 nm, respectively, according to the values in Fig. . The estimated values generally align with the experimental measurements; however, the value for citric acid is over-predicted, while caffeine is under-predicted, as shown in Fig. . The under-prediction of the peak caffeine diameter indicates a lower effective density of caffeine particles compared to the bulk value; this is consistent with the SEM results shown in the next section as the collected dried caffeine samples are not spherical in shape. The over-prediction of the peak citric acid diameter may be attributed to inaccuracies associated with the construction of the initial droplet distribution of water and possible mixing effects reducing the surface tension of the water–citric acid solution and changing the diameter; a decreased surface tension is consistent with less energy being required to break the liquid jet into droplets, resulting in smaller droplets overall.

SEM images were collected for the three analytes selected in Table  according to the methodology described in Sect. . The efficiency of the collection grids used for SEM imaging reaches minimum efficiencies below 20 % in the size range of 5–300 nm . Therefore, while the images can be analysed for particle size distribution, they are only representative for particles larger than 300 nm. Here we present SEM images to gain insight into the morphology of dried particles in the ELSD and into what extent particle shape might affect the scattering properties which directly lead to light detection.

Figure  shows SEM images of grids with collected particles for the three selected analytes under the same operating conditions for caffeine, dextran, and citric acid, in order of increasing spatial resolution. Caffeine samples produced particles with a notably elongated morphology, with a few shorter particles with crystalline character. This is consistent with literature reports of caffeine crystallising into needles in bulk . This finding may have significant consequences for the detection of caffeine via light scattering since the morphology found via SEM differs significantly from that of a sphere. Dextran produced spherical particles with an approximately spherical morphology with a large variety of diameters, as shown in Fig. . These are often agglomerated into larger particles with different primary particle sizes. This is also consistent with literature reports for dried dextran particles . Finally, samples of citric acid produced particles which are approximately spherical and not agglomerated. Particles tended to collect in the regions around the holes of the TEM grid. This suggests that the citric acid particles may have particular surface tension properties associated with liquids (possibly water) as they were deposited onto the TEM grids. This is in contrast to available literature on bulk drying of aqueous citric acid, which suggests that citric acid formed crystals with distinct networks of multi-layer agglomerates (; ). The difference may suggest that there is a difference in terms of crystallisation in bulk compared to atomised droplets.