A scattering methodology for droplet sizing of e-cigarette aerosols

Figures & data

Figure 1. Experimental set-up bench used for the Laser Aerosol Spectrometer (LAS) calibration.

Figure 2. Polystyrene Latex Sphere (PSL) calibration curve. The y-axis represents the integrated energy of the light scattered as a function of the tested PSL sizes (six sizes tested).

Figure 3. LAS response as a function of supplier-provided size values for a selection of four PSL using the calibration curve shown in Figure 2. The different symbols correspond to the different testing days.

Table 1. Fitting parameters calculated from fitted LAS linear size response against PSL supplier claimed values.

Day	Slope	Intercept	R^2
1	0.99	−25.74	0.997
2	1.15	−57.97	0.996
3	0.96	10.33	0.999

Table 2. PSL calculated particle (CMD) from the measured size distribution based on the PSL calibration (Figure 2).

Size* of PSL (nm)	No. of replicates	Experimental CMD (nm)	St Dev (nm)	RSD (%)
147 ± 10	15	147	0.3	0.18
498 ± 34	15	471	31.9	6.77
707 ± 44	15	695	11.6	1.67
1361 ± 83	15	1393	99.2	7.13

PSL, polystyrene latex spheres; CMD, count median diameter; St Dev, standard deviation; RSD, relative standard deviation.

*The uncertainty displayed corresponds to that of the PSL and the LAS supplier claimed values.

Table 3. Statistical parameters used to calculate intra- and between-day variance (Snedecor & Cochran, 1989).

Parameter	Definition	Equation
Si	Standard deviation for day i	$\sqrt{\frac{1}{n_i-1}{\displaystyle \sum {}_{J=1}^{n_i}}{(X_{ij}-\overline{X_i})}^2}$
Xi	Arithmetic mean of day i	$\frac{1}{n_i}{\displaystyle \sum {}_{J=1}^{n_i}}{X}_{ij}$
X	Global arithmetic mean	$\frac{1}{{{\displaystyle \sum }}_{i=1}^p{n}_i}{{\displaystyle \sum }}_{i=1}^{p}n{}_i\overline{X}$
Sr^2	Residual variance	$\frac{\mathrm{\backslash mathop}{\sum }_{i=1}^p(n_i-1)S_i^2}{\mathrm{\backslash mathop}{\sum }_{i=1}^p(n_i-1)}$
Sd^2	Day to day variance	$\frac{1}{(p-1)}\mathrm{\backslash mathop}{\sum }_{i=1}^p{n}_i(\overline{X_i}-{\overline{\overline{X}}}_{\mathrm{\backslash square}}){}^2$
SL^2	Between day variance	$\frac{S_d^2-S_r^2}{\overline{\overline{n}}}$
n	Average number	$\frac{1}{(p-1)}[\mathrm{\backslash mathop}\sum _{i=1}^p{n}_i-\frac{\mathrm{\backslash mathop}{\sum }_{i=1}^p{n}_i^2}{\mathrm{\backslash mathop}{\sum }_{i=1}^p{n}_i}]$

Table 4. Calculated statistical parameters for the three testing days for PSL particles.

PSL size provided by supplier (nm)	147			498			707			1361
Day, No.	1	2	3	1	2	3	1	2	3	1	2	3
Average calculated  size (nm)	147.42	146.98	146.86	427.62	494.88	490.86	679.89	706.66	697.69	1335.69	1526.32	1315.93
Standard deviation (nm)	0.05	0.03	0.09	0.33	0.77	0.72	1.35	0.60	1.42	8.08	24.19	8.46
Between-day standard  deviation (nm)	0.30			37.73			13.62			115.98

Figure 4. Measured LAS response for selected PSL particles and Di-Ethyl-Hexyl-Sebacat (DEHS) droplets as a function of expected or claimed values. Circles (•) and triangles (▴) represent averaged Count Median Diameters (CMDs) calculated for PSL and DEHS size distributions, respectively. Error bars represent the standard deviation of the data point. Dashed straight lines are upper and lower limits within which no bias is considered considering instrument uncertainty.

Table 5. Fitting parameters calculated from fitted DEHS linear size response against the DEHS size values measured with PAM.

Day	Slope	Intercept	R^2
1	0.906	−78.610	0.995
2	0.913	−71.620	0.993
3	0.872	−17.495	0.999

Table 6. Calculated statistical parameters for the three testing days for DEHS droplets.

PSL size provided by supplier (nm)	600			1000			2000
Day, No.	1	2	3	1	2	3	1	2	3
Average calculated size (nm)	499.04	517.97	514.05	822.07	824.39	885.83	1705.50	1773.23	1730.48
Standard deviation of calculated size (nm)	0.66	1.24	1.49	2.15	3.85	6.26	4.99	3.90	1.51
Between-day standard deviation of calculated size (nm)	9.98			36.11			34.21

Figure 5. Calculated aerosol mass (AM)_LAS plotted as a function of the gravimetrically determined (AM)_gravimetric. Triangles (▵) represent the average calculated (AM)_LAS. Solid line represents the theoretical expected curve.

Table 7. Commercially available e-cigarettes tested in the study.

Product	Formulation composition	Refractive index of liquid formulation
PSL	N/A	1.59^a
DEHS	N/A	1.45^a
e-cigarette A^b	75% glycerin, 25% water	1.436 ± 0.005
e-cigarette B^b	1.14% nicotine, 50.96% glycerin, 27.86% propylene glycol, 15.91% water, 4.13% others	1.436 ± 0.005
e-cigarette C^b	1.18% nicotine, 2.29% menthol 50.96% glycerin, 26.36% propylene glycol, 15.94% water, 3.27% others	1.429 ± 0.005
e-cigarette D^b	20.20% glycerin, 74.13% propylene glycol, 5.96% water	1.433 ± 0.005

Abbreviations: PSL, polystyrene latex spheres; DEHS, di-ethyl-hexyl-sebacat.

a Literature values (Eidhammer et al., 2008); ^bMeasured values via an Abbe refractometer.

Figure 6. (a and b). Two set-ups used to determine the size distributions of selected e-cigarettes.

Figure 7. Typical size distribution response obtained from the Laser Aerosol Spectrometer (LAS) when using the Programmable Dual Syringe Pump (PDSP) and the mono-port aerosol generator.

Table 8. Calculated CMD, GSD and MMAD for different tested marketed e-cigarettes.

	Mono-port			PDSP
Sample	CMD (nm)	GSD	MMD (nm)	CMD (nm)	GSD	MMD (nm)
A	138 ± 11	1.42	200 ± 26	166 ± 4	1.42	242 ± 19
B	136 ± 8	1.42	197 ± 25	191 ± 10	1.46	293 ± 19
C	130 ± 4	1.37	176 ± 10	158 ± 5	1.41	225 ± 9
D	136 ± 3	1.40	191 ± 8	163 ± 3	1.44	245 ± 6

Snedecor GW, Cochran WG. (1989). Statistical methods. 8th ed. Ames (IA): Iowa State University Press

 Google Scholar

Eidhammer T, Montague D, Deshler T. (2008). Determination of index of refraction and size of supermicrometer particles from light scattering measurements at two angles. J Geophys Res 113:1–19

 Web of Science ®Google Scholar