Spe-ca Acta. Vol. 35B. pp. 73 to 79. 0 Pergamon Press Ltd., 1980. printed in Great Britain

0031-6987/80/02014l073$02.00/0

A method for investigating size distributions of aqueous droplets in the range OS-10 pm produced by pneumatic nebulizers

M. S. CRFLQGER* and R. F. BROWNER School of Chemistry, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

(Received 2 July 1979)

AMract-A novel method is described for the measurement of the droplet size distributions produced by nebulizers commonly employed in analytical atomic spectroscopy. It is shown theoretically that, at sufficiently

high concentrations of dissolved sodium chloride, the evaporation of water from droplets as small as 0.5 @rn

in diameter may be reduced to a negligible level. When evaporation is reduced by the presence of a dissolved salt, a conventional cascade impactor may be used to elucidate the droplet size distribution. Empirical

observations confirm that, at a sodium concentration of 10,000 ~gml-I, evaporation is negligible: the

method may be used to study particle size distributions over the size range OS-10 km.

1. INTR~DU~~~~N

THERE ARE many instances in analytical atomic spectrometry when a knowledge of the droplet size distribution produced by pneumatic nebulizers would be of value. Most arise from one or more of three basic needs, namely:

1. a need to be able to relate nebulizer design parameters and their modification to changes in droplet size distribution;

2. a need to be able to understand phenomena related to the transport of droplets from the nebulizer to a flame or plasma, including the influence of spray chamber geometry and impact beads, mixer paddles and similar components upon transport efficiency; and

3. a need to have an accurate knowledge of the droplet size distribution of aerosol reaching a flame or plasma in order to be able to interpret phenomena related to desolvation of droplets and volatilization and dissociation processes associated with residual solid particles in flames and plasmas.

Numerous techniques have been employed by analytical spectroscopists in attempts to make meaningful measurements of droplet size distributions. In the majority of instances these have relied upon impingement of aerosol particles upon solid surfaces, either to produce measurable craters in a powder surface or measurable stain patterns from dyes dissolved in the aerosol solution [l-2]. Trapping of droplets in suitable oil films has also been used to study aerosols [3]. These impingement-based procedures are of limited value in the present context, however, because they suffer from two serious limitations. Firstly, a very high impingement velocity is required to trap small droplets. Secondly, even if droplets less than 5 pm in diameter are adequately trapped, they cannot be measured meaningfully by optical microscopy.

In an attempt to circumvent this problem, WILLIS [4] employed a thermal pre- cipitator, sampling the solid particles obtained after evaporation of the aerosol droplets. Willis commented in that work that not much reliance should be placed upon the absolute values of droplet sizes obtained, because of the problem of preferential settling of larger particles. Nevertheless the paper was a valuable one because it provided evidence that more than 90% of the droplets reaching burners were less than

[l] J. STUPAR and J. B. DAWSON, Appl. Opt. 7, 1351 (1968). [2] S. R. KOIRTYOHANN and E. E. P~cxmr, Anal. Chem. 38, 1087 (1966). [3] S. NUKNAMA and Y. TANASAWA, Trans. Sot. Mech. Engrs Japan 5, 68 (1939). [4] J. B. WILLIS, Spectrochim. Acta 23A, 811 (1967).

* On leave from the University of Aberdeen, Department of Soil Science, Old Aberdeen AB9 2UE, U.K.

S.A.(B) 35/2--c 73

74 M. S. CRIXSER and R. F. BROWNER

5 pm in diameter. In an interesting recent study by SKOGERBOE and OLSON [5] a cascade impactor was employed to study the aerodynamic distribution of desolvated salt particles.

For reasons which will become clearer later, procedures based upon complete desolvation also suffer from serious limitations. Elevated temperature is required to ensure complete desolvation, which may drastically alter the aerosol transport charac- teristics. The aerodynamic diameters determined must be corrected for the geometry and higher density of the salt crystals. The size range over which the technique may be employed is limited by the requirement for residual solid particles of suitable diameters for fractionation and measurement.

One of the major problems associated with the direct fractionation of aqueous aerosols if complete desolvation is not achieved is that of the shift in distributions caused by varying degrees of desolvation. It is possible, however, to make measure- ments directly on aerosols if an involatile organic solvent is used to generate the aerosol. Dioctylphthalate (DOP) is often used for this purpose and has been employed in this laboratory in a study of pneumatic nebulizers from various analytical spectrome- ters [6]. The primary benefits of the measurement system which has been developed for use with DOP are the wide range of droplet sizes which can be measured (0.03-10 pm) and the speed of measurement. This makes rapid comparative studies with different nebulizers very convenient. The major limitation to this approach, however, is that although DOP has a density close to that of water, its viscosity and surface tension are widely different from those of water. Moreover of necessity the high viscosity restricts investigations to nebulization rates appreciably less than 1 ml min-‘. Therefore the droplet distributions and transport efficiency might be expected to differ markedly from those produced for aqueous solutions at nebulization rates from 3 to 6 ml mine1 which are typically used in analytical flame spectrometers.

The degree of evaporation of small aqueous droplets may be reduced to a negligible level if the droplets contain a sufficiently high concentration of a dissolved salt [7]. The present paper demonstrates how this effect may be exploited to minimize evaporation effects and thus allow meaningful measurements of droplet size distributions to be made directly over the diameter range cu. 0.5-10 pm.

2. EXJERIMENTAL

AU measurements were made using an inverted Perk&Elmer spray chamber and nebulfzer, in some

instances with the mixer paddles removed. The aerosol leaving the spray chamber was passed via a

connecting tube of a diameter chosen to give isokinetic sampling to an Andersen Cascade Impactor (Model 21,000, Anderson 2000, GA). The air flow through the impactor was checked periodically using a Matheson Linear Mass Flowmeter (Model 8116, Matheson Gas Products, NJ). Nebulization rate was controlled by

employing a peristaltic pump (Buchler Multi-Staltic Pump).

3. THEORETICAL CONS~ERATIONS

3.1 Evaporation of water droplets

The importance of evaporation from the surfaces of droplets in an aerosol generated from very dilute aqueous solutions has long been recognized in analytical spectrometry, at least in qualitative terms. The rate of change of radius r of a droplet of mass m, density p and radius T with time t is given by the general equation

[.5] K. W. OLSON and R. K. SKOGEREIOE, Appf. Spectr. 32, 181 (1978).

[6] J. NOVAK and R. F. BROWNER, Anal. Chem (in press). [7] J. PORSTEND~FWER, J. GEE-T and G. R~BIG, J. Aerosol Sci. 8, 371 (1977).

A method for investigating size distributions of aqueous droplets 75

The rate of evaporation is a steady-state solution of the diffusion equation in polar coordinates [7]:

dm hrD,M Ap --_= dt RT ’

where D, is the diffusion coefficient for solvent vapor, M is the molecular mass of the solvent, R is the gas constant, T is the absolute temperature and Ap is the pressure difference between the droplet surface and the surrounding air. Combination of the above equations to eliminate dmldt leads to a general equation for the evaporation of droplets

dr DJ4Ap

-rdt= pRT . (1)

The pressure difference between the droplet surface and the surrounding air at a relative humidity of 100% is due to the curved droplet surface and is given by the Kelvin equation [7]

where pS is the saturated vapor pressure and (T is the surface tension of the water. Expansion of the exponential function in this equation leads to the following expression for Ap

2aMp, Ap=-

PRT ’

Combining this expression with equation (1) and integrating gives an equation showing how r varies with t, when the initial droplet radius is r,, namely

r3 = rz - 6D,upSA4?(pRT)-2.

Insertion of appropriate values [7] of D,, a, pS, M, p, R and T in this equation leads to the expression

d’=d;-13.13t,

where d is the droplet diameter in pm after t seconds, d, is the initial diameter, and the temperature is 298 K.

This equation may be used to calculate how the diameter of water droplets changes with time in saturated air, and this has been done in Fig. 1. Even in the fraction of a second required for droplets to pass through a spray chamber water droplets with an initial diameter of less than 1 pm will undoubtedly evaporate totally and the diameters of droplets with initial diameters of up to 3 pm will be significantly reduced. In the time taken to pass through a cascade impactor and a spray chamber, the droplet distribution would change beyond recognition. Figure 1 also serves to illustrate why elevated temperatures would be required to achieve complete evaporation of aqueous droplets over the complete size range of interest in analytical atomic spectroscopy.

3.2 Evaporation of salt solution droplets

In the presence of a dissolved salt the water vapor pressure is equal to the saturated vapor pressure of the salt solution, p_ rather than to p., the saturated vapor pressure of water. For a salt of molecular mass MS and dissociation fraction (Y at a concentration c % by mass

.

76 M. S. CRESSER and R. F. BROWNER

”

0 1 2 3 4 5 6 7 6 9 10 11 12

Time, seconds

Fig. 1. Plots illustrating the variation in theoretical droplet diameter with time at 100% relative

humidity and 298 K.

It has been shown [S] that the vapor pressure at the surface of a droplet of salt solution, p, is given by the equation

2Ma Mea

’ =” exp --___ pRTr lOOM, ’

The radius of a droplet of salt solution is decreased by evaporation until the droplet vapor pressure is equal to the saturated vapor pressure of the salt solution, this being the vapor pressure in the surrounding air, so that the equilibrium droplet radius, r,, may be calculated from the equation

Rexp(-E)=p,exp(z-s),

where c, is the equilibrium droplet concentration. Simplification of this equation leads to the expression:

r3 ; 200eJ r2 = r3

X pRTca ’ ‘* (3)

c, has been eliminated by putting c, = cr$r:. The new equilibrium diameters are reached in a fraction of a second for all practical purposes [7]. Equation (3), which was derived by PORSTEMD~RFER and co-workers [7], may be used to calculate the change in diameter as a function of initial droplet diameter for salt solutions of various initial concentrations. Typical results for sodium chloride are shown in Fig. 2. These calcula- tions demonstrate that for sodium at a concentration of 10,000 Fg ml-’ the change in droplet diameter will be less than 5% even for droplets as small as 0.5 pm and less than 2.5% for droplets equal to or greater than 1 pm in diameter.

Thus if a 10,000 pg ml-’ sodium solution is nebulized, evaporation effects on diameters of droplets greater than 0.5 pm should be virtually negligible. Moreover if the sodium chloride solution collected on each plate of the cascade impactor is washed off and diluted to a known volume with deionized water, the concentration of sodium may be readily determined by flame emission spectrometry, and hence the mass of droplets deposited may be calculated. It is also a relatively simple matter to convert this mass distribution data to approximate numerical distribution data if required, if certain

[8] G. ZEBEL, Z. Aerosol-Forsch.-T’her. 5,263 (1956).

A method for investigating size distributions of aqueous droplets II

60

0 1 2 3 4

Initial droplet

5 6

diameter,

7

pm

6 9 10

Fig. 2. Plots illustrating the theoretical % decrease in droplet diameter relative to the initial diameter as a function of initial diameter at various sodium concentrations. (A)

10,000 wgml-i; (B) 8000 pgml-’ (C) 5000 pgml-’ (D) 1000 pgml-’ (E) 200 pgml-I.

simplifying assumptions about a smooth distribution are made. Mass distributions are, however, more appropriate for present purposes.

4. EXPERIMENTAL RESULTS

As a check of the agreement between experimental results and theoretical predictions 200, 1000, 5000, 8000 and 10,000 wgml-’ sodium solutions were prepared and the aerosols generated from them by a conventional Perkin-Elmer pneumatic nebulizer-spray chamber combination were analyzed using the cascade impactor. Measurements were made for both low and high nebulization rates in the presence and absence of the mixer paddle respectively. The mass of sodium collected on each plate is converted to a mass % of the total amount of sodium collected on all eight impactor stages. This figure is then divided by the difference between the logarithms of the cut-off diameters of the plate concerned and the immediately preceeding plate to allow normalized distribution curves to be plotted through the points thus obtained. The results are shown in Figs. 3 and 4. At both nebulization rates of 0.62 and 4.2Oml mini the very pronounced effects of evaporation at sodium concentrations below 5000 kg ml-’ are clearly discernible. The effect of increasing the concentration above 5000 pg ml-’ is relatively slight, as would be anticipated from the results shown in Fig. 2, indicating that evaporation effects are indeed reduced to a negligible level at high sodium concentrations. The apparent shift to higher mean droplet diameters with decreasing concentration of sodium in Fig. 4 occurs because evaporation causes smaller droplets to be lost totally from the collection system. The larger droplets then assume greater relative importance, because the sodium is expressed in terms of per cent by mass of the total sodium collected. The effect is not observed in Fig. 3 because the number of droplets above 5 pg is always negligible.

The duration of a single run is approximately 1 min, and this produces solutions containing O-20 pg ml-’ sodium if the washings from each impactor plate are diluted to 5Oml prior to analysis by flame emission spectrometry.

The equilibrium diameters calculated from equation (2) are based upon the assumption that the water vapor pressure in the air surrounding the droplets is equal to the saturation vapor pressure of the salt solution being nebulized. This assumption is reasonable for the spray chamber because the spray chamber walls become saturated with the salt solution very rapidly during a run. The additional air entering the impactor at the sampling point will attain its equilibrium vapor pressure by evaporation of water from the droplets collected in the preimpactor and on the upper impactor plates. If water started to pass into the vapor phase

M. S. CRESSER and R. F. BROWNER

1 2 Droplet diameter, pm

Fig. 3. Effect of sodium concentration on the apparent droplet distributions of a Perkin-Elmer nebulizer/spray chamber assembly at a nebulization rate of 0.62 ml mini. 0 10,000 pg ml-‘; 0

8000 t~grn-r ; 0 5000 pg ml-‘; A 1000 pgml-‘; A 200 kg ml-‘.

predominantly by evaporation from smaller droplets, as might be anticipated from their large number and high surface area/mass ratio, the concentration of sodium in these droplets would tend to increase rapidly. Since concentration varies inversely with radius raised to the power 3, it follows from equation (2) that the droplet vapor pressure, p, would fall. Evaporation would therefore then tend to occur from the most dilute sodium solution, which will be on the spray chamber walls and in the larger droplets, both before and after deposition on the preimpactor and upper impactor plates, to establish equilibrium, and evaporation from smaller droplets is limited. Thus any modification of the droplet size distribution caused by evaporation will be small, which is why the proposed procedure appears to be satisfactory even at nebulimtion rates as low as 0.62 ml min-i.

Initially at least the small droplet size found to dominate the distribution may be surprising, since the Nukiyama and Tanasawa equation would predict the mean droplet diameter produced by the nebulizer to be

01 * . *a’ I 1 . . ..I

0.5 1 2 5 10

Droplet diame.ter, pm

Fig. 4. Effect of sodium concentration on the apparent droplet distributions of a Perkin-Elmer nebulizer/spray chamber assembly with mixing paddles removed at a nebulimtion rate of 4.2 ml min-‘. 0 10,000 hgml-r; 0 8000 pgml-‘; •I 5000 pg ml-‘; A 1000 pg ml-‘; A 200 pg ml-‘.

A method for investigating size distributions of aqueous droplets 79

above 10 pm. However it must be remembered that the distributions shown here are not in fact the actual distributions produced by the nebulirer but are the distributions of droplets which have successfully passed through a spray chamber system designed purposely for the removal of large droplets from the air stream. For most of the applications of droplet size distribution data it is this modified distribution which is of interest, rather than the distribution produced by the nebulizer, since up to 90% of the latter distribution will normally pass to drain. It is highly probable that the distribution will be further modified by passage through the burner head, especially if this is flat-bottomed. The proposed procedure could be successfully applied to the aerosol emerging from the burner head if necessary, provided the air stream was sampled isokinetically. It could also be applied to sampling the complete aerosol in the absence of the spray chamber, although care would be necessary to minimise deposition losses and a significant part of the distribution, that above 10 km diameter, would be lost in the preimpactor stage using the cascade impactor chosen for the present investigation.

5. CONCLUSIONS

The proposed procedure offers a simple and rapid method for studying the size distributions of aqueous droplets produced by pneumatic nebulizers over the size range OS-10 pm. It is superior to dioctylphthalate-based procedures in so far as it allows studies to be made at nebulization rates typically employed in analytical flame spec- trometry but cannot be usefully employed for droplets outside the above mentioned range. The proposed technique is ideally suited to studies of the influence of nebulizer and spray chamber design parameters, and for producing reliable basic data for studies of the kinetics of evaporation, volatilization and atomization processes in flames and plasmas.

Acknowledgement-This material is based on work supported by the National Science Foundation under grant number CHE77-07618.