Design theory and calibration of a field type aerosol spectrometer

DESIGN FIELD

School of Chemical

THEORY TYPE

AND CALIBRATION

AEROSOL

SPECTROMETER

MICHAEL

J. MATTESON*, GEORGE

Engineering,

Georgia

Institute

OF A

of Technology,

F. BOSCOE? Atlanta,

Georgia

30332, U.S.A.

and OTHMAR I. Physics

Institute,

PREINING$

University

of Vienna, Austria

(First received 9 April 1973; and injnalform

7 June 1973)

Abstract-A cylindrical-type aerosol spectrometer, of simple compact design has been constructed *and tested. The aerosol particles are injected into a horizontal centrifugal field through two portsa pin-hole orifice situated opposite a larger port. Aerosol moving through the larger port is removed in a cumulative size deposition on half of a foil on the outer wall, and serves as clean air for aerosol injected through the pin-hole and deposited according to discrete sizes on the other half of the foil. The instrument based on a modification of a device developed by Hochrainer and offers the advantage of confining the aerosol deposit to a narrow streak or dot in the case of monodisperse particles. The spectrometer was calibrated with monodispersed polystyrene latex particles and the results were compared with a theoretical expression developed for sedimentation distances appropriate to aerosols flowing in the plane of rotation.

NOMENCLATURE area, cm’ Fuchs-Stechina correction factor, see equation (24) aerodynamic dia., cm centrufugal force, dyn channel height, cm sedimentation distance. cm mass, g molecular weight pressure, dyn/cm2 volumetric flow rate in orifice, cmJ/sec radii, cm gas constant, erg/mol “K temperature, “K time, set mean linear gas velocity in channel in tangential direction sedimentation velocity of particle in radial direction volume, cm3 21/D,, where i, is mean free path of gas molecule (6.53 x 10-P cm) Greek notation defined by equation (7) defined by equation (9) ; 8’ term in C,, 0.42, dimensionless * Person to whom correspondence should be sent. Present address: Georgia Institute Georgia 30332, U.S.A. t Supported by EPA Training Grant AP-00086-02. $ NSF Senior Foreign Scientist Fellow, 1971-1972, Georgia Institute of Technology. 71

of Technology,

Atlanta,

72

M . J . MArnsso:,,, G. F. B o s c o l and O. Pm~INp<(~ term in CFs, 1,35, d i m e n s i o n l e s s viscosity, g / c m sec gas density distance in direction of flow, cm a n g u l a r velocity of centrifuge, sec

Subscripts I 2 3 4 atm

c o n d i t i o n at inner wall of a n n u l a r channel, R L = 1.27 cm outer wall of a n n u l a r channel, R 2 = 1.75 cm outer snrface of centrifuge, R 3 = 3-0cm reside wall of protective cylinder, R,, - 5"0 cm a t m o s p h e r i c conditions.

INTRODUCTION

The aerosol centrifuges recently introduced (St6ber and Zessak, 1964; St6ber and Zessak, 1966; St6ber, 1967; Hauck and Schedling, 1968; Berner and Reichelt, 1969; and St6ber and Flachsbart, 1971), involve complicated and expensive machining, especially with respect to the aerosol injection system. In the Berner-Reichelt design, e.g. the aerosol enters the interior of the spectrometer through a ring slit located near the center of r6tation ; they need in addition a supply of clean air which was drawn from the room air. Hochrainer and Brown (1969) pointed out that this auxiliary air stream is subject to contamination and needs extra cleaning. Later, Hochrainer (1971) developed a cylindrical centrifuge which split the aerosol into two streams. Particles were removed from the larger of the two streams in part of the centrifuge, and this clean air formed a carrier stream through which the aerosol particles from the superimposed, second, smaller stream deposited in a discrete size spectrum in another part of the centrifuge. Because the aerosol enters the channel through a slit, the deposition pattern of monodispersed aerosols takes the form of narrow and bent bands. To avoid the necessarily narrow entrance slit of Hochrainer's design the centrifuge described in the following was constructed. By introducing the aerosol through a cylindrical hole of 1 mm dia. located midway between the top and bottom of the flow channel, the particle trajectories are least disturbed by the upper and lower walls of the channel. If the size distribution of the analyzed aerosol is monodispersed the particles are deposited as a discrete "dot" on the foil lining on the outer wall of the annular channel. DESCRIPTION

OF

THE

AEROSOL

SPECTROMETER

The aerosol spectrometer (see Figs. 1 and 21 consist of only three major parts, the inner rotor R (brass), a cover C (brass) which holds a removable foil for depositing the particles and the exchangeable flow-limiting orifice E, and the outer nut N (aluminium) which screws on R and holds C in position so that the two 0-rings provide an air-tight seal of the flow channels. The angular position of C relative to R is fixed by a baffle D (nylon) mounted on R which fits tight into a groove in C, and has the two-fold function of positioning of B and of interrupting the annulus formed by a circular groove in R of rectangular cross-section in such a way as to force the aerosol flow from the entrance port to the flowlimiting orifice at the exit. The shaft of R is mounted in the chuck of a Stanley 1/4 hp, highspeed router motor connected to a rheostat and a Sola constant voltage transformer. The centrifuge rotation was measured with a General Radio Strobotac strobe light. Aerosol was introduced into the centrifuge through the central bore in R either by flooding the top surface with aerosol or inserting a lance into it. The aerosol then travelled

A field type aerosol spectrometer

central bore

0-rings~r e m o v a b l e

73

foil

/ ~ ~ "annularchannel large inlet channel

'small inlel channel

Fig. 1. Cross-section through the assembled centrifuge. The aerosol enters through the central bore (dia. 5 mm), and is split into two streams through the large inlet channel (bore of dia. 5 mm)~ and the small inlet channel (bore of dia. 1 mm), the main stream flows then counter-clockwise through the annular channel of square cross-section 5 × 5 mm (see Fig. 2 part R); the particles are removed in the first half of the annulus. Then, the second aerosol stream is superimposed to the first stream at an angular position of 180 ° relative to the main stream entrance port; the combined streams leave the centrifuge at an angular position of 300 ° (see Fig. 2 part C) through the flow-limiting orifice. The annular channel is interrupted by a baffle at an angular position of 330 ° (see Fig. 2 part R cross-section D).

HIH

r~ H

\\1

EL K

~ I

.

.

.

.

.~o

'

I

5~

Fig. 2. The major parts of the centrifuge: the rotor R, carrying the nylon baffle, the cover C locked in its angular position by the baffle and carrying the flow-limiting orifice, and the nut N screwing on R to hold C air-tight by virtue of the O-rings against R with a hole to leave the exit of the flow-limiting orifice open.

74

M.J. MATTESON,G. F. BOS¢'OI and O. PREINING

radially outward through two circular channels with openings spaced 180 apart. The diameter of the larger channel was the same as the annular channel height. The purpose of this stream was to provide a carrier stream, free of aerosol, for the deposition of aerosol entering the annulus through the small channel. This was accomplished since the deposition from the larger stream was completed in the flow through the first half section of the annulus, the particles in the smaller stream which was superimposed on the clean air stream were separated discretely according to aerodynamic diameters on the outer wall of the annular channel. The combined air streams then moved out of the centrifuge through an exit orifice which controlled the flow rate. The air was prevented from re-entering the annulus by the baffle D placed between the large channel opening and the exit orifice. An aluminium foil strip 1 × 4 c m was inserted in the outer wall, and, once the aerosol was deposited on it, the foil was analyzed with a light microscope to find the mean deposition distance for each particle size and aerosol flow rate. A set of orifices were calibrated by inserting them in a tube with manometer taps for presst, re drop measurements at various flow rates. From these data. once the pressure drop within the centrifuge is known, the flow rate could be determined for a particular orifice size. For safety reasons a mechanical shield m form of a cylinder (ahuninium) of an i.d. of 10 cm and a wall thickness of 8 mm was mounted co-axially with the cenl,'ifuge.

AEROSOL

GENERATI{)N

The aerosol used to calibrate the spectrometer was generated from an aqueous suspension of Dow polystyrene latex spheres. These were obtained in sizes from 0-481 to 1.305 #m, and the original concentration is 10 per cent by weight. It was necessary to dilute this suspension in order to minimize the occurrence of multiples of latex particles leaving the generator in the same liquid droplet. Once a droplet containing more than one particle dries, the latex particles will adhere in aggregates. A dilution of the original suspension of 40:1 yielded a minimum of aggregates while still providing a sufficient concentration to measure. For a generator No. 40 DeVilbiss glass nebulizer at an air pressure of 0"83 arm. was chosen. The gas flow rate was 7.4 l./min. The aerosol was dried by mixing with 101./rain dry air which had been passed through a silica gel column. Both gas streams were passed through 0.22 #m pore size Millipore filters at their source. The drying gas and aerosol were mixed in a 600 cm 3 glass tube prior to entering the aerosol centrifuge.

DESIGN

THEORY

Much of the previous aerosol spectrometer design has been empirical. Sedimentation distances have been predicted only after flow characteristics, appropriate to a particular design was established. In the following development sedimentation distance is determined from the pressure drop across the flow-limiting, exit orifice. This theoretical distance will be compared to actual sedimentation distances obtained in the above described centrifuge with calibration aerosols. The flow in the exit orifice is determined by the pressure gradient through the orifice. This pressure gradient can be found analytically. The pressure on the upstream end of the orifice is greater than atmospheric, and is a result of the centrifugal field acting in the hori-

A field type aerosol spectrometer

75

zontal direction across the annular flow channel. The radial increase in pressure across a volume element of thickness dR and unit height is dP =

o~2R

dm

(1)

dm = p(R)dV

(2)

dV = 27zRdR.

(3)

P(R)M p(R) - - R'T

(4)

2nR

where and For an ideal gas

and substituting 2, 3 and 4 in equation (1) and integrating, one obtains (c°2M

P2 = Po exP,2~ ( R 2 2

}

- R2) -

(5)

Choosing Ro (0.25 cm) to be the entrance site at the axis of the centrifuge, and assuming Po = Patm = 1 atm then P2

Patm { 1 + M e ° 2 REt

=

(6)

since R 2 ~ R~ and Me~2R2/2R'T ~ l*. Equation (6) may be abbreviated P2

=

P,,m{ 1 + ~}.

(7)

The pressure at the exit of the exit orifice is less than atmospheric because of the high velocity of the outer surface of the centrifuge. Our apparatus incorporated a protective cylindrical shield of 10 cm i.d. within which the centrifuge rotated. The pressure distribution between a concentric rotating cylinder, and an outer stationary cylinder is found from the Navier-Stokes equations (Schlichting, 1968) lnP4 _

=

Pa

2 2

Mm2~ R~R4 R ' T ~2(R 2 - R~)

2R, R,2 R, 1 (R 2 _ R32)2 In R33 + 2(R~ - R32)~ "

(8)

Now if P4 = Patm, and if the term on the right is fl ,~ 1 P3 ~ P~tm(1 -- fl)'

(9)

The pressure drop limiting flow across the orifice and through the centrifuge is, then, from equations (7 and 9) P2 - P 3 = Patm( ~ -b fl).

(10)

In our design P 2 - - P3 was found to be 179 dyn/cm 2. This consists of a calculated pressure elevation, Pa,~ ~, of 52 dyn/cm 2, and a measured vacuum, Patm fl, of 127 dyn/cm 1. Vacuum measurements were made at the edge of the rotating centrifuge, and the results at 10,000 rpm (127 dyn/cm 2) agrees fairly well with the value predicted by equations (8, * For to = 200 sec-l, M = 30, T = 300°K, R 2 = 2 cm, M~,fl R~/2R'T ~ 10 -4 .

76

M.J. MAI~TESON,G. F. BOSCOt~and O. PRlilNING

9) (147 dyn/cm2). One might expect a somewhat lower value than theoretical, since the knurled outer surface of the centrifuge tends to disturb the boundary layer. Also the Taylor Number between the centrifuge and the protective slaield is

T, = ~')R3(R4 -~ R3)x/R4-- R.~ = 5500

V

R3

which is characteristic of a turbulent flow. pattern. Therefore, we chose to use the measured value in our pressure drop calculation. The pressure drop having been determined, we obtained the volumetric rate of flow, Qo, and the average linear flow in the annular channel, Uo, from the orifice calibration data. At 179dyn/cm 2 the three orifices limited the velocity in the channel to 0.22, 0-35 and 0-52 cm/sec. We may now proceed to determine the sedimentation distance. For an approximation of the flow pattern in the annulus we chose the solution for flow between infinite parallel planes. It is customary to assume the solution for the velocity profile of the gas in the channel to be the forward component of the particle velocity. This, together with the sedimentation velocity in the radial direction, describes the particle trajectory. For a rigorous solution, based on flow in a square channel, one may apply the equations developed by Cornish 11928). However, since the particle trajectory is at the mid plane between the upper and lower walls, we chose an approximate solution which ignored the influence of these boundaries on the velocity distribution of the gas at mid plane. (11) For a square channel (Purday, 1949) the average velocity is 12)

U0 = 0.49 Um~ therefore U

,,

~ 2"04U~)I 1 -

"X'2 1 (iji i

13)

mid p[~tnc

where l = R - R1. The particle sedimentation velocity in the radial direction is obtained from Stokes' Law: URs=

d t ,~-

18/~

\1 + f l ' x +

i~ I

114)

where the term in brackets is the Fuch~Stechina (1962) correction for slip, henceforth abbreviated Cvs, and R is the radial position, which in Cartesian terms is R =y+(R1

+~)=y+?.

Therefore (dR/dt)~ = (dy/dt)s and equations (13 and 14) can be combined to yield dO

36.7#~

~

l

+

y-'

115)

A field type aerosol spectrometer

77

Taking as boundary conditions, 0 = 0 at R = R t and 0 = L at R = R2, the above equation can be integrated to yield L.

(R2+Rx~2]In~-2~ . . R2 - R1] .J /z [(R2)2

36"7pUe . ~[1

D.~coZPpCvs[|

(R1) 2] +

4(R2+R~)}.

(16)

\R2

Therefore, with a knowledge of the speed of rotation, co, external radii R 3, R 4 and internal radii R1, R2, one can predict the pressure drop in the flow-limiting orifice. For a given pressure drop, calibration data will provide the volumetric flow rate, Qo, from which the average channel velocity, U0, is determined. Once Go is obtained we can, with equation (15), find the sedimentation distance appropriate to a given aerodynamic diameter. For sampling purposes we are usually interested in a range of diameters, the lower limit of which will deposit at L. This fixes Dae in terms of angular velocity, channel speed and centrifuge radii. RESULTS

AND

DISCUSSION

The aerosol deposition patterns are described in Table 1 in subgroups according to the different channel velocities. The location and size of the deposit are denoted by L~, L2, Table 1. Aerosol spectrometer sedimentation characteristics Particle*

Equivalent aerodynamic

dia. (/~m)

dia. (pm)

L1

L2

L,.

Ltheory

w,

w~

w,,

0-822(s) 0.822(d) 0.577(s) 0.577(d) 0.577(t) 0.577(g) 0.481(s) 0.481(d)

0.822 0.970 0.577 0-680 0.767 0-845 0-481 0-567

0.90 0.70 1.60 1.22 1.00 0.80 1-60 1.35

1-00 0.75 1-80 1.29 1-10 1.00 1.90 1.40

0.95 0.72 1.70 1.25 1.05 0.90 1-75 1.38

1.04 0.77 1.97 1.47 1.13 1.00 2.73 2.04

0.20 0.20 0.20 0.15 0.15 0.15 0.20 0.20

0.30 0.30 0.30 0.30 0-30 0.25 0.30 0.30

0-25 0-25 0.25 0.23 0.23 0.20 0.25 0.25

No. 2 Go = 0"35 (cm/sec)

1"10 (s) 1"10 (d) 0.822(s) 0.577(s) 0-577(d) 0"577(0 0-481(s) 0-481(d)

1.10 1"30 0'822 0"577 0"680 0.767 0-481 0-567

0.70 0"50 1.45 2"45 2'00 1"55 2"80 2-20

0"90 0"65 1"60 2-75 2"25 1"75 3'00 2.40

0-80 0.60 1"53 2.60 2"13 1"65 2-90 2"30

0"98 0.735 1.66 3"15 2-35 1"81 4"37 3.26

0"20 0-20 0"20 0"20 0"20 0"20 0'20 0"20

0-30 0"30 0"30 0"35 0"30 0"30 0-40 0"30

0.25 0"25 0-25 0"28 0"25 0"25 0"30 0-25

No. 3 Go = 0"52 (cm/sec)

1"30 (s) 1"30 (d) 1"10 (s) 1"10 (d) 1"10 (d) 0"822(s) 0"822(s) 0"822(d) 0"822(d) 0"822(0

1"30 1"53 1"10 1"30 1"30 0'822 0"822 0"970 0"970 1"09"

0"90 0"70 1"00 0"70 0"80 2"00 1"85 1"40 1"35 1"10

1"10 0"80 1"15 0"90 0'95 2"20 2"10 1"60 1"60 1"30

1"00 0"75 1"08 0"80 0"88 2'10 1"98 1"50 1'48 1"20

1"10 0'79 1"47 1"10 1"10 2"49 2"49 1"85 1"85 1"50

0"20 0"20 0"20 0"20 0"20 0"17 0"20 0"15 0"20 0"20

0"30 0"30 0"30 0"30 0"30 0"35 0"30 0"30 0'30 0"30

0"25 0"25 0"25 0"25 0"25 0"26 0"25 0"23 0"25 0"25

Orifice No. 1

U° = 0.22 (cm/sec)

* (s) Singlets; (d) Doublets; (t) Triplets.

Sedimentation lengths (cm)

Widths (cm)

78

M, J. MATTf-SON. G. F'. Boscof and O. PRtlNING

W~, and W,. The term L t denotes the sedimentation distance where the deposit first appears and L2 is that distance corresponding to the trailing edge of a given deposit. The term W~ denotes the distance from the top of the foil to where the deposit appears and W2 is the distance from the top of the foil to the opposite edge of the deposit. From this notation the length of a given deposit is L 2 - L 1 and the width W 2 - W1; L,, and W,, are mean sedimentation dimensions. For the lowest channel velocity, 0.22 cm/sec, the average deposit dimensions were I x 1 mm which corresponded quite well to the injection port dimensions. At the higher velocities, 0.35 and 0.52 cm/sec, somewhat greater scatter is evident and the average deposit dimensions are 2 × 1 mm. The mean deposition height, W,,, fell quite regularly at the center of the foil. -[

.

1

I

I

I

3o ~ o~o~. .Ue=O.cm/ 52secE o 20 15

•

:)\,\

....

•

,_~

I 0

2

o.e

_

"\ o\: \

E (/3

0-6

Oo=O~2 em/see

\

O.L

1

o.4

I

l

1

0.6 0.8 ~o A e r o d y n o m i c dia ,

1

r.5 p-M

Fig. 3. A e r o s o l S p e c t r o m e t e r C a l i b r a t i o n Curves. Solid lines r e p r e s e n t t h e o r e t i c a l s e d i m e n t a t i o n d i s t a n c e s at three flow rates. E x p e r i m e n t a l results i n d i c a t e d b y Q for U, = 0-22 cm/sec, O for U, = 0.35 cm/scc, • for U, = 0-52 cm/sec. ~o - 10.000 rpm.

Sedimentation distances varied, as expected, with particle size, and with the number per aggregate. Aggregates of latex spheres were observed in multiples of two, three, and four. Preining (1962) observed multiple aggregates of spheres of diameter 0.5/~m or less when testing aerosols generated from liquid suspension by pneumatic dispersion. The formation of these aggregates may be reduced by further diluting the liquid suspension, but excessive dilution leads to reduced number concentration in the aerosol. St6ber (1969) measured equivalent aerodynamic diameters for aggregates of latex particles for groups containing up to 11 particles. From these measurements he calculated shape factors by which the single particle diameter must be multiplied to obtain an equivalent aerodynamic diameter for each group. In our case these factors are 1-18 for doublets, 1.33 for triplets, and 1.46 for quadruplets. The theoretical expression for sedimentation distance is compared, in Table 1 and Fig. 3, with experimentally observed distances at the three average channel velocities. The theoretically derived distances are about 10 15 per cent greater than those obtained experi-

A field type aerosol spectrometer

79

mentally; this may be attributed to the approximation in the theoretical derivation which neglects the upper and lower boundary effects. F r o m the theoretical development, an increase in pressure drop across a given orifice will yield a greater velocity. In a treatment similar to that for the pressure distribution between two concentric cylinders, one can show that if the outer stationary cylinder is at progressively greater distances from the inner rotating cylinder, and if the system is isolated, lower pressure can be expected at the exit side of the orifice. In our case the sedimentation distance for a given aerodynamic diameter would be approximately double the values obtained if the stationary cylinder were removed. Since the sedimentation distances are sensitive to this outside pressure, care should be taken in the design of any protective shield. Change in the speed of rotation offers little flexibility in extending the range of aerodynamic diameters measured by the centrifuge. While the channel velocity is a function of the exit orifice pressure drop, which in turn is related to 0 ) 2 (equation 10), the radial velocity of the particle is also a function of 0)2, so that in general, increasing the speed of rotation does not have much effect on particle trajectory. SUMMARY A theory has been developed to describe the relation between sedimentation distance and design parameters in a modification of an aerosol spectrometer described by Hochrainer. The pressure drop across the exit orifice can be calculated from design variables, and, assuming that the aerosol volumetric flow rate in the annular channel is limited by the pressure drop across the exit orifice, this flow rate is obtained from orifice calibration data. Satisfactory agreement was found between theoretically predicted sedimentation distances and those from tests with aerosols of polystyrene latex. The modified device described here provides for a 1 m m dia. aerosol injection port at mid-distance between top and b o t t o m of the flow channel. This offers the advantages of reduced aerosol loss at injection, less interference with the channel surfaces, and better deposition patterns. Deposits were quite uniform and were confined to an approximately circular spot of 1 m m dia. at the lowest channel flow rate. Particle aggregates of doubles, triplets and quadruplets were easily distinguished at various sedimentation distances. It is felt that this design is suited for field type sampling of aerosols in the submicron range. REFERENCES Berner, A. and Reichelt, H. (1969) Staub 29, 92-95. Cornish, R. J. (1928)Proc. Royal Soc. Lond. 120-A, 691-700. Fuchs, N. A. and Stechkina, I. B. 0962) Trans. Farad. Soc. 58, 1949 1952. Hauck, H. and Schedling, J. A. (1968) Staub 28, 18 21. Hochrainer, D., and Brown, P. M. (1969) Environ. Sci. Technol. 3, 830-835. Hochrainer, D. (1971) J. Colloid Interface Sci. 36, 191-194. Preining, O. (1962) Staub 22, 45~463. Purday, H. F. P. (1949) An Introduction to the Mechanics ~?f Viscous Flow, p. 16. Dover, New York. Schlichting, H. (1968) Boundary Layer Theory, p. 80. McGraw-Hill, New York. St6ber, W. and Zessack, U. (1964) Staub 24, 295-305. St6ber, W. and Zessack, U. (1966) Z. biol. Aerosolforsch. 13, 263-281. St6ber, W. (1967) Proceedings of a Symposium of the IAEA Assesment of Airborne Radioactivity, pp. 393~404. Stfber, W. Berner, A. and Blaschke, R. (1969) J. Colloid Interface Sci. 29, 710-719. St6ber, W. and Flachsbart, H. (1969) Environ. Sci. Technol. 3, 1280-1296. St6ber, W. and Flachsbart, H. (1971)J. Aerosol Sci. 2, 103 116.