(13) that was applied to the microscope counts to account for differences in drift velocity. A second set of experiments was performed with aerosols generated from a binary solution of uranine and methylene blue. Results for the case of a 0.05% uranine and 0.25% methylene blue aerosol are shown in Figure 7, where three spectra are included. Each spectrum gives the mass of particulate phase in a cubic centimeter of aerosol associated with particles in a given size range. This means that all three spectra should be similar since all particles are of identical chemical composition. This is, in fact, borne out in spite of the fact that methylene blue and uranine were analyzed separately and the respective spectra deduced from the results. Conclusions and Recommendations The experiments carried out here confirm the simulation study of Melo and Phillips, and indicate the feasibility of obtaining particle size and chemical composition spectra with a Nuclepore filter sampler. The agreement between the spectra obtained with the Nuclepore sampler and results obtained by electron microscopy was good. Very little difference was encountered between the four solution methods and between the four filter arrangements. The experimental error was estimated a t 6.770, and a value of y of 0.003 was often found adequate to solve the constrained equation for the size spectrum. The possibility of using the sampler for chemical composition spectra has been demonstrated. In actual practice, however, this analysis depends on the ability to collect enough sample for chemical composition determination during the period when the efficiency of filtration is constant. This requirement will constrain the choice of chemical species for analysis and of the analytical method. In any case the size spectrum should be obtainable in all cases either by measuring filter loading as was done here or by measuring particle counts before and after passage of the aerosol through the filters. This last aspect is now undergoing investigation.
Nomenclature
A = sampling matrix g = discrete size spectrum vector g j = components of vector g giving the value of the spectrum at x, x = particle size parameter (x = log D, where
D is particle diameter) c j = error associated with the j t h observation X i = ith eigenvalue of A y = Lagrange multiplier involved in the constrained solution of the sampling equation
Literature Cited (1) Silverman, L., Billings, C. E., First, M . W., “Particle Size Analysis in Industrial Hygiene,” Academic Press, New York, N.Y., 1971. (2) Fuchs, N. A,, “The Mechanics of Aerosols” (Rev. ed.), Pergamon Press, Oxford, 1964. (3) Whitby, K . T., Clark, W. E., “Tellus XVIII,” 573, 1966. (4) Binek, B., Dohnalova, B., Przyborowski, S., Ullmann, W., Staub, 27,379 (1967). (5) Spurny, K . R., Lodge, J . P., Frank, E . R., Sheesley, D. C., Enuiron. Sci. Technol., 3,453 and 464 (1969). (6) Melo. 0. T.. Phillius. C. R.. ibid.. 8. 67 (1974). . . (7) Whitby, K.’T., L;ndgren,’D. A’., Peterson, C. M., Znt. J . Air Water Pollut., 9,263 (1965). (8) Billings, C. E., Silverman, L., J . Air Pollut. Contr. Assoc., 12, 586 (1962). ~~, ( 9 ) Skoog, D. A,, West, D. M., “Fundamentals of Analytic Chemistry,” Holt, Rinehart and Winston, New York, N.Y., 1963. (10) Spurny, K . R., Madelaine, G., Coll. Czech. Chem. Commun., 36,2857 (1971). (11) Twomey, S.,J. FranklinInst., 279,95 (1965). (12) Stein, F., Esmen, N., Corn, M., A m . Ind. H y g . Assoc. J., 27, 428 (1966). (13) Robinson, M . , in “Air Pollution Control Part I,” W. Strauss, E d . , Wiley-Interscience, New York, N.Y., 1971. ~
~
Received for reuieu: M a y 7, 1974. Accepted December 23, 1974. Work supported by Ministry for the Environment, Ontario, and the Atkinson Charitable Foundation. O.T.M . was supported by a National Research Council of Canada Scholarship.
Inertial Collection of Aerosol Particles at Circular Aperture Terence N. Smith’ and Colin R. Phillips*
Department of Chemical Engineering and Applied Chemistry, University of Toronto, Ont., M5S 1 A4, Canada Particles of sufficient mass may be separated from an aerosol by the inertial mechanism. The aerosol is subjected to accelerations and changes of direction as it flows through the geometry of the collecting system. While the finest and lightest particles respond to the motions of the fluid and follow its streamlines as they conform to the boundaries of the system, larger and more massive particles are not able to do so. The inertia of such particles causes them to cross streamlines and perhaps to impinge upon the bounding surfaces, to adhere, and so to be collected. This principle is utilized extensively in various designs of equipment for gas cleaning and aerosol sampling. A comprehensive discussion of the mechanics of the process of inertial separation is given by Fuchs ( I ) . A collecting device of some interest for sampling and, perhaps, for size analysis of aerosols is the Nuclepore 1 Present address, Department of Chemical Engineering, University of Adelaide, Adelaide 5001, Australia.
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Environmental Science & Technology
membrane filter. This consists of a membrane typically 10 pm in thickness perforated by uniformly sized pores which are straight, parallel, and circular in section. Filters with various pore sizes ranging down to small fractions of a micrometer can be obtained. Spurny and Pich (2, 3) consider the flow of an aerosol through such a filter and identify mechanisms of inertia, interception, and diffusion in the collection of particles. Inertial collection results if a particle is too massive to respond sufficiently to the changes in direction of the fluid streamlines as they converge to enter the filter pore. This process is illustrated in Figure 1. Interception of a particle following a fluid streamline occurs if the particle touches the surface of the filter as it moves by. Recovery by this mechanism is evidently dependent upon the size of a particle. The inertial effects on some particles in an aerosol approaching the pore of a filter may not be great enough to cause them to continue to travel across streamlines and so
The flow of a real, viscous fluid t o a circular aperture in a flat plate is computed using a relaxation method. This flow field and the trajectories of spherical particles through it are used to derive efficiencies of collection by the combined mechanisms of inertia and interception, of
E
t
O---Q-.O 0 .
0 0,’
---- *
c
0--
’I-
Collection of particles by inertia-deviation from fluid streamline (upper path) and by interception-contact while moving along fluid streamline (lower path)
Figure 1.
1. T
aerosol particles on the surface of a membrane filter of the Nuclepore type. Complete results for a filter porosity of 0.111 are given, and a generalization to smaller porosities issuggested.
to this acceleration and to the curvature of the streamlines must be crucial for the process of inertial recovery. The subject of this study is the determination of the pattern of flow of a real, viscous fluid to a circular aperture in a solid boundary and of the trajectories of spherical particles through this field. Efficiencies of collection are derived from the flights and positions of the particles. One value of filter porosity or pore density in the surface is chosen for the analysis, but a method for generalization of the results to a membrane of any porosity is suggested.
Determination of Flow For the purpose of detailed consideration, the flow of fluid to a single pore in a membrane with uniformly distributed pores may be isolated into a cylindrical volume coaxial with the pore. The ratio of the area of the pore to that of the cylinder is the porosity of the membrane. In fact, Nuclepore membranes have randomly distributed pores, but it is necessary, for tractability of the problem, to make this idealization. Figure 2 shows the system for a porosity of 0.111 that gives a ratio of cylinder diameter to pore diameter of 3.0, a typical value for Nuclepore filters. The boundary of the cylindrical fluid volume is contiguous with similar cylinders leading to adjacent pores and there is no flow across it. Far upstream of the filter face the fluid velocity is the uniform aerosol approach velocity, while deep into the pore the fluid must assume the normal pattern for flow in a tube of circular section. The equations of steady motion for axially symmetric flow of a real, incompressible fluid are, in axial and radial coordinates, x and r,
au
pu-
ax
+
au ap a~ + ax
pu-
v[--yl aay
(YZ)
8%
=0
Figure 2. Flow system and boundary conditions taken for com-
putations
Cylindrical approach envelope with uniform velocity three diameters upstream from filter face The filter porosity I S 0 11 1
with the continuity condition that to strike the face of the filter, but may be sufficient to relocate them on a streamline further from the axis of flow than that on which they entered. The particles may then be intercepted when the aerosol enters the pore. It is necessary, in reckoning the total effect of inertia, to consider subsequent interception. Application of Nuclepore filters in sampling or size analysis is possible only with adequate knowledge of the efficiency of collection of particles of a specified size. Results for diffusion to the walls of the pores based on the analysis of Twomey ( 4 ) seem to be satisfactory, but estimates of the inertial effect cannot be made with the same assurance. Pich ( 5 ) analyzes the motion of particles through a certain flow field taken as an approximation to that of fluid entering a pore. Parabolic shapes are assigned to the converging streamlines, but a feature of the stream functions chosen to represent these is that the axial component of fluid velocity remains constant. In fact, there must be a very substantial increase in axial component as the fluid nears and then enters the pore. The response of particles
If we use the concept of stream function to incorporate the continuity condition, the two dynamic equations may be written as
~---~-1 apa2p+ 3-1 aPaP + 1ap
1 aPa2P
ayayax
Y
-
-
axar
Y
aYax
-
pax
+---
where P is the stream function. The dynamic pressure, p , may be eliminated by differentiation and the equations can then be combined to give Volume 9, Number 6, June 1975
565
where
This fourth order equation may be solved by a relaxation technique if boundary values are assigned for the stream function P. It is appropriate here to specify P = 0 along the axis and a constant value, corresponding to the total fluid flow, around the cylindrical envelope and a t the face of the filter and at the wall of the pore. Moreover, zero values of the vorticity function, Q, may be assigned along the flow axis and at the fluid envelope but not, of course, on the filter surface. Finally a rectangular profile upstream and a laminar tube flow profile deep in the pore complete the specification. The computation is executed with a mesh size of 0.05 pore diameter, extending 3 diameters upstream and 2 diameters into the pore. From the computation, values of the stream function at each point on the mesh are defined, so specifying the flow pattern. Given the flow pattern, the trajectories of spherical particles arriving with the fluid at any radius within the cylindrical envelope can be followed. The acceleration
comes necessary to apply the appropriate Cunningham correction factor. Some particle trajectories are shown in Figure 4 . Each begins on the P = 0.5 streamline. The most massive particle, that with Ns, = 100, does not respond well to the convergence in the flow and crosses streamlines to strike the face of the filter with a scarcely diminished axial component of velocity. The particle with Nst = 10 deviates strongly from the fluid path but does respond ultimately to inward, radial acceleration so that it passes into the pore. However, it occupies a much less central position than the streamline with which it approached. The behavior of the particle with Nst = 1 is rather more complex. It responds well to the convergence in the flow and, though crossing the streamline, follows a closely parallel path. At the change in direction of the streamline just prior to entry to the pore, however, the velocities of the fluid and of the closely following particle are now several times the approach velocity to the filter. Now the particle does not respond so well but continues its flight to move radially inward across the streamline as the streamline turns to an axial direction. This constitutes a negative effect of inertia in terms of particle recovery. For the smallest Stokes Number, 0.1, response to fluid acceleration is rapid and the particle follows the streamline more closely even at the turn toward the axis to enter the pore.
in the axial and radial directions can be computed a t any point and the path can be plotted stepwise through the mesh of the flow field. It is assumed that the general flow of the fluid is qot affected by the presence of particles in or by the motion of particles relative to it.
Flow Pattern In the computation, a pore diameter of 1.0 pm and an aerosol approach velocity of 1.0 m/sec are used. With these values and the physical properties of air, Equation 1 is dominated by the viscous terms. The solution, presented in Figure 3, is essentially for slow flow of the fluid. As is characteristic of this type of flow, streamlines are shifted away from solid boundaries leaving a relatively quiet zone at the face of the filter and giving a fast acceleration along the axis of flow. It is evident also that the pattern for flow in a tube is almost fully developed as the 'fluid enters the pore. Under the condition of constant fluid flow pattern which, of course, is realized for all slow flows in the same geometry, particle trajectories may be characterized by the Stokes Number. Conventionally, this parameter is defined as the ratio of the particle relaxation distance, itself in slow flow, to the system dimension. The characteristic velocity is taken as the velocity through the pore, and the system dimension is the pore radius so that
The centers of particles with the same Stokes Number follow similar trajectories in similar flows. This definition of Stokes Number includes no allowance for the effect on fluid-particle drag of small ratios of particle diameter to molecular mean free path. Except in special circumstances, such a very low gas density, inertial effects would diminish to insignificance before it be566
Environmental Science 8 Technology
~
Figure 3. Streamlines in solution to flow equations Values represent the fraction of the total fluid flow between the streamline and the axis
Figure 4. Trajectories of particles with Stokes Numbers of 0.1, 1, IO, and 100 all starting at the same streamline shown in the figure
Recovery of Particles As discussed previously, a particle is collected by the inertial mechanism if it moves across fluid streamlines either to strike the surface of the filter or to be located in such a position that it is intercepted when the stream enters the pore. Given the trajectories of particles beginning their flights a t various radial locations, it is possible to find the trajectory which passes by the surfaces of the filter with a specified minimum clearance. A particle with radius equal to this clearance moving along this line is just arrested. A particle following a more central line passes through the filter. The results of the computations allow the critical starting radius for a particle of any Stokes Number and diameter, expressed as the fraction d / D of the pore diameter, to be found. The recovery of such particles from the aerosol flowing to the pore is simply that fraction of the flow which approaches the filter from outside that radius. Recoveries derived in this way are presented in Figure 5 as functions of the diameter ratio d / D and the Stokes Number. The curve for infinite Stokes Number gives the recovery of massive particles which are not deflected a t all by convergence of the fluid flow. That for 0 Stokes Number is the result for particles which follow the fluid streamlines exactly. In fact, this is the recovery for the mechanism of interception alone when no displacement of particles across streamlines Occurs. In Figure 5 , the curve for Nht-= 5 is shown as coincident with that for NSt = 0. This is a reflection of the negative effect referred to previously and shown in Figure 4. In the case of Nbt = 5 , the particle leaves the streamline at the initial convergence and just returns to it, by radial flight, a t the ultimate straightening before entering the pore. While the curves for smaller Stokes Numbers should, therefore, fall below that for Nh, = 5 and NYt= 0, they are not represented as doing so on Figure 5 . The reason is that diffusion of particles is likely to be significant at these levels. Diffusion tends to counter the effects of inertia by redistributing particles across the aerosol stream. Further, the contribution of inertia to the combined recovery is small compared with that of interception so that it seems proper to regard the value of 5 as the Stokes Number which is critical for the appearance of the inertial recovery mechanism.
a t least at some distance from the pore, may be regarded as radiating from a point. All flow patterns are similar; those for smaller porosities extend to a wider cylindrical approach envelope. The Stokes Number characterizing the trajectory of a particle through the general flow field must account for the linear scale of the system. In terms of the Stokes Number for the system with porosity of 0.111, the appropriate, modified Stokes Number can be defined as
where eo represents the value 0.11i. Particles with given values of Nst' follow the trajectories indicated in Figure 4 'for the same values of Nst . The degree of recovery shown in Figure 5 is derived from the particle trajectory which finishes a t the radius ( D / 2 - d / 2 ) so that the particle just touches the wall of
o.2
t
t
0 0
01
32
03 PARTC-E
b14
35
7 G PCRE 3
36 AME c i
37 -A1
C^i
38
3
3
Recovery of spherical particles by combined mechanisms of inertia and interception as a function of particle-pore diameter ratio and with Stokes Number as a parameter
Figure 5.
0.9 \
Generalization to Various Porosities The results presented are for a porosity of 0.11, typical of Nuclepore filters. Other porosities represent different geometries which, if they are to be treated rigorously, require separate computations of flow fields and particle trajectories. However, a useful extension to small porosities is possible by invoking the analytical result for the limiting case. For very small porosity, the slow flow to a pore is that to a hole in an infinite flat plate. The stream function for such a flow is given by Happel and Brenner (6) as
0.5 0.4
4 P =(1 - COS^^) 271
where q is the flow rate through the hole and 0 is the angle with the axis. This flow field is therefore a series of straight lines radiating from the hole as depicted in Figure 6. There is evident similarity between this flow pattern and that shown in Figure 3. Solutions to the flow at sma!ler porosities must correspond even more closely with the analytical result. In a generalization based on this limiting case, the streamlines in a system of any porosity are straight and,
/
1
0.3
0.2 0.1
Figure 6.
Streamlines for slow flow to a hole
in
F
an infinite flat
plate Values represent the fraction of the total fluid flow between the streamline and the axis
Volume 9, Number 6, June
1975
567
the pore. To utilize this graph for porosities other than the value of 0.111 for which it is prepared, an equivalent d / D must be generated. This is done by converting the finishing diameter to the appropriate linear scale which leads to the result
(d/D)’ = 1 - (1 - d / D ) (e/eo)’” Recovery is found from Figure 5 by indexing the appropriate modified Stokes Number and diameter fraction, Nst’ and (d/D)’, respectively.
Conclusion Recoveries of particles by a membrane filter of the Nuclepore type, for the combined mechanisms of inertia and interception, are given in Figure 5. These values are derived from a computation of the slow flow of a viscous fluid to a pore of circular section and from the trajectories of particles through the resulting flow field. A means of applying the result, which is for a porosity of 0.111, to membranes of smaller porosity is suggested. A factor of evident importance, and one which because of its complexity has not been pursued here, is the distribution of pores in the membrane. The geometry adopted here, coaxial approach volume and pore, is appropriate to a membrane with uniformly spaced pores. In fact, Nuclepore filters have randomly distributed pores. Some deviations in recovery must be expected when the volume from which the approaching aerosol is drawn is neither cylindrical nor coaxial with the pore. Some comprehensive experimental work will be needed t o define the scale of this effect.
eo = filter porosity, reference value of 0.111 p = fluid dynamic pressure r = radial position t = time
u = axial component of fluid velocity u = radial component of fluid velocity w = axial or radial component of particle velocity x = axial position D = porediameter Ns, = particle Stokes Number = psd2U/9qDe Nst’ = modified particle Stokes Number = (psd2U/qDeo) (e/eoP2 P = stream function Q = vorticity function U = aerosol approach velocity Greek Letters q = fluid dynamic viscosity
p = fluid mass density ps
= particle mass density
Literature Cited (1) ~, Fuchs. N. A.. “The Mechanics of Aerosols.” Macmillan. New York, N:Y., 1964. (2) Spumy, K . R., Pich, J., Collect. Czech. Chem. Commun., 28, 2886 (1963). (3) Spumy, K . R., Pich, J., ibid., 29,2276 (1964). (4) Twomey, S., Bull. Obs. Puy de Dome, 10,173 (1962). (5) Pich, J., Collect. Czech. Chem. Comm., 29,2223 (1964). (6) Happel, J., Brenner, H., “Slow Reynolds Number Hydrodynamics,” p 140, Prentice Hall, Englewood Cliffs, N.J., 1965.
Received f o r review J u n e 10, 1974. Accepted December 23, 1974. This program of work was started with the support of the Ministry of Environment, Ontario, and t h e Atkinson Charitable Foundation, and continued with the support of the Department of the Environment, Canada.
Nom e nc 1at ure d = particle diameter e = filterporosity
Formation of Photochemical Aerosol from Hydrocarbons Chemical Reactivity and Products Robert J. O’Brien,’v* John R. Holmes, and Albert H.Bockian C a l i f o r n i a Air R e s o u r c e s
Board, 9528 Telstar Ave., El M o n t e , Calif. 91731
The formation of photochemical aerosol-the haze associated with photochemical smog in polluted urban atmospheres-has been the subject of both study and speculation for more than 20 years. A totally satisfactory understanding of this phenomenon has not yet been achieved. Chemical analyses indicate that urban aerosol, a t least that portion of it that can be isolated on filters having submicronsize pores, is primarily inorganic in nature: metal oxides, salts-principally nitrates and sulfates-sulfuric acid, possibly absorbed nitric acid, and water. The organic portion, accounting for a t most 25-30% of the mass, is complex and variable in composition, insofar as its composition has been investigated. Despite representing a small percentage of the mass of urban aerosol, the organic portion is largely in the respirable range and 1 Present address, Department of Chemistry, Portland State University, Portland, Ore. 97207.
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Environmental Science & Technology
hence may contribute to a potential health hazard. Moreover the organic portion contributes significantly to light scattering and visibility reduction. If one assumes that the observed correlation in time between photochemical activity and rapid reduction in local visibility (Figure 1) indicates the existence of photochemical aerosol (however it may be constituted), one is forced to look for a mechanism by which a relatively small amount of photochemical oxidation products can contribute disproportionately to the overall process of visibility reduction by aerosol formation. Haagen-Smit ( 1 ) pointed out that cyclic olefins a t high concentrations-e.g., cyclohexene and indene-formed aerosol when allowed to react with ozone. He postulated that these compounds underwent oxidative ring opening and, possibly, subsequent polymerization. A number of investigators a t the Stanford Research Institute looked into the problem during the fifties and early
