Aerosol diffusion coefficient

Turbulent agglomeration. Far turbulent agglomeration two cases should be considered. First, if the inertia of the aerosol particles is approximately the same as that of the medium, the particles will move about with the same velocities as associated air parcels and can be characterized by a turbulence or eddy diffusion coefficient DT. This coefficient can have a value 104 to 106 times greater than aerosol diffusion coefficients. Turbulent agglomeration processes can be treated in a manner similar to conventional coagulation except that the larger diffusion coefficients are used. 

FIGURE 9.8 Aerosol diffusion coefficients in air at 20°C as a function of diameter. 

Raghunath, B. and P. Kotrappa, Diffusion Coefficients of Decay Products of Radon and Thoron, J. Aerosol Sei. 10 133 (1979). 

Approaching from another direction, Sinclair et al (1978) and Knutson et al (1984) report that diffusion battery measurements of radon daughter aerosol-size distributions often show a small peak which could be interpreted as the unattached fraction. Its position would indicate diffusion coefficients from 0.0005 to 0.05 cm /sec. 

Porstendorfer, J. and T. Mercer, Diffusion Coefficient of Radon Decay Products and their Attachment Rate to the Atmosphere Aerosol, in Natural Radiation Environment III. (T. F. Gesell and W. M. Lowder, eds.), CONF-780422, Vol. 1, pp. 281-293, National Technical Information Service, Springfield, Virginia (1980). 

Mechanisms and rates of transport of nuclear test debris in the upper and lower atmosphere are considered. For the lower thermosphere vertical eddy diffusion coefficients of 3-6 X 106 cm.2 sec. 1 are estimated from twilight lithium enhancement observations. Radiochemical evidence for samples from 23 to 37 km. altitude at 31° N indicate pole-ward mean motion in this layer. Large increases in stratospheric debris in the southern hemisphere in 1963 and 1964 are attributed to debris from Soviet tests, transported via the mesosphere and the Antarctic stratosphere. Most of the carbon-14 remains behind in the Arctic stratosphere. 210Bi/ 210Pb ratios indicate aerosol residence times of only a few days at tropospheric levels and only several weeks in the lower stratosphere. Implications for the inventory and distribution of radioactive fallout are discussed. 

Following the report on The Chemistry of the Atmosphere, it appears urgent to intensify sustained observational work in order to establish facts about any eventual evolution of our global environment. Such facts need to be gathered not only for physical parameters (temperature, albedo, variations of the solar ultraviolet irradiance below 3200 A, diffusion coefficients, aerosols, etc.) but also for a growing number of chemical species whose telluric concentrations are ultimately controlling the state of that environment. In 1960, a dozen molecules were known to exist in our atmosphere by 1980, 25 more species have been added to these and experimenters are asked now to look for another 40 molecules likely to play a role in the complex aeronomical scheme outlined by Professor M. Nicolet. 

Raghunath, B. Kotrappa, P. (1979) Diffusion coefficients of decay products of radon and thoron. Journal of Aerosol Science, 10,133-8. 

Table 1 compares the dimensionless coagulation coefficient predicted by the present model with other models. Since the Hamaker constant for most of the aerosol systems is of the order of 10"12 eig, this value is used in the calculation of the lower bound. Particle diffusion coefficients based on Philips slip correction factor for an accommodation coefficient of unity are used for the calculation of the coagulation coefficients ft (the Fuchs interpolation formula) and fts (the Sitarski... 

Fick s second law represents the time-dependent case in which the change in concentration of an aerosol, with respect to time at a point in space, is proportional to the divergence of the concentration gradient at that point, the constant of proportionality again being D, the diffusion coefficient (Jost, 1952). 

Equation 9.12 indicates that the diffusion coefficient of an aerosol particle is independent of particle density and hence is independent of particle mass. But is this really so Since particle mass is so much greater than molecular mass and the particles are continually undergoing bombardment by the molecules, one would expect changes in the direction of the particle to be gradual, compared to the rapid changes in direction with molecular diffusion. But if this is true, then particle momentum (mass) should be considered in the particle diffusion coefficient equation. 

For turbulence it is convenient to describe particle flux in terms of an eddy diffusion coefficient, similar to a molecular diffusion coefficient. Unlike a molecular diffusion coefficient, however, the eddy diffusion coefficient is not constant for a given temperature and particle mobility, but decreases as the eddy approaches a surface. As particles are moved closer and closer to a surface by turbulence, the magnitude of their fluctuations to and from that surface diminishes, finally reaching a point where molecular diffusion predominates. As a result, in turbulent deposition, turbulence establishes a uniform aerosol concentration that extends to somewhere within the viscous sublayer. Then molecular diffusion or particle inertia transports the particles the rest of the way to the surface. 

The product cv represents a diffusion current, i.e., the number of particles crossing a unit area in unit time. But Fick s first law of diffusion states that the diffusion current is proportional to the concentration gradient, the constant of proportionality being the diffusion coefficient D. Thus the diffusion coefficient for an aerosol particle is, from Eq. 9.11,... 

This process governs the rate of deposition of the molecules of nonvolatile compounds on the surface of gas ducts, and contributes to broadening of the chromatographic zones. Being of the order of 0.1 pm at STP, the mean free path of molecules, which is inversely proportional to pressure, reaches 1 cm only at about 0.01 mmHg. In dense enough gas, in the absence of convective flow, the macroscopic picture of migration of molecules (as well as of aerosol particulates) is described by the equations of diffusion. The mean squared diffusional displacement z2D of molecules, the time of diffusion t and the mutual diffusion coefficient >i 2 are related by ... 

Fig. 2.2 Diffusion coefficients of the aerosol particulates as a function of their size at 300 K according to Eq. 2.37.

Several published works have been devoted to the mathematical solution of the problems of penetration of aerosols through a diffusion battery, which is essentially a bundle of identical circular or rectangular channels in parallel [11]. The deposited matter is characterized only by its diffusion coefficient it means that the derived formulae hold for aerosol particulates, as well as for molecular entities. 

The mathematics of diffusional deposition is the same for particles ranging from atoms to aerosol particulates. Because of smaller diffusion coefficients, tiny aerosols deposit more slowly than do the molecular entities. 

There is an extensive literalure on solutions to (3.1) for various geometries and flow regimes. Many results are given by Levich (1962). Results for heat transfer, such as those discussed by Schlichting (1979) for boundary layer flows, are applicable to mass transfer or diffusion if the diffusion coefficient, D, is substituted for the coeflidenl of thermal diffusivity, K/pCp, where k is the thermal conductivity, p is the gas density, and Cp is the heat capacity of the gas. The results are directly applicable to aerosols for point panicles, that is, iip = 0. 

The diffusion battery consists of banks of tubes, channels, or screens through which a submicron aerosol passes at a constant flow rale. Particles deposit on the surface of the battery elements, and the decay in total number concentration along the flow path i measured, usually with a condensation particle counter. The equations of convective diffusion (Chapter 3) can be solved for the rate of deposition as a function of the particle diffusion coefficient. Because the diffusion coefficient is a monotonic function of particle size (Chapter 2), the measured and theoretical deposition curves can be compared to detennine the size for a monodisperse aerosol. 

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