Velocity of deposition

In specifying settling chamber dimensions, gas flow velocities must be maintained below the reentrainment velocity (pick-up velocity) of deposited particulate. As a general guideline, linear gas velocities are kept below 10 ft/sec (600 ft/min = 304.8 cm/sec). This is satisfactory for most materials however, some low-density particulates are reentrained at lower velocities. 

Qlu, Qia Flux of unattached, attached 218Po to surface (Bq m-2 s 1) vu, va Velocity of deposition of unattached, attached 218Po (m s 1) Aj, X2, A3 Radioactive decay constants of 218Po, 214Pb, 214Bi (s 1)... 

The velocities of deposition of attached and unattached decay products are the fluxes divided by the concentrations... 

If the velocities of deposition are averaged over all the surfaces, and S (m 1) is the ratio of surface area to volume in a room, the rate constants for removal by deposition are... 

In the simple case of airflow over an aerodynamically smooth surface, with a fully developed boundary layer, the velocity of deposition can be calculated as a function of the diffusivity of the vapour or particle and the air speed. Formulae, developed for mass and heat transfer (Brut-saert, 1982) have been shown to apply to both attached and unattached 212Pb in wind tunnel experiments (Chamberlain, 1966,1968 Chamber-lain etal., 1984). 

Figure 1.10 shows the velocities of deposition to a smooth surface of attached and unattached decay products, with a range of possible values of D. The scales are m s-1 for the attached and mm s 1 for the unattached decay products, illustrating the effect of attachment on diffusivity. For a nucleus of unit density with diameter, dp, equal to 0.17/um, the sedimentation velocity is 2 jum s 1, and deposition by Brownian diffusion and by sedimentation to upwards-facing surfaces are of comparable efficiency. For smaller particles, Brownian diffusion is always more effective. 

Fig. 1.10. Velocity of deposition of attached (left-hand scale) and unattached (right-hand scale) decay products to smooth surfaces. Curves A, B, C, D, E corresponding dp (am), 0.17,0.12, 0.08, molecular, molecular D (m2 s 1), 3 x 10 10, 5 x 10 10,1 x 10 9,0.05, 0.07.

Deposition other than in rain is termed dry deposition, and this includes sedimentation of particles, molecular and Brownian diffusion to surfaces, impaction on roughness elements and deposition under electrical or thermophoretic forces. The velocity of deposition is defined... 

Strictly, vg should be defined relative to the reference height at which the airborne concentration is measured. When this is not specified, it is understood to be about 1 m above ground. On the electrical analogy, the velocity of deposition is sometimes called the conductance, and its reciprocal the resistance. 

Sr calculated by dividing the annual deposit gauge collection by the average air concentration. The contribution of dry deposition to the deposit gauge is in fact usually ignored in calculating the washout ratio. Hence the velocity of deposition by washout is... 

Table 2.13. Velocity of deposition of bomb-derived nuclides... 

The velocity of deposition of radioiodine, defined as in equations (2.3) and (2.4), is controlled by the rate of adsorption at the surface. When the adsorption or chemisorption at the surface is strong, the rate of deposition of 131I, when expressed in terms of suitable non-dimensional parameters, is similar to the rate of heat transfer to or from the surface (Chamberlain, 1953). In field experiments, artificial leaves of copper or silver foil were attached to vegetation, and it was found that the uptake of 131I to real leaves was typically 0.4 to 0.7 times the uptake to artificial leaves. Since a thin film of paraffin was found to inhibit... 

Fig. 3.3. Velocity of deposition of radioiodine vapour to bean leaves. In light O, Guenot etal., 1982 A, Garland etal., 1984. In dark , Garland etal., 1984.

Table 3.4 also shows the velocity of deposition of iodine vapour normalised in respect of herbage density as ... 

Only limited information is available on the washout of radioiodine vapour by rain. Measurements of stable iodine in rain, compared with iodine vapour in air (Whitehead, 1984), give a value about 30 for the washout ratio W, defined as the ratio (I per kg rain)/(I per kg air). For a moderately heavy rainfall of 1 mm h-1, this would imply a velocity of deposition in rain of 7 mm s-1, which is the same order of magnitude as the velocity of dry deposition. The washout ratio of particulate fission products is typically about 500 (Table 2.12), so radioiodine deposited in... 

Garland Cox (1980) placed PVC enclosures over soil at various sites in southern England, introduced T2 vapour, and measured the rate at which it disappeared. The loss was exponential, and assuming it was caused by deposition to the ground the velocity of deposition averaged 0.4 mm s-1. This is three times the value deduced for HT in the previous section, but it is not known whether there is a real difference between deposition of HT and T2. There was some seasonal... 

The difference %i Xo in concentration of a vapour or aerosol in the free stream and at a surface is the driving force for deposition. Since the ratio Q/(x 1 — Xo) has the dimensions of a velocity, it is called the velocity of deposition, denoted vg. Alternatively, on the electrical analogy, vg is the conductance and its reciprocal, r is the resistance to mass transfer. If the boundary layer of an airflow over a surface has two or more parts, for example above and below the top of the roughness elements, the resistances of these layers are additive, since... 

Shoots of nettle, white poplar and beech were placed in the tunnel which was operated at a wind speed of 2.5 m s 1. Beech leaves are smooth, whereas those of white poplar and nettle have hairs. The velocities of deposition to the leaves of the three species are shown in Table 6.1. As expected from the lower diffusivity of the larger particles, vg was less for the 0.2- m than for the 0.03-,am particles. Deposition to... 

Velocity of deposition relative to area of both sides of leaf. 

When the wind blows past an obstacle, the streamlines of air flow diverge to pass round it. Particles carried in the wind tend to carry straight on and may impact on the obstacle. The efficiency of impaction C, is defined as the ratio of the number of impacts to the number of particles which would have passed through the space occupied by the obstacle if it had not been there. If vg is the velocity of deposition relative to the profile area of the obstacle, then C = vglux where ux is the free stream air velocity. C, is thus analogous to Cd, the drag coefficient of the obstacle. 

Figure 6.5 shows velocity profiles obtained in the wind tunnel depicted in Fig. 6.2. The floor of the tunnel was covered with an artificial sward consisting of plastic spills 75 mm tall and 5 mm wide fixed in a wax substrate (Chamberlain, 1966). With a zero displacement, d, equal to 50 mm, the profile for different wind speeds met on the axis giving z0 = 10 mm, and the slope of the lines gave a in accordance with (6.12). When wind speed is normalised by dividing by a, the profiles all fall on one line. Figure 6.6 shows u/a plotted against log(z — d) for three surfaces with different z0. Since the flux of momentum is pau, and the concentration of momentum at height z is pu(z), u2Ju z) is the velocity of deposition of momentum, denoted vm. Its reciprocal is the resistance to momentum transport and /+(z) = u(z)lu t is the normalised resistance.

Figure 6.9 shows the velocity of deposition of particles to grass about 70 mm high (Chamberlain, 1967 Clough, 1975). Results of Porstendorfer et al. (1981) with barley of similar height are also shown. Figure... 

Figure 6.11 shows the velocity of deposition of Lycopodium spores to bare soil in the wind tunnel (Chamberlain Chadwick, 1972). The roughness length was 3 mm. When the soil was wet, v, increased with u, but levelled off at high speeds (in the field, = 1 m s-1 would correspond to u = 20 m s-1 at z = 10 m). With dry soil, vg hardly... 

The results of the field experiments are summarised in Table 6.4. The velocity of deposition of Lycopodium spores to dry grass and cereal crops was about twice the sedimentation velocity, so vv and vt were about equal. When the cereal crop was thoroughly wetted, v, was about twice vv. 

The capture of acid particles, or acid droplets, by forests is considered an important cause of acidification of soils and water courses in mountain regions (Lovett, 1984 Lovett Reiners, 1986). Field experiments on the required scale are hardly feasible. Several authors have made calculations of the wind profile within the forest, and the capture efficiency of model leaves and twigs in the canopy. Figure 6.12 shows the results of calculations by Belot (1975), Slinn (1982), and Lovett (1984). When expressed in terms of the normalised velocity of deposition v., there is little difference in Fig. 6.9 between the calculated... 

Fig. 6.12. Normalised velocity of deposition A, radioactive particles to grass, m = 0.35 m s 1 B, C, D, calculations for forests by Slinn (Eucalyptus, M = 0.7 m s 1), Belot (pine, M = 0.6 m s-1) and Lovett (fir, u — 1.1m s-1). Reference height = twice canopy height.

Wet removal processes are further controlled by precipitation types and rates. Dry deposition processes on surfaces are affected by atmospheric transport rates that mix fresh pollutant into the surface boundary layers and by the physical properties of particles. For the Eastern U.S., the approximate annual deposition rates of sulfate can be compared as follows (Table III), considering that deposition flux is the product of a concentration and a velocity of deposition (Vd) (20) ... 

An important parameter used to quantify dry deposition processes is the velocity of deposition (Kg) (Chamberlain, 1953). Vg is defined as the downward flux of aerosol or gas to a vegetation or soil surface, normalised to the ambient atmospheric gas or aerosol concentration above that surface. In the case of radionuclide deposition processes flux and concentration are, respectively, measured in units of radioactivity per unit area and volume, hence... 

This expression yields an empirical parameter with units of velocity (cm s-1) which are independent of atmospheric concentration. Vg may be calculated on the basis of exposed leaf area, in the case of spaced plants, or in terms of the horizontal surface area for continuous swards such as cereal or grass crops. Both soil and plant are potentially available for contamination and the total velocity of deposition to a canopy can then be defined as... 

In the case of particles, it is physical form rather than chemical characteristics which controls the velocity of deposition to vegetation, although the latter is important with respect to the subsequent processes of foliar absorption, translocation or... 

Direct electrolytic preparation of lithium from aqueous solutions of its salts is not feasible, but can be effected when the salts are dissolved in organic solvents such as acetone and pyridine.7 A solution of lithium chloride in pyridine was electrolyzed by Kahlenberg8 with a cathode of sheet platinum or iron wire and a current density of 0-2-0 3 ampere per 100 sq. cm. Patten and Mott9 found that amyl alcohol is a suitable solvent, provided the current density is sufficiently high to ensure the velocity of deposition of the metal being greater than that of its solution in the alcohol. 

The relative contribution of particulate and gaseous deposition to total dry deposition is not certain, but given the low velocity of particulate deposition, gaseous deposition is considered to be much more important. The velocity of deposition depends upon particle size for particle diameter. 02 microns -.025 cm/sec for diameter 0.2 microns - 0.6 cm/sec and for diameter 2 microns - 0.1 cm/sec. 

Deposition of vehicle exhaust lead aerosol to plant and soil surfaces by diffusion and impaction mechanisms has been studied by Little and Wiffen [3]. These workers found that rough or hairy leaf surfaces were up to eight times more efficient at collection of lead than were smooth surfaces. The velocity of deposition, Fg, of lead aerosol was determined and some results are shown in Fig. 4.1. 

Fig. 4.1 Velocity of deposition of ° Pb-labelled exhaust to adaxial (upper) and abaxial (lower) leaf surfaces (mean values 95% confidence limits) [3].

In the next three chapters, the principles discussed in the present chapter will be applied to calculate the velocity of deposition, the critical velocity, the stratification ratio, and the friction loss in closed and open conduits for heterogeneous and homogeneous mixtures. 

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