Total number concentration

Because the total number concentration [A totai] is the sum of [N] + [A capped], we can combine this relationship with the equilibrium equation to obtain ... 

Commonly the size description is given as the number, dN, (or, less frequently, mass, dM) of particles per radius interval as a function of radius (Seinfeld and Pandis, 1998, p. 408 fif.). Alternatively, the size description is given as the number, dN, (or, less frequently, mass, dM) per logarithmic interval of radius as a function of radius. The total number concentration or total mass concentration of aerosol particles is the integral over the size... 

For a plot of dS/d( og dp) versus log dp that is similar to Figure 14.3c, the integrated area under the resulting curve from d to d2 would represent the total concentration of surface area in a suspension provided by particles in the size interval from di to 2- A plot of dN/d( og dp) versus log dp would provide similar information about the total number concentration. 

A scanning mobility particle sizer (SMPS) was applied to analyze nanoparticles [2][4]. Size distributions and total number concentrations (TNC) of particles in the range from 0.01-0.7 pm are determined by analysis of particle mobility. An impactor with a cut-off size of 1 pm is used to withdraw the coarse particle fraction. Exhaust gas is taken with a probe, which is also fed with particle free air. The resulting dilution factor is adjusted by the flow rate of the diluting air and the total flow. To prevent condensation of water onto the particle surface, the dilution factor is chosen high enough, to achieve a dew point below ambient temperature. The analytical set-up is shown in Figure I. 

The characteristic data of particles are given by the mode diameter (MD) as the most frequent size of a particle population, the geometric mean diameter (OMD) of the particles and the total number concentration (TNC) as the total amount of particles over the whole measured range. The TNC is based on the flue gas volume at a standard oxygen content of 13%. 

The particle distribution graphs are done as commonly used in aerosol measurement the channel width, which represents particle diameter (dp) range, is plotted on a logarithmic scale against the total number concentration (TNC), that is calculated from the measured number of particles (dN) divided by the logarithm of the channel width (d og(dp)), where dp is the mobility diameter. 

With higher excess air ratios there is a slight decrease in size but an increasing total number concentration. The increase of particle concentration was more distinct towards enhanced surplus air. 

The combustion chamber of the moving grate boiler system was run over a wide range ofbum rates, starting from 150 kW up to 600 kW. The analysis of particle emissions such as particle diameter or total number concentrations (TNC) showed only little variations with the process parameters (Fig. 3). Similar to the 70 kW burner system, all test runs resulted in mode diameters most frequent size diameter) of 100 nm. The geometric mean diameter (GMD) has been analysed in the range of 90.45 nm up to 95.0 nm. The total number concentration (TNC) was between 2.8IE-i-7 and 5.12E-I-7, depending on excess air supply. 

Table 2 Comparison of total number concentration, surface and total sus-... 

Figure 1. Number (AN/Alog D), surface area (AS/Alog D), and volume (AV/Alog D) distributions for a typical urban aerosol. The solid lines are the size distributions, while the dashed hnes show the tails between intersecting modes. The total number concentration, surface area, and volume equal the areas under the curves of each mode. From Finlayson-Pitts and Pitts (2000). Used by permission of Academic Press.

Monomer molecular weight (kg/mol) Average number of radicals per particle Surfactant agglomeration number Number of moles of monomer Total number concentration of particles (1/L)... 

TOTAL NUMBER CONCENTRATION CONDENSATION PARTICLE COUNTER... 

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. 

Figure 7.2 The variations in N o. nj, ni vith time for an initially monodisperse aerosol. The total number concentration, Woe. and the concentration of n j both decrease monotonically with increasing time. The concentrations of nj... pass through a maximum. (After Smoluchowski, 1917)...

The change in the total number concentration with time is found by integrating over all collisions ... 

Equation (7.76) is of the same form as (7.21) for the decay of the total number concentration in a monodisperse system. However, the constant has a somewhat different value. Substituting (7.75) in (7,73) and consolidating terms, the result is... 

The dynamics of the total number concentration, and volume fraction of aerosol material. 0, are momenrs of special interest. There is a problem in defining the total number concentration, N, in all experimentally meaningful way. This parameter is usually measured with a condensation particle counter (CPC) (Chapter 6). The CPC detects particles larger than some minimum size that depend.s to some extent on their chemical nature and shape. Let v,i be the minimum detectable particle volume. Then... 

The dynamic equation for the total number concentration Ls obtained by Integrating the GDE with respect to v over all values of w > vj ... 

A monodisperse aerosol enters a CSTR in which growth occurs only by diffusion. Show by integration of (11.78) that the total number concentration is conserved. 

At fixed volume fraction oip, reducing increases the collision rate because the total number concentration of particles N increases significantly. 

It is straightforward that the quantity ( )d represents the number density of disperse entities contained in the phase-space volume d centered at per unit of physical volume. If we integrate the NDF over all possible values of the internal-coordinate vector we obtain the total number concentration N(t, x) ... 

A special case of considerable interest occurs when the internal-coordinate vector is the particle-velocity vector, which we will denote by the phase-space variable v. In fact, particle velocity is a special internal coordinate since it is related to particle position (i.e. external coordinates) through Newton s law, and therefore a special treatment is necessary. We will come back to this aspect later, but for the time being let us imagine that otherwise identical particles are moving with velocities that may be different from particle to particle (and different from the surrounding fluid velocity). It is therefore possible to define a velocity-based NDF nv(t, x, v) that is parameterized by the velocity components V = (vi, V2, V3). In order to obtain the total number concentration (i.e. number of particles per unit volume) it is sufficient to integrate over all possible values of particle velocity Oy ... 

The zeroth moment Wl.o is equivalent to the total number concentration N and its transport equation follows fromEq. (2.18) ... 

As it is possible to see, the drift term has disappeared since the continuous growth of particle size does not change the total number concentration (if Gl > 0). However, N is influenced by the rate of formation of particles (e.g. nucleation), and the rates of aggregation and breakage, which cause appearance and disappearance of particles. These processes are all contained in the source term /tL.o The third-order moment mL,3 is related to the fraction of volume occupied by particles with respect to the suspending fluid and can be easily found fromEq. (2.18) ... 

The very same approach as described above for the PBE can be applied to the GPBE (Eq. (2.16) on page 37). On applying the moment transform to Eq. (2.16) for the zeroth-order moment, the transport equation for the total number concentration is obtained ... 

Here n(dp) is a particle size distribution function, dN is the number concentration of particles in the size range from dp to [ dp to d(dp)], and A is a coefficient related to the total number concentration of particles. The exponent / describes the particle size distribution a value of 4 is assumed here. 

The quantity of sea salt particles, identified as NaCl, was found to be particularly important over the Indian Ocean. This is explained by stormy weather conditions during the sampling period. Curve 1 in Fig. 35 gives the size distribution of sea salt particles measured over the Indian Ocean (the total number concentration, N, is also plotted). T o represent the ad vection of sea salt particles over the continents, two other spectra are also shown. Curve 2 was measured by Metnieks (1958) in Ireland while distribution 3 was observed in the surface air in Hungary (E. Meszaros, 1964). These latter investigators used gelatin layers sensitized with silver nitrate to identify chloride particles. Figure 35 makes clear that the sea salt concentration is very small... 

The total number concentration of air as a function of altitude falls off approximately with the scale height H of atmospheric pressure ... 

Predicting the nucleation rate of H2S04-H20 on the basis of the theory presented above is somewhat involved appropriate thermodynamic data need to be assembled, including the equilibrium constants for H2S04 hydration. Figures 11.11 a—d show predicted nucleation rates (cm 3s 1) as a function of /Vh2so4, the total number concentration of... 

The lower and upper limits of the integral become 0 and oo, respectively. The resulting integral is identical at all times in form with the integral of the original lognormal distribution, which we know is equal to the total number concentration. 

In order to solve (13.72) we also need to know N(t). We have seen that the total number concentration N(t) for any aerosol distribution assuming constant coagulation coefficient is given by (13.66). Substituting this expression for N(t) into (13.72), we find that the continuous coagulation equation becomes... 

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