Measurement of the Particle Size Distribution

If two filters with decreasing pore sizes in the direction of flow are coupled together, then in between these two filters particles with a particle size smaller then the pore size of the first filter and larger than the pore size of the second filter can be collected. 

If a series of filters with decreasing pore size are collected, then the particle size distribution can be obtained by such a device. If the amount of particles collected in each cascade are plotted against the pore sizes then a histogram is obtained. An example for such a plot is shown in Fig. 20.3. The histogram in this example is equidistant. This means that the pore sizes of the filter decreased linearly here. 

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The particle light scattering coefficient has been continuously measured at this location since 1976. Measurements of the particle size distribution have been made daily since 1978, providing the data base necessary to assess the variability of the normalized aerosol volume distribution. 

Poster, D.L., R.M. Hoff, and J.E. Baker. 1995. Measurement of the particle size distributions of semivolatile organic contaminants in the atmosphere. Environ. Sci. Technol. 29 1990-1997. 

Table 2.12. Measurement of the particle size distribution of a sample of precipitated calcium carbonate by the Andreasen pipette method...

Chapter 19 is dedicated to the measurement of the particle size distribution of polymer powders by a variety of methods. 

To fully assess the properties of suspension concentrates, three main types of measurements are required. Firstly some information is needed on the structure of the solid/solution interface at a molecular level. This requires investigation of the double layer properties (for systems stabilised by ionic surfactants and polyelectrolytes), adsorption of the surfactant or polymer as well as the extension of the layer from the interface (adsorbed layer thickness). Secondly, one needs to obtain information on the state of dispersion on standing, such as its flocculation and crystal growth. This requires measurement of the particle size distribution as a function of time and microscopic investigation of flocculation. The spontaneity of dispersion on dilution, i.e. reversibility of flocculation needs also to be assessed. Finally, information on the bulk properties of the suspension on standing is required, which can be obtained using rheological measurements. The methods that may be applied for suspension concentrates are described briefly below. 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

In principle, the velocities c and ti can be determined by taking a series of pictures at a very high frequency of the flow through a transparent plastic tube. Because of the particle size distribution, each particle moves at a different velocity, and this makes this method difficult to apply in practice. We have therefore used an indirect method, where we have measured the pressure losses of pneumatic conveying for two mixture ratios and then fit the parameters so that Eq, (14.126) coincides as accurately as possible with measured pressure losses. 

The other state variables are the fugacity of dissolved methane in the bulk of the liquid water phase (fb) and the zero, first and second moment of the particle size distribution (p0, Pi, l )- The initial value for the fugacity, fb° is equal to the three phase equilibrium fugacity feq. The initial number of particles, p , or nuclei initially formed was calculated from a mass balance of the amount of gas consumed at the turbidity point. The explanation of the other variables and parameters as well as the initial conditions are described in detail in the reference. The equations are given to illustrate the nature of this parameter estimation problem with five ODEs, one kinetic parameter (K ) and only one measured state variable. 

Despite these potential problems, remarkably little work has been published on particle degradation in pneumatic conveying systems. That may be explained by experimental problems that are even much more serious than with fluidized beds. According to the different problems mentioned above, there are more individual measurement techniques and assessment procedures required than with fluidized bed attrition. Usually, the assessment is restricted to the comparison of the particle size distribution before and after conveying. Moreover, there is no steady-state attrition that could be measured. It is only possible to measure an integrated value, which... 

It has been reported for many years that condensation nuclei can be produced by ionizing radiation. Recent studies have improved the measurement of the activity size distribution of these ultrafine particles produced by radon and its daughters (Reineking, et al., 1985 Knutson, et al., 1985). It seems that the Po-218 ion is formed by the radon decay, is neutralized within a few tens of milliseconds, and then attached to an ultrafine particle formed by the radiolysis generated by the polonium ion recoil. Although there will be radiolysis along the alpha track, those reactions will be very far away (several centimeters) from the polonium nucleus when it reaches thermal velocity. The recoil path radiolysis therefore seems to be the more likely source of the ultrafine particles near enough to the polonium atom to rapidly incorporate it. 

Methods for analysis of the particle size distribution in the aerosol cloud include techniques such as time of flight measurement (TOE), inertial impaction and laser diffraction. Dynamic light scattering (photon correlation spectroscopy) is confined to particles (in suspension) in the submicron range. In addition to the size distribution, the particle velocity distribution can be measured with the Phase Doppler technique. 

To test the applicability of statistical techniques for determination of the species contributions to the scattering coefficient, a one-year study was conducted in 1979 at China Lake, California. Filter samples of aerosol particles smaller than 2 ym aerodynamic diameter were analyzed for total fine mass, major chemical species, and the time average particle absorption coefficient, bg. At the same time and location, bgp was measured with a sensitive nephelometer. A total of 61 samples were analyzed. Multiple regression analysis was applied to the average particle scattering coefficient and mass concentrations for each filter sample to estimate aj and each species contribution to light scattering, bgn-j. Supplementary measurements of the chemical-size distribution were used for theoretical estimates of each b pj as a test of the effectiveness of the statistical approach. 

Distortion of the particle size during the sampling process is a concern in the use of this probe on an aircraft. Compressional heating due to deceleration of the particles may distort the size distribution, because evaporation of water from aerosol particles reduces their diameters. Likewise, particle sizes can be reduced by use of a heater, incorporated into some models of this probe, to prevent icing when supercooled clouds are being flown through. One study (88) indicated that the probe heater removes most of the water from aerosol particles sampled at relative humidities of 95%. Thus, size distributions of aerosol particles measured with the probe heater on correspond to that of the dehydrated aerosol. These results were confirmed by a later study (90) in which size distributions of aerosols measured with a nonintrusive probe were compared to size distributions measured with a de-iced PCASP probe. Measurement of the aerosol size distribution with the probe heater on may be an advantage in certain studies. 

On-line particle sizing by ultrasonic (acoustic attenuation) spectroscopy was developed for use during batch crystallization processes.14 Crystallization of the alpha polymorph of (l) -glutamic acid from aqueous solution was monitored by continuously pumping the crystallizing solution through an on-line ultrasonic spectrometer. The method enabled measurement of the crystal size distribution and solid concentration throughout the... 

All the samples measured showed characteristic superparamagnetic behavior with a blocking temperature TB. An independent method of determining the parameters of the particle size distribution g(D) is by means of the analysis of magnetic measurements under equilibrium conditions, i.e. at temperatures above the superparamagnetic blocking temperature Tb- For this purpose we performed magnetization measurements as a function of field M(H) at different temperatures [4,5]. 

Here, z0 10-10 -10 13s is the inverse attempt frequency that depends on the damping of the magnetic moments by the phonons. The superparamagnetic blocking occurs when r equals the measuring time of each experimental point, te, therefore TB = all / kB ln(/(, / r0 ), where a is a constant that depends on the width of the particle size distribution. 

The overall conclusion from the analysis of equation 18 over the complete domain of a is that, in principle, information about the shape of the particle size distribution can be obtained directly from turbidity, or in general, from scattering measurements. However, the discriminating power of the measurements in terms of the particle size distribution depends upon the wavelength range selected for the analysis. The major difficulty in the interpretation of the data arises from the behavior of the extinction itself as function of the size parameter which causes the measurements "see" a different average at every wavelength. 

In the small particle size regime, two equivalent formulations lead to the interpretation of the data in terms of ratios of moments of the particle size distribution or in terms of powers of the D32 average (equations 15 and 20). It is clear that in either case a sufficient number of terms in the series has to be included in order to account for the behavior of the extinction as function of a. The number of terms required cannot be decided a priori, rather the data itself has to dictate how many terms in the power series approximation the measurements can detect. 

Therefore, in principle, the parameters of the particle size distribution can be estimated from specific turbidity measurements at different wavelengths. This is not true, however, in the Rayleigh regime (i.e. small particles, (D/Am) less than 0.1). In this case, the extinction coefficient is proportional to (D/Am)4 and... 

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