Electrical Mobility Equivalent Diameter

FIGURE 9.15 A micrograph of a single NaCl particle with electrical mobility equivalent diameter of 550 nm. The dry NaCl is almost cubic with rounded edges. Also shown is a polystyrene latex (PSL) particle with diameter of 491 nm (Zelenyuk et al. 2006). 

Electrical mobility analyzers, like the differential mobility analyzer, classify particles according to their electrical mobility Be given by (9.30). The electrical mobility equivalent diameter Dem is defined as the diameter of a panicle of unit density having the same electrical mobility as the given particle. Particles with the same Dem have the same migration velocity in an electric field. Particles with equal Stokes diameters that cany the same electrical charge will have the same electrical mobility. 

Instruments such as the differential mobility analyzer (DMA) (Liu et al. 1979) size particles according to their electrical mobility equivalent diameter. 

Electrical Mobility Equivalent Diameter. The diameter of a particle of unit density having the same electrical mobility as the given particle. It is measured by instruments like the differential mobility analyzer (Liu et al., 1979). 

Up to this point we have considered spherical particles of a known diameter Dp and density pp. Atmospheric particles are sometimes nonspherical and we seldom have information about their density. Also a number of techniques used for atomospheric aerosol size measurement actually measure the particle s terminal velocity or its electrical mobility. In these cases we need to define an equivalent diameter for the nonspherical particles or even for the spherical particles of unknown density or charge. These equivalent diameters are defined as the diameter of a sphere, which, for a given instrument, would yield the same size measurement as the particle under consideration. A series of diameters have been defined and are used for such particles. 

In these correlations, is the void fraction of the soot deposit, the soot particle size, and 2 the mean free path of the fluid. Soot deposits are typically very low in density (50-150 g/1), equivalent to soot void fractions of 92-98 %, and have particles with an electrical mobility diameter in the range of 50-150 nm. As a result, the permeability of the soot layer is in the range of 10 m, more than two orders of magnitudes lower than the permeability of a clean wall. 

Next, let us consider the application of Equation (21) to a particle migrating in an electric field. We recall from Chapter 4 that the layer of liquid immediately adjacent to a particle moves with the same velocity as the surface that is, whatever the relative velocity between the particle and the fluid may be some distance from the surface, it is zero at the surface. What is not clear is the actual distance from the surface at which the relative motion sets in between the immobilized layer and the mobile fluid. This boundary is known as the surface of shear. Although the precise location of the surface of shear is not known, it is presumably within a couple of molecular diameters of the actual particle surface for smooth particles. Ideas about adsorption from solution (e.g., Section 7.7) in general and about the Stern layer (Section 11.8) in particular give a molecular interpretation to the stationary layer and lend plausibility to the statement about its thickness. What is most important here is the realization that the surface of shear occurs well within the double layer, probably at a location roughly equivalent to the Stern surface. Rather than identify the Stern surface as the surface of shear, we define the potential at the surface of shear to be the zeta potential f. It is probably fairly close to the... 

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