Particle diffusion charging

Fig. 12. Comparison of actual and predicted charging rates for 0.3-pm particles in a corona field of 2.65 kV/cm (141). The finite approximation theory (173) which gives the closest approach to experimental data takes into account both field charging and diffusion charging mechanisms. The curve labeled White (141) predicts charging rate based only on field charging and that marked Arendt and Kallmann (174) shows charging rate based only on diffusion.

The potential difference across the mobile part of the diffuse-charge layer is frequently called the zeta potential, = E(0) — E(oo). Its value depends on the composition of the electrolytic solution as well as on the nature of the particle-hquid interface. 

For many particles, the diffuse-charge layer can be characterized adequately by the value of the zeta potential. For a spherical particle of radius / o which is large compared with the thickness of the diffuse-charge layer, an electric field uniform at a distance from the particle will produce a tangential electric field which varies with position on the particle. Laplace s equation [Eq. (22-22)] governs the distribution... 

Cross-flow-elec trofiltratiou (CF-EF) is the multifunctional separation process which combines the electrophoretic migration present in elec trofiltration with the particle diffusion and radial-migration forces present in cross-flow filtration (CFF) (microfiltration includes cross-flow filtration as one mode of operation in Membrane Separation Processes which appears later in this section) in order to reduce further the formation of filter cake. Cross-flow-electrofiltratiou can even eliminate the formation of filter cake entirely. This process should find application in the filtration of suspensions when there are charged particles as well as a relatively low conduc tivity in the continuous phase. Low conductivity in the continuous phase is necessary in order to minimize the amount of elec trical power necessaiy to sustain the elec tric field. Low-ionic-strength aqueous media and nonaqueous suspending media fulfill this requirement. 

Other Considerations In general, dry ESPs operate most efficiently with dust resistivities between 5x10 and 2 x lO ohm-cm. In general, the most diffieult particles to collect are those with aerodynamie diameters between 0.1 and 1.0 / m. Particles between 0.2 and 0.4 m usually show the most penetration. This is most likely a result of the transition region between field and diffusion charging. 

The traditional unipolar diffusion charging model is based on the kinetic theory of gases i.e., ions are assumed to behave as an ideal gas, the properties of which can described by the kinetic gas theory. According to this theory, the particle-charging rate is a function of the square of the particle size dp, particle charge numbers and mean thermal velocity of tons c,. The relationship between particle charge and time according White s... 

The most straightforward approach is to assume that the field charging and diffusion charging are independent processes i.e., particle charge can be presented as a sum of charges due to field (s ) and diffusion (sj) charging. Another simple approach to estimating the combined effect is... 

According to this approximation, the drift velocity is proportional to the square of the electric field. This is a clear indication of the importance of the electric field inside an electrostatic precipitator. Equation (13.60) is a valid approximation for large particles [dp > 0.5 m), provided that particle charge is close to the saturation level. In the case of small particles, the effect of diffusion charging must be taken into account. 

Pui, D. Y. H. Experimental Study of Diffusion Charging of Aerosols. Thesis, Particle Technology Laboratory, Mechanical Engineering Department, University of Minnesota (1976). 

Overbeek and Booth [284] have extended the Henry model to include the effects of double-layer distortion by the relaxation effect. Since the double-layer charge is opposite to the particle charge, the fluid in the layer tends to move in the direction opposite to the particle. This distorts the symmetry of the flow and concentration profiles around the particle. Diffusion and electrical conductance tend to restore this symmetry however, it takes time for this to occur. This is known as the relaxation effect. The relaxation effect is not significant for zeta-potentials of less than 25 mV i.e., the Overbeek and Booth equations reduce to the Henry equation for zeta-potentials less than 25 mV [284]. For an electrophoretic mobility of approximately 10 X 10 " cm A -sec, the corresponding zeta potential is 20 mV at 25°C. Mobilities of up to 20 X 10 " cmW-s, i.e., zeta-potentials of 40 mV, are not uncommon for proteins at temperatures of 20-30°C, and thus relaxation may be important for some proteins. 

Molecular-level studies of mechanisms of proton and water transport in PEMs require quantum mechanical calculations these mechanisms determine the conductance of water-filled nanosized pathways in PEMs. Also at molecular to nanoscopic scale, elementary steps of molecular adsorption, surface diffusion, charge transfer, recombination, and desorption proceed on the surfaces of nanoscale catalyst particles these fundamental processes control the electrocatalytic activity of the accessible catalyst surface. Studies of stable conformations of supported nanoparticles as well as of the processes on their surface require density functional theory (DFT) calculations, molecular... 

The possibilities afforded by SAM-controlled electrochemical metal deposition were already demonstrated some time ago by Sondag-Huethorst et al. [36] who used patterned SAMs as templates to deposit metal structures with line widths below 100 nm. While this initial work illustrated the potential of SAM-controlled deposition on the nanometer scale further activities towards technological exploitation have been surprisingly moderate and mostly concerned with basic studies on metal deposition on uniform, alkane thiol-based SAMs [37-40] that have been extended in more recent years to aromatic thiols [41-43]. A major reason for the slow development of this area is that electrochemical metal deposition with, in principle, the advantage of better control via the electrochemical potential compared to none-lectrochemical methods such as electroless metal deposition or evaporation, is quite critical in conjunction with SAMs. Relying on their ability to act as barriers for charge transfer and particle diffusion, the minimization of defects in and control of the structural quality of SAMs are key to their performance and set the limits for their nanotechnological applications. 

Early work by Boyd et al. (1947), performed on zeohtes, showed that the ion exchange process is diffusion controlled and the reaction rate is limited by mass transfer phenomena that are either film-diffusion (ED) or particle-diffusion (PD) dependent. Under natural conditions, the charge compensation cations are held on a representative subsurface solid phase as follows within crystals in interlayer... 

The diffusion process in general may be viewed as the model for specific well-defined transport problems. In particle diffusion, one is concerned with the transport of particles through systems of particles in a direction perpendicular to surfaces of constant concentration in a viscous fluid flow, with the transport of momentum by particles in a direction perpendicular to the flow and in electrical conductivity, with the transport of charges by particles in a direction perpendicular to equal-potential surfaces. 

When the particles are charged, the strong inter-ion forces modify the diffusion. The (Coulombic) force on ion i is then [48]... 

This is the expression we were looking for. What does it tell us For one thing, that the potential decays exponentially as the distance from the electrode increases pig. 6.64(b)], Further, as the solution concentration c0 increases, k increases and falls more and more sharply. This potential-distance relation [Fig. 6.64(b)] is an important and simple result from the Gouy-Chapman model. It forms a valuable basis for thinking about the interaction of the diffuse charges around what are called colloidal particles (see Section 6.10.2). 

Fig. 6.140. The variation of the numerical factor fwith the ratio of the radius a of the particle to the effective thickness k-1 of the diffuse-charge region.

The quantity /is a numerical factor that depends on the ratio a/K, where a is the radius of the spherical or cylindrical particle. In other words, / depends on the ratio of the radius of the particle to the effective thickness K 1 of the diffuse layer. When alKX is large, (the particle large in comparison with the diffuse-charge thickness), the numerical factor is always equal to irrespective of the shape of the particle. When the particle is small compared with the thickness of the double layer,/is i for cylindrical particles parallel to the field and for spherical particles (Fig. 6.140). 

Attention has so far been focused on reaction between spherical particles diffusing in a hydrodynamic continuum with no forces acting between reactants. In this chapter, the most important force, the coulomb interaction, between ions in solution is included. The potential energy, [/(rj — r2),of ions at r (= y l5 zx) and r2 having charges z,e and z2e is... 

The diffusion charging of particles in the presence of an external electric field is available in Murphy (1956) and Liu and Yeh (1968). 

---