Collectors surface

The high resistivity of Inconel 600 (11 OjtI 0 8 Dm) demanded the application of this material as a composite with a central aluminum core. The aluminum was totally enclosed in Inconel 600 so that the Inconel was only exposed to sulfur and polysulfides. In a test over more than three years, cells with a composite current collector of this kind suffered from a high capacity decline. Post-test analysis showed that Inconel sustained polysulfide attack with the formation of a duplex nickel and chromium sulfide layer on the current collector surface. 

The Smoluchowski-Levich approach discounts the effect of the hydrodynamic interactions and the London-van der Waals forces. This was done under the pretense that the increase in hydrodynamic drag when a particle approaches a surface, is exactly balanced by the attractive dispersion forces. Smoluchowski also assumed that particles are irreversibly captured when they approach the collector sufficiently close (the primary minimum distance 5m). This assumption leads to the perfect sink boundary condition at the collector surface i.e. cp 0 at h Sm. In the perfect sink model, the surface immobilizing reaction is assumed infinitely fast, and the primary minimum potential well is infinitely deep. 

Besides the resuspension of particles, the perfect sink model also neglects the effect of deposited particles on incoming particles. To overcome these limitations, recent models [72, 97-99] assume that particles accumulate within a thin adsorption layer adjacent to the collector surface, and replace the perfect sink conditions with the boundary condition that particles cannot penetrate the collector. General continuity equations are formulated both for the mobile phase and for the immobilized particles in which the immobilization reaction term is decomposed in an accumulation and a removal term, respectively. Through such equations, one can keep track of the particles which arrive at the primary minimum distance and account for their normal and tangential motion. These equations were solved both approximately, and by numerical integration of the governing non-stationary transport equations. 

Thus far, these models cannot really be used, because no theory is able to yield the reaction rate in terms of physically measurable quantities. Because of this, the reaction term currently accounts for all interactions and effects that are not explicitly known. These more recent theories should therefore be viewed as an attempt to give understand the phenomena rather than predict or simulate it. However, it is evident from these studies that more physical information is needed before these models can realistically simulate the complete range of complicated behavior exhibited by real deposition systems. For instance, not only the average value of the zeta-potential of the interacting surfaces will have to be measured but also the distribution of the zeta-potential around the mean value. Particles approaching the collector surface or already on it, also interact specifically or hydrodynamically with the particles flowing in their vicinity [100, 101], In this case a many-body problem arises, whose numerical... 

Specialty Chromium-Plating Baths. Chromic acid baths using sodium chromate and sodium hydroxide to form a tetrachromate (92) have had limited use. Porous chromium is used in lubricated wear applications, and is made by chemically etching regular chromium plate, sometimes with light grinding after the etch. Black chromium is used on solar collector surfaces (see PHOTOVOLTAIC CELLS Solarenergy). Baths are sulfate-free, and include fluosilicic acid or acetic acid (91). 

Figure 10.4 The correlation among collector surface coverage, contact angle, zeta potential, and flotation recovery for the flotation of quartz using dodecylammonium acetate. From Leja [91]. Copyright 1982, Plenum Press.

The superposition of electrostatic forces on particle behavior near a filter mat can have appreciable influence on filtration efficiency. The deposition patterns can take on significant treeing or branching of agglomerates on individual fibers. This aerodynamically distorts the cylindrical collector surface and branches the surface area, as well as distorting the electrical field around the collector. 

Ideally, electrical precipitators generally achieve collection efficiencies of more than 99% for a full range of particle size. The efficiency depends on the ratio of the collector surface area particle size and dielectric properties and the volumetric gas flow rate times the charged particle migration speed induced by the applied electrical field. 

In general, this low conductivity weakness is circumvented by coating a thin active carbon layer on an aluminum current collector which provides a much better conductivity by minimizing the charge path length in the carbon. The electrode performance is sensitive to the adhesion of the carbon layer in contact with the current collector surface [21], It is important to ensure a good quality of this contact over time, even in presence of a solvent at elevated temperature, in order to maintain a low series resistance of the device. 

The rale of collection of Brownian particles under the influence of interaction forces between the collector surface and the particles is calculated by (a) incorporating the interaction forces in the rate constant of a virtual, first order, chemical reaction taking place on the surface of the collector, and by (b) solving the convective diffusion equation subject to that chemical reaction as a boundary condition. Several geometries (sphere, cylinder, rotating disc) are considered for the collector. 

Consider a thin region, in contact with the collector surface, within which convection and tangential diffusion are negligible. Then the radial flux, is inde-... 

When the particles adhere to the collector surface they are no longer a part of the dispersed phase. Consequently, eqn (8) can be solved using the boundary condition... 

The distance from the collector surface over which each mechanism or effect exerts an influence was found to be a useful characteristic parameter. Table 1 lists the five lengths used to identify each of the limiting cases summarized by Table 2. Three principal limiting cases were considered (1) situations where London forces are ncgli-... 

Because colloidal particles have finite size, their mobility and diffusion coefficients depend not only upon their size but also upon, the distance from the collector surface. This variation with distance stems from friction between the collector surface and the fluid which increases the force required to push the fluid out of the path of the approaching particle. In the usual transport equation containing only convective and diffusive terms, the size of the molecules is small enough for the thickness in to be small compared to the length du, where fim and Bp are explained in Table 1. Other situations arise In which these conditions are not met, or in which London or gravitational forces are important To identify the limiting cases, it is useful to seek some quantity for each mechanism which allows the ordering of its relative importance. 

Fig. 1. Profile of the total energy of interaction between a colloidal particle and the collector surface arising from the double-layer repulsion and London attraction.

For large Peelet numbers and small Hamaker s constants, appreciable concentration variation occurs only very near to the collector. Then Stokes s expressions for the fluid velocity may be expanded in a Taylor series about the collector surface and higher order terms together with curvature effects may be neglected, yielding... 

Figure 7 shows the effect of proximity to the isoelectric pH upon the deposition rate. Particle and collector surfaces are identical in composition, both having equal numbers of acidic and basic groups (iVa = rYb). When widely separated, both surfaces were chosen to have a potential of —20 mV for all cases. This implies pH = 6.658 if pH, = 7. Next, p b was set at 10 for all cases and pNa was selected with the help of Eq. [10] so that pH — pH,-so has the value indicated on each curve. Finally, the number of acidic and basic groups was chosen to give the desired surface potential of —20 mV when the surfaces do not interact. 

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