Yang Fluidization, Solids Handling, and Processing
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Eq. (3) |
qMaxwell = π3κεoD2E/6 |
This induction mechanism plays the central role of particle charging in electrosuspensions, that is, beds of highly conductive particles subjected to an externally applied DC electric field (Colver, 1977). Induction also will occur if isolated conductive objects (such as tramp metal debris or hand tools) in a bed of triboelectrically charged, insulating, granular solids make momentary wall contact. The breakdown-imposed limit on particle charge, that is, Eq. (2), is as applicable for induction charging as it is for triboelectrification. It should also be recognized that an externally imposed electric field can influence particle charging via electrolysis and other mechanisms, even when the particle conductivity is too low to support conventional conduction (Loeb, 1963).
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conducting wall
Figure 2. Charging of a conducting particle with diameter D making contact with a conducting wall in the presence of an electric field E.
2.4Electrostatic Fields and Potentials
Some Basics. The field theory of electrostatics expresses experimentally observable action-at-a-distance phenomena between electrical charges in terms of the vector electric field E (r, t) , which is a function of position r and time t. Accordingly, the electric field is often interpreted as force per unit charge. Thus, the force exerted on a test charge qt by this electric field is qt E . The electric field due to a point charge q in a dielectric medium placed at the origin r = 0 of a spherical coordinate system is
826 Fluidization, Solids Handling, and Processing
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Eq. (4) |
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where r = |
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is the unit radial vector. Equation (4) is clearly |
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consistent with Coulomb’s inverse square law. The electrostatic potential function F(r , t ) , a scalar, is related to the electric field: E = -ÑF . For the point charge
Eq. (5) |
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To determine the electrostatic field and potential in a vessel containing charged solids, we must sum the contributions from all the electric charges within the vessel. This is done by invoking the reasonable approximation that the charge may be represented as a continuous distribution and then by performing an appropriate integration over the volume of the charge. Gauss’s law expressed in integral form is
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Eq. (6) |
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where S is the closed surface of integration enclosing the volume V, κ is the dielectric constant of the charged medium, and ρ(r ) is a continuous distribution of electric charge per unit volume.
The convenience of Eq. (6) is realizable only in the rather unrealistic situation where the charge distribution exhibits cylindrical or spherical symmetry. For storage silos, blenders, fluidized bed reactors, and other real vessel geometries, integral solutions are usually not possible, necessitating an alternate problem formulation. Poisson’s equation serves this need, relating the volume charge distribution to the electrostatic potential.
Eq. (7) |
Ñ2F = -ρ /κε 0 |
To compute electrostatic potential and field distributions in very complex geometries, this equation, or one of its subsidiaries, can be solved numerically subject to a set of boundary conditions (McAllister et al.,
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An Example. Rough estimates for the electric field strength and maximum space potential in a fluidized bed can be obtained from a very simple model, namely, a very long cylinder entirely filled with uniformly charged powder. This model ignores the bed surface, placing the resulting estimate for the potential on the high side, but well within the accuracy requirements of an order-of-magnitude calculation. Assume the grounded cylinder is of diameter Dc and contains a charged powder having dielectric constant κ and uniform volume charge density ρ0. Using Eq. (6) and cylindrical symmetry, the vector electric field and scalar electrostatic potential are:
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Eq. (8) |
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Here, rc is the radial distance from the axis and rˆc is the radial unit vector in cylindrical coordinates. These equations correctly predict the maximum field strength to exist at the wall, that is, rc = Dc /2, and the maximum potential to be on the axis at rc = 0. We may use them to estimate the electric field and potential values in a fluidized bed by selecting typical values for the bed parameters:
q/m = 0.01 µC/kg (rather modest triboelectric charging value for polymers)
ε = 50% (nominal value for void fraction in fluidized bed)
ρm = 2000 kg/m3 (mass density of solid material)
κ = 2 (typical dielectric constant for insulating solid in fluidized state)
Dc = 2 m (typical fluidized bed diameter)
Using these values in Eq. (8), the electric field at the wall is estimated at 280 kV/m, which is very close to Eb = 300 kV/m, the breakdown strength of air. The maximum electrostatic potential, measured at the center of the cylindrical vessel, is calculated to be 560 kV. Such high values for electrostatic field and potential guarantee some sort of electrostatic discharge in a vessel. What, in fact, takes place is that a corona discharge (or some other electrical discharge) occurs, probably as the charged material is added. The lesson to be learned from the above calculation is that, even for relatively modest powder charge levels in vessels of moderate size, the
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resulting electric field and potential are sufficiently high to produce electrostatic activity when insulating materials are bulked, transported, or fluidized.
Discussion. The triboelectric charging of particulate solids is largely unavoidable during handling. When the electrical conductivity of the material is low, the particles can retain this charge for a long time. The longevity of this charge can be attested to by many processing plant operators and workers, who have experienced powerful electrostatic shocks while attempting to gather samples of polymer granules from grounded tote bins and barrels that have been sitting in place for extended periods. When sufficiently large amounts of charged particles accumulate in a vessel or container, the nuisance value of electrostatic charge transforms into a true hazard. Sparks generated by electric charge from tribocharged powder can ignite suspended dust (or, even more readily, flammable vapors or gases) causing serious fires and explosions. Electrostatic phenomena in fluidized beds are the subject of the next section of this chapter.
3.0FLUIDIZED BED ELECTRIFICATION
Because of the unavoidable tendency of granular solids to become triboelectrically charged when handled, it is no surprise that electrostatic phenomena are often quite pronounced in fluidized and spouted beds. The vigorous motion of fluidized particles—with constant particle-particle and particle-wall contacts—guarantees that electrical charging will take place. Electrostatic adhesion and cohesion, observed and recorded in the very earliest experimental investigations of fluidization, were immediately identified as experimental nuisances to be overcome. Somewhat later, the hazardous nature of electrostatics came to be appreciated.
3.1Background
Early Investigations. In the late 1940’s and early 50’s, research interest in fluidization as a new technological process surged. Almost from the start, experimentalists reported strong electrostatic effects (Wilhelm and Kwauk, 1948; Leva, 1951; Miller and Logwinuk, 1951; Osberg and Charlesworth, 1951). What these and other investigators observed in common included charge-related adhesion of particles to vessel walls and to the glass windows of observation ports and, much more importantly, an
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apparent influence of electrostatics on the conditions for minimum fluidization. These effects in their various manifestations were discovered to depend strongly on humidity. Because of the erratic behavior and significant experimental irreproducibility, some workers simply chose to avoid materials found to exhibit strong electrostatic effects while others sought to minimize charging by using humidified air. In these early experiments, it became well established that electrostatics was a nuisance in fluidized bed systems that could not be ignored. At this time, however, safety concerns were not prominently mentioned.
With the better understanding of fluidization achieved during the 1950’s came an improved appreciation for the important role played by electrostatics. Katz tested a fluidized bed consisting of two different size cuts of glass beads and observed an elevation-specific size segregation effect, which was exacerbated by static electrification (Katz, 1957). When humidified air was used at a sufficient level to reduce electrostatics, no practical benefit was obtained because high moisture content simply replaced electrostatic with capillary forces. Work that followed established the link between electrostatic interparticle forces and fluidization conditions and, furthermore, demonstrated the importance of particle size in controlling triboelectric charging (Davies and Robinson, 1960).
The first systematic investigation to focus on electrostatic phenomena in fluidized beds was published by Ciborowski and Wlodarski (1962). They monitored electrostatic activity in air-fluidized beds of sand and various polymers by lowering a spherical electrode into the bed and then measuring the static voltage it attained when connected to a high-impedance voltmeter. By varying the position of the electrode, they mapped the distribution of the potential within the bed, finding maximum values just under the surface of the bed exceeding 15 kV. They verified the strong dependence of electrostatic effects on the relative humidity and also noticed that particle charging disrupted good fluidization by promoting the formation of flow channels. Finally, they pointed out the possibility that electrostatic forces might be exploited in new applications for fluidization. Another investigation using a suspended ball electrode to measure electrostatic activity in polymer resins, hydroquinone, and ammonium sulfate provided direct verification that charge accumulation is related to particle resistivity (Kisel’nikov et al., 1967).
Boland and Geldart reported experiments with glass ballotini in a specially designed two-dimensional bed (Boland and Geldart, 1971). To
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avoid the influence of suspended or protruding electrodes on fluidization, they used an electrostatic probe mounted flush with the wall. The principal objective of their investigation was to investigate the effectiveness of various measures, including humidification, particle surface treatments, and air ionization in suppressing triboactivity. They found that relative humidities in the 60 to 70% range, while not actually reducing the charging, do increase the surface conductivity so that the charge dissipates more rapidly. They also obtained evidence that bubbling might be an important charge separation mechanism in fluidized beds.
Summary and Critique. All these early studies share in common the quantification of fluidized bed electrostatics in terms of voltages or electric fields measured inside a vessel. Such measurements, with suspended electrodes or wall-mounted probes, are only an indirect indication of particle charging. Though the electrostatic distribution of charge within a bed is geometrically related to the electrostatic potential and the field (see Sec. 2.4), inference of the first from measurement of the second or third is quite difficult in the case of highly insulating granular materials. The value of measuring voltage with suspended electrodes must be questioned on several grounds. First, the probe disturbs the flow, changing the very nature of the solids circulation. Second, particle collisions with the probe introduce a triboelectrification mechanism not present in the undisturbed bed. Third, the connection cable to the probe seriously distorts the electrostatic potential within the bed (Fujino et al., 1985). Because of the problems with suspended probes, the knowledge gained about particle charging in early experiments was largely qualitative. The controlling factors in triboelectrification remained imperfectly understood, the distribution of charge within a bed was not known, and the absolute charge levels attained by the granular solids were unmeasured. The motivation of the research performed on the phenomenon was only to minimize a known experimental nuisance.
Wall-mounted probes, which measure field rather than electrostatic potential, may seem a better choice than suspended probes, but they suffer from the serious problem that charged fines often adhere tenaciously to the sensing electrodes and other surfaces of probes. These charged particles will shield the sensing electrode from the field within the bed and interfere with the measurements. Probably for this reason, very few attempts to use wall-mounted probes are found in the literature.
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3.2More Recent Work
About twenty years ago, intriguing new applications for fluidization in air pollution control—including fluidized bed coal combustion and scrubber technologies—were proposed and investigated. These new concepts were intended to exploit the strong coulombic forces of attraction between fluidized bed particles and submicron particulate pollution. As a result, the direct measurement of particle charge began to take on importance (Tardos and Pfeffer, 1980). While the motivation at the time for such measurements might have been an interest in enhancing the performance of fluidized bed air cleaning systems, the data are just as valuable for the assessment of ESD-induced fire and explosion hazards in fluidized beds (Cross, 1987; Glor, 1988; Jones and King, 1991). Ordinarily, the charging of granular materials and powders is quantified by means of the specific charge q/m, that is, charge per unit mass. Representative specific charge data for fluidized bed particle charging are summarized in Table 4 and some key experiments are briefly reviewed below.
Direct Measurement of Particle Charge. In one experiment, small samples of 2 mm diameter porcelain granules were drawn from the middle of an air-fluidized bed into a Faraday cage to perform charge and mass measurement (Tardos and Pfeffer, 1980). The specific charge values ranged from ~0.01 to ~0.1 μC/kg. Fujino and his colleagues fluidized glass beads and certain polymers including PMMA granules, reporting values from ~0.1 to ~1.0 μC/kg (Fujino et al., 1985). Very recently, similar values were obtained using glass particles in size cuts from 5–40 up to 70–100 μm (Tucholski and Colver, 1993).
Some investigators have reported significantly higher specific charge values than those reviewed above and it remains quite unclear whether such results can be attributed to differences in the particulate media, to the means used to withdraw particles from the bed, or to the different locations from which particles were collected. For example, in one experiment individual glass beads withdrawn from the freeboard region of a fluidized bed of glass beads were found to have a specific charge in excess of 100 μC/kg (Fasso et al., 1982). In this investigation, it was found that the absolute charge per particle varies approximately as the 1.4 power of the diameter, that is, q D1.4. In a second test, ~1000 μm polystyrene particles, withdrawn by a vacuum sample collector and deposited in a Faraday cage, were found to have a charge of ~40 μC/kg (Wolny and Opalinski, 1983). Still another experiment, employing a pneumatic gun to eject individual particles from a
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electrodes were measured with an electrostatic voltmeter having very high impedance. By using different electrode geometries, bed diameters, and grounded electrode placements, information about scaling laws for electrification was revealed. Unfortunately, no specific charge data were reported.
Summary of Available Data. Table 4 summarizes the results of the specific charge measurement experiments reviewed above. It is interesting to compare these data to the process-based classification scheme of Table 2. In general, one would not expect fluidization to create the high specific charge levels encountered with pneumatic transport. In pneumatic transport, high speed particle-wall contacts dominate inside the pipe, while in a fluidized bed, lower-speed particle-particle contacts are overwhelmingly favored. At the same time, fluidization might be expected to charge particles more strongly than pouring or sieving. Based on these arguments, one might then estimate that in a vigorously fluidized bed
Eq. (9) |
0.01 μC/kg > q/m > 1.0 μC/kg |
In general, the data of Table 4 tend to confirm this estimated range; however, the upper limit of 1.0 μC/kg is considerably exceeded in the case of data obtained with individual particles of tribo-active, insulating polymers. Whether or not significant volume separation of positive and negative charges occurs with these polymers is not known. Thus, the validity of the upper limit in Eq. (9) is difficult to judge.
For fluidized beds consisting of two or more particulate constituents (for example, distinct size cuts or different materials), charge separation is virtually inevitable. An example of bipolar charging is provided by crushed coal which, in the narrow size range from 63 to 75 μm, exhibits a bipolar charge distribution ranging from about -30 to +30 μC/kg with the average charge near zero (Harris, 1973). These values depend strongly on sulfur content. The likely reason for this strong bipolar charging is the heterogeneous nature of coal; when crushed, individual particles vary considerably in their mineral makeup. It should be pointed out that particle-particle triboelectrification does not create significant net volume charge ρ unless the various particle populations segregate within the bed. As shown in Sec. 2.4, only charge segregation can create strong electrostatic fields and the associated high electrostatic potentials. If strong particle-wall triboelectrification occurs in a bed of homogeneous particles, then segregation is much more likely.