Electromechanics of Electrofluidized Beds Thomas W. Johnson and James R. Melcher* Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02739
Air-fluidized beds of electrically semi-insulating particles with imposed electric fields are shown to exhibit dynamics that differ dramatically from the conventional fluidized beds. Photographs, and measurements of pressure drop as a function of flow rate, imposed field, and humidity are presented in a heuristic description of electrofluidized beds of sand with the flow perpendicular to the field. Qualitative descriptions are given of electrofluidized beds with field and flow parallel, and of an electromechanical distributor plate that effectively prevents loss of particles through a %-cm slit orifice.
The generation of electric fields in fluidized beds is documented by Ciborowski and Wlodarski (1962). By using relatively insulating particles, Anderson and Silverman (1958) and Johnstone (1960) have in fact encouraged frictional electrification with the intent of using the associated fields to collect particulate matter. There are three distinctions between such work and the studies presented here. First, here the fields are imposed. Second, the particles are semi-insulating. Thus, the electrical conductivity is sufficiently low that field intensities approaching the breakdown strength of air can be used without drawing an appreciable current, but still high enough that a given particle can exchange its charge during a collision with either an electrode or another particle in a time on the order of the collision time. And third, the mechanical consequences of the forces associated with the field-that is, the effects of the field on the bed dynamics-are studied. In the literature of fluidized beds, imposed fields are used as either a diagnostic tool or to gain an advantage from the heating current that can be created with highly conducting particles (see for example Jones and Wheelock (1970) and Reed and Goldberger (1966)). In either case, the fields are not likely to be intense enough for electromechanical effects to become consequential. At the present time, the greatest practical motivation for understanding electrofluidized bed (EFB) behavior comes from applications to air pollution control, where the bed particles are sites for electrically induced agglomeration with gas-entrained charged particles (see Zahedi and Melcher (1974)). However, there also appear to be promising applications for EFB’s in the control of heat and mass transfer. Of the many configurations for the imposed field relative to the bed, the cross-flow and co-flow configurations shown in Figure 1appear basic. In the following sections, the cross-flow configuration is given the most attention. The objective is to give a heuristic description of the bed electromechanics, especially in the semi-insulating regimes where phenomena are relatively reproducible and subject to enough order that a meaningful description can be given. At the outset, it is important to recognize the key role played by particle conductivity, and the relation of conductivity to air humidity. Then, the regimes of operation of the bed (which are somewhat hysteretic) are sorted out in a parameter space of volume rate of flow Qv, voltage V, and relative humidity w . This is done by describing the bed pressure drop and the visual flow characteristics as functions of these parameters. Finally, experiments are described that show how imposed fields can be used to stabilize the support of a conventional bed against loss of particles through a relatively open distributor plate. 146
Ind. Eng. Chem., Fundam., Vol. 14. No. 3, 1975
Particle Properties Sand particles having an average diameter of 0.5 mm are used. The equivalent electrical resistivity (resistance times area divided by electrode spacing) of the packed sand particles is measured in a conduction cell and the results are shown in Figure 2. The measurements are performed after placing the particles in a desiccator overnight, with saturated solutions of various compounds chosen to control the relative humidity ( w )at the desired levels. Resistance is measured at the relatively high field strengths of interest in the experiments (6 kV/cm) and by means of an electrometer. These alternatives give results more consistent than measurements on different samples. The reproducibility is reflected in the data and is typical of what would be expected in dealing with irregular particles under varying conditions of packing. From the fact that sand is primarily silica, with a bulk resistivity of the order of 1015 ohm-m, it is clear that the conduction is dominated by phenomena at the particle surfaces and is strongly influenced by the relative humidity of the ambient air. This observation is consistent with documented effects of humidity on the surface resistance of quartz glass, as reported by Clark (1962). His data show a variation of surface resistance of 6 decades with an extremely strong dependence on relative humidity near 50% relative humidity while the equivalent resistivities shown in Figure 2 vary by approximately 5 decades. The issues involved in deducing electrical properties from the bulk measurements and in the interactions between particles in the EFB are brought out by a simple model for the conduction and particle-particle contact. A particle is taken as spherical, with radius R, with no bulk conduction except through a finite surface conductivity u s . The surface current density R is proportional to the component of electric field intensity E in the plane of the surface Ks = usEs. Starting from the fact that the steady conduction current on the particle surface is solenoidal, the total current through the particle is i = K92nR sin 9 (1) and it follows that the electric field distribution on the particle surface is i Eg = 2nRus sin 9 and hence, by integration, that the resistance of a single particle is (3)
where a is the radius of a circular cap, a t each pole of a particle, through which current passes to a neighboring
particle. It has been assumed that a / R
