Fluidized beds particle forces

The temporal change of the molar quantity of the element sulfur in the film on a fluidized-bed particle is caused by inflow and outflow of the material. This mass balance is needed only once, since the fluidized-bed particles and, thus, the liquid films on the particles are regarded as ideally mixed. The condition of the ideal mixing leads to the fact that with the mass and energy balance of the film, the average variables of state of the gas in the respective driving force approximations find the following form... 

As a result of the mechanical action of mixing tools in high intensity mixers (see Section 7.4.2) an aerated, turbulent particulate matter system with stochastic particle movement develops. Similar conditions exist if the particles are suspended in a fluidized bed. The main difference between the two methods is that in the mixers particle movement is caused by mechanical forces while in fluidized beds drag forces, that are induced by a flow of gas, are the main reason for the movement of the particulate matter. Therefore, fluidized beds are not only used as excellent environments in which gas efficiently and intimately contacts particles but also for dry mixing of particulate solids and coalescence of particles which, in the presence of binding mechanisms, causes agglomeration. 

Ikazaki, F. and M. Kamamura, Electric Adhesion Force of a Single Particle and of a Powder at Room Temperature and Above Ambient Temperature and its Application to a Fluidized Bed, Particle Sci. Tech., 2, 3, 1984, pp. 271-283. Inculet, I. I., N. H. Malak, and J. A. Young, Corona Charging of Immobilized Spherical Particles, in Electrostatics 1983, Ed. S. Singh, Conf. Ser., 66, Inst. Phys, 1983. pp. 98-105. 

Tubular reactors Packed bed and fluidized bed reactors are included in this cat ory. Particulate forms of enzymes/cells are bundled inside a cylindrical vessel, either in close contact with each other in a packed bed, preferably by forcing the fluid to circulate in downflow mode, or, in the form of a fluidized bed, by forcing the fluid upward, so that the bed of solid particles expands and behaves in a fluidlike manner, which favors contact between individual solid particles, hence enhancing mass transfer. The monolith reactor, where the bed of particles is replaced by a single structure, is a variation of the packed bed with minimal pressure drop. 

In the case of fluidized bed flocculators the power dissipated is the energy of drag past the fluidized bed particles per unit time. This occurs in the floe blanket clarifier where the previously formed floe particles comprise the fluidized bed. For a fluidized bed the drag force past the floe particles is equal to their weight in the liquid. 

To characterize the gas flow in the fluidized bed, important forces are viscous and inertia as well as par-ticle-to-gas forces. For the particles, the important forces include gravity, particle inertia, gas interaction with the particles such as drag, collisional forces between particles and between particles and wall, and particle surface forces such as electrostatic and adhesion forces. For larger particles, in Geldart groups B or D, the particle surface forces can be neglected. The question is complicated for smaller particles because the surface forces are difficult to quantify. We must... 

The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

Transport Disengaging Height. When the drag and buoyancy forces exerted by the gas on a particle exceed the gravitational and interparticle forces at the surface of the bed, particles ate thrown into the freeboard. The ejected particles can be coarser and more numerous than the saturation carrying capacity of the gas, and some coarse particles and clusters of fines particles fall back into the bed. Some particles also coUect near the wall and fall back into the fluidized bed. 

Flue particles ia a fluidized bed are analogous to volatile molecules ia a Foiling solution. Therefore, the concentration of particles ia the gas above a fluidized bed is a function of the saturation capacity of the gas. To calculate the entrainment rate, it is first necessary to determine what particle sizes ia the bed can be entrained. These particles are the ones which have a terminal velocity less than the superficial gas velocity, assuming that iaterparticle forces ia a dilute zone of the freeboard are negligible. An average particle size of the entrainable particles is then calculated. If all particles ia the bed are entrainable, the entrained material has the same size distribution as the bed material. 

Dry dense medium (pneumatic fluidized-bed) separation has been used, but has not received wide attention by the industry. An area of promise for future development is the use of magnetically stabilized dense medium beds by using ferro or magnetic fluids (2,10). Laboratory and pilot-scale units such as Magstream are available. In this unit, material is fed into a rotating column of water-based magnetic fluid. Particles experience centtifugal forces and... 

Designing a model fluidized bed which simulates the hydrodynamics of a commercial bed requires accounting for all of the mechanical forces in the system. In some instances, convective heat transfer can also be scaled but, at present, proper scaling relationships for chemical reactions or hydromechanical effects, such as particle attrition or the rate of tube erosion, have not been established. 

Rietma, K., Cottaar, E. J. A., and Piepers, H. W., The Effect of Interparticle Forces on the Stability of Gas-fluidized Beds — II. Theoretical Derivation of Bed Elasticity on the Basis of Van der Waals Forces between powder Particles, Chem. Eng. Sci., 48 1687 (1993)... 

Entrainment from fluidized beds is also affected by temperature and pressure. Increasing system pressure increases the amount of solids carried over with the exit gas because the drag force on the particles increases at higher gas densities. May and Russell (1953) and Chan and Knowlton (1984) both found that pressure increased the entrainment rate from bubbling fluidized beds significantly. The data of Chan and Knowlton are shown in Fig. 13. 

It is instructive to simplify the above picture somewhat and consider the coalescence or sticking of two particles schematically shown in Fig. 13. One can assume that due to shear forces in the mixer, a fluidized bed in the present case, the two particles posses a relative velocity U0 which ensures collision at some point on their trajectory and possible sticking under appropriate conditions. It is essential that some binder be present at the point of contact, as depicted in the figure. From this simplified picture, allmechanisms... 

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