Foscolo-Gibilaro equation

Hie Foscolo-Gibilaro equation indicates multiple solutions for st. However, two solutions at maximum are to be expected in the operating range between 0.4 and 1. The second solution exists because bubbling beds are known to revert to particulate behavior at high voidages (Foscolo and Gibilaro, 1984). 

From the analysis presented in the last two paragraphs, it is evident that the gravitational force acting upon the particle is used for the derivation of the equations for the terminal velocity and the pressure drop in the fluidized bed. Then, it is clear that the hydraulic density should be used in these equations as well as in any other equations that are derived from a similar force-balance analysis. For instance, this is the case of the Foscolo-Gibilaro criterion for determining the fluidization pattern (Section 3.8.2). 

Comparing this equation to that of a single particle (eq. (3.565)), it is evident that in applying the Archimedes principle to a particle in a fluidized suspension, it is an average suspension density, including the particle density, rather than that of the fluid alone, that determines the buoyancy force (Foscolo and Gibilaro, 1984). The gravity force is... 

We will here adopt the buoyancy convention incorporated in Eqs. (2) and (6) rather than (3) and (7). However, since the latter convention has made significant inroads into the literature, the reader is referred to Table 1 of Khan and Richardson (1990) for useful drag coefficient relationships based on the above alternate conventions, as well as on alternate definitions of the characteristic liquid velocity, and to conversions by Jean and Fan (1992) of several equations incorporating buoyancy as defined by Eq. (3) [derived by Foscolo et al. (1983, 1989), Foscolo and Gibilaro (1984, 1987) and Gibilaro et al. (1985a, 1986)] to the corresponding equations based on buoyancy as defined by Eq. (2). 

Jean R-H, Fan L-S. On the model equations of Gibilaro and Foscolo with corrected buoyancy force. Powder Technology 72 201-205, 1992. 

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