Self-Diffusion in a Gas-Fluidized Bed of Fine Powder

Jose Manuel Valverde, Antonio Castellanos, Miguel Angel Sanchez Quintanilla
2001 Physical Review Letters  
We have investigated the self-diffusion in a stable gas-fluidized bed of fine powder. Two regimes have been observed: for gas velocities y g above the minimum fluidization velocity y m and below a critical gas velocity y c smaller than the minimum bubbling velocity y b the powder does not mix. Experimental measurements show the existence of yield stresses in this regime which are responsible for the static behavior of the bed. For y g . y c the yield stress vanishes; the bed behaves like a
more » ... behaves like a fluid and displays a diffusive dynamics. In this region we have found that the diffusion coefficient D increases with gas velocity until the bed expansion approaches its maximum value. The diffusive mixing of granular materials was first studied in granular shear flows of noncohesive coarse grains [1]. An analogy was made between the fluctuating or random component of particle motions (which are in a stationary nonequilibrium state) and the random motion of molecules in a dense gas (which is in thermodynamical equilibrium), and an effective granular temperature was defined in terms of the ensemble average of the squared fluctuation velocity, 3T ͗v 2 ͘ 2 ͗v͘ 2 . Wildman et al. [2] showed that the kinetic theory predictions used to relate granular temperature to self-diffusion in granular gases were accurate to within 10%-20% for packing fractions up to 0.6 in vibrofluidized granular beds. Fine powders are capable of being fluidized by a gas flow being the agent of transfer of momentum between particles [3]. Disequilibria created during collisions due to particle surface irregularities and local fluctuations in the gas velocity field are expected to be responsible for a random motion of particles. Because of the random component of particle motion in the gas-fluidized bed, the particles could exhibit a diffusive motion similar to that found in dense gases. The concept of granular temperature was extended to gas-fluidized beds by Cody et al. [4] who derived the granular temperature of the particles at the wall of a gas-fluidized bed by measuring the acoustic noise due to random particle impact at the wall. They showed that the granular temperature depends strongly on the fluidizing gas velocity. In their experimental study they used noncohesive glass spheres with diameters from 60 to 600 mm. They found that above the minimum fluidization velocity the average granular temperature increased directly proportional to the square of the gas superficial velocity. They also found that granular temperature changed inversely proportional to the square of particle diameter. Menon and Durian [5] reported on measurements by diffusion-wave spectroscopy of velocity fluctuations in gas-fluidized beds of spherical glass beads of diameters 49, 96, and 194 mm. Surprisingly, they found no fluctuations in the interval of uniform fluidization. This finding led them to the conclusion that "the uniformly fluidized state was a completely static state." They argued that particles in the fluidized state are held by enduring contacts. Velocity fluctuations were initiated by the instability to bubbling. However, it must be noted that the interval of uniform fluidization shrinks to almost zero for the 96 and 194 mm particle diameter materials (see Fig. 1 of Ref. [5]). And for the bed with particles of 49 mm in diameter the interval of stable fluidization, although appreciable, was very short (gas velocity from 0.2 to 0.25 cm͞s). Furthermore, the bed expansion in the interval of uniform fluidization is quite small (a maximum of 4% of the initial bed height). The same results also apply to the gasfluidized beds of Cody et al. (minimum particle size 60 mm) who did not report on this short interval of null fluctuations but found an increase of the fluctuation velocity in the uniform fluidized bed as particle size was reduced due to enhanced gas flow in the dense phase. Rietema [6] outlined that interparticle cohesive forces could stabilize the homogeneously fluidized bed. These contact forces were assumed to give an effective elastic modulus to the bed that stabilizes the system against small disturbances. In that state the bed would behave like a weak solid rather than a fluid. To corroborate his thesis he showed that when the homogeneously fluidized bed was tilted the bed surface remained stable because of the existence of a certain mechanical strength. Tsinontides and Jackson [7] found experimentally that the mechanism of stabilization in the fluidized regime was the presence of yield stresses in the particle assemblies which form the fluidized but nonbubbling bed. However, Foscolo and Gibilaro [8] rejected Rietema's ideas. They stated that particles were free floating in the fluidized bed and proposed a stability criterion based on the dependence of the gas-particle drag force on the free volume. Whether stresses in the uniform fluidized bed are carried out by particle contacts or by collisions is still a matter of strong controversy. The absence of velocity fluctuations in the uniform fluidized bed before the onset of bubbling found by Menon and Durian [5] gives support to Rietema's arguments. On the other hand, the work of Cody et al. [4], who measured particle fluctuations in uniformly fluidized 3020 0031-9007͞01͞86(14)͞3020(4)$15.00
doi:10.1103/physrevlett.86.3020 pmid:11290097 fatcat:euryiaifr5dq5ekpdqqnmu425m