The separation of the solids from the carrier gas during submerged powder injection
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Particle Piston
The "excess force" will be balanced at steady state by drag due to the relative motion of the penetrated particles with the liquid and the buoyancy of the particle-liquid jet. The excess force may be expressed in terms of the mass flow rate of penetrating particles and the particle velocity by F x~ = rnpe,Up
[7]
Combining these relationships gives an expression for the penetration efficiency: Fig. 1---Conceptual diagram of particle piston working on bubble/liquid interface.
injection of nonwettable powders in the bubbling regime at finite solids loadings ranging from 1 to 25 has been undertaken. A simple mathematical model has been proposed to predict the penetration efficiency in terms of a jet Weber number based on the mass flow rate of solids, the particle discharge velocity, the surface tension, and the nozzle diameter. An experimental technique originally described by Lee et aL t~u has been further developed and used to measure the penetration efficiency during submerged injection in a cold model system (air-water-polyethylene powder). This study has produced a relationship which can be used to predict the minimum conditions for efficient separation of the injected particles from the carrier gas during submerged injection at finite solids loadings in the bubbling regime. II.
n~ =
D, ~ Do
np =
m,
[31
Penetration is assumed to occur when the jet force of the particles exceeds the force required to overcome the surface tension resistance to particle penetration. The jet force of the particles is given by F j = mpU,
[4]
The resistance due to surface tension opposing penetration of the particles into the liquid is Fsr = 7"ro'Dj
[5]
where D j is the particle jet diameter at the point of impact with the bubble surface. The assumption underlying Eq. [5] is that the particles piling up at the gas-liquid interface behave as a densely packed "piston" with diameter D j push774---VOLUME 27B, OCTOBER 1996
[9]
Equation [8] can be simplified with these assumptions to give 7/"o ' O 0
mpUp
rip = 1
[10]
A particle jet Weber number may be defined by the ratio of the jet force of the solid phase and the surface tension force: We~ - meUe o-Do
The penetration efficiency of the injected solids from the primary bubble into the liquid is defined by
[81
If it is assumed that the particle jet does not expand significantly before reaching the bubble surface (particle jet cone angles of only 2 to 7 deg have been reported by Engh et al.t~21), then the particle jet diameter will approximately equal the nozzle diameter:
MODEL
mpen
m,U,
[11]
and Eq. [ 10] becomes 7r
~Tp = 1
Wej
[12]
Equation [12] predicts the critical particle jet Weber number for incipient penetration to be Wej.c = 7r
[13]
Equation [12] is applicable for Wej > zr. Analysis of the experimental data is simplified if the penetration behavior is expressed in terms of the retention efficiency of particles within the primary bubble, defined by r/~ = 1 - "Op 7r
Wej
[ 14]
- hW% (U~) where A is the solids loading, and the gas Weber
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