Pressure drop resulting from accelerating particles

The pressure drop resulting from the movement of particles can be determined by an energy balance. The overall energy balance round the flow of suspension inside the accelerating tube is written as... 

On the other hand, the collisions of particles on the inside wall of the tube and between particles also result in a certain pressure drop, which is denoted by -Apac>p2. Some researchers let it be a fraction of the pressure drop caused by pure airflow [67] however, it would be more convenient and reasonable to correlate it with that resulting from the acceleration of the particles, -ApaCiPi, because the factors affecting the two kinds of collision are the same as those for —Ap ac.pi. In this way, we have... 

Gas distributors of fluidized beds are often designed as perforated or nozzle plates. Since a minimum pressure drop is required to obtain a uniform gas distribution over the bed s cross-sectional area, the open surface area is rather small, and the gas jets issuing from the distributor holes are at high velocity. Particles are entrained by these jets, accelerated to high velocities, and impacted onto the fluidized bed suspension at the end of the jets, resulting in particle degradation similar to that in jet grinding processes (Kutyavina and Baskakov, 1972). 

An interesting historic note concerns the proper prediction of the pressure drop in a fluidized bed. It is an empirical fact that in a stationary fluidized bed, the pressure drop (times area) is close to the particle plus fluid weight. From Eq. (2), this result can be easily obtained Assume stationary state such that the left-hand side equals zero and assume that the contribution of the fluid stress is negligible. The two external forces acting on particles are the force applied by the liquid on the particles (Sf p = —Sp, f) and the gravitational puU on the particles. If we assume that the particle phase has no net acceleration, the two forces need to (nearly) balance, so Sf p= p/3pg and therefore the (average) pressure gradient is close to... 

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