A kinematic description of unsteady-state behaviour

The response of homogeneously fluidized beds to sudden changes in fluid flux 

Consider a homogeneously fluidized bed of void fraction ei in equilibrium with a fluid flux of U. At time zero the flux is suddenly switched to a lower value U2, causing the bed to contract, eventually attaining a new equilibrium at void fraction 2. 

The behaviour just described is clearly not possible for particles at the bottom of the bed, in contact with the distributor these cannot move downwards and so remain stationary, soon to be joined by others arriving from above. This gives rise to a growing zone of stationary particles at the bottom of the bed, which adjusts to the equihbrium void fraction corresponding to zero particle velocity and the new fluid-flux U2, this is 2, the value eventually to be reached by the whole bed after the transient rearrangement period has been concluded. 

A sudden increase in fluid flux from U to U2 gives rise to a net upward force on all the particles these therefore immediately start to accelerate upwards together, without change in void fraction ei, until the relative fluid-particle velocity and the interaction force drop back to their previous equilibrium levels from this point on it would appear that the bed should continue its upward motion, piston-like at constant velocity, as was suggested in Chapter 1 on the basis of the analogy with single-particle suspension. The fact that this does not happen in practice (fluidized beds would never form if it did) has to do with the instability of the interface separating the bottom of the particle piston from the clear fluid below. 

The particle piston, created as described above, possesses two interfaces with the fluid through which it travels. The stability of each can be determined on the basis of the following simple qualitative considerations. 

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