Fluidized beds voidage propagation velocity

It has been mentioned earlier that the voidage propagation velocity is the same as the sharp front velocity. Thus, the equation for is the same in gas-solid fluidized beds and liquid-solid fluidized beds. However, for bubble columns, the sharp front velocity is given by the following equation ... 

Verloop and Heertjes (1970) used Eq. (36) for the voidage propagation velocity. The elastic wave velocity was calculated on the basis that the fluidized bed was considered to be an elastic substance ... 

Equation (36) gives the voidage propagation velocity (sharp front or continuity wave velocity) for gas-solid and solid-liquid fluidized beds. However, for the other multiphase dispersions, the procedure given by Eqs. (32) to (37) should be used. Thus, for gas-liquid dispersions, the sharp front velocity is given by Eq. (37). 

The Hydrodynamic Theory of fluidized bed stability was proposed by Foscolo and Gibilaro who adapted the stability principle of Wallis. They postulated that a fluidized bed is composed of two interpenetrating fluids. One fluid is the gas phase, and the solids phase is also considered as a continuous fluid phase. In this theory, voidage disturbances in the bed propagate as dynamic and kinetic waves. The stability of the fluidized bed depends upon the relative velocities of these two waves. The velocities of the kinetic wave (ue) and the dynamic wave (nj are ... 

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