Fournol et al., (1973) describes the TDH (F) - as inversely proportional to the Froude number. Despite this proposition, the authors note that this height is significantly higher than predicted by Zenz and Weil (1958):

Hamdullahpur et al., (1986) proposed an equation that characterizes the TDH(C) as dependent on the bubble diameter:

Baron et al., (1988) suggested a new correlation to estimate the TDH(F), in which the maximum height reached by the large *clusters* is directly proportional to the velocity square of the particle (KU_{b}) ejection, which in turn would be the gas velocity:

Sciazko et al., (1988) have shown though, that the ratio between both the *splash-zone* height and the bed height is strongly influenced by the excess gas velocity (U-U_{mf}). This volumetric fraction would be the critical value of the bubbles fraction, which is related to the difference in the velocities mentioned above:

Sciazko et al., (1991) determined a new correlation for the TDH(C) depending on the diameter of the bubble on the bed surface:

Pinto et al., (1999) proposed a correlation for the TDH(C) depending on the physical characteristics of both the particles (particle diameter), and the gas (density and viscosity) and the operating conditions (solid mass and gas velocity):

Cipolato et al., (2004 stablished a new correlation for the TDH(C) depending on the solid mass through the statistical analysis, for a first order model with two interactions: