Solids-free liquid wake

El-Temtamy and Epstein (1979) later found that the assumption of sohds-free liquid wake behind the bubbles is tenable only for relatively coarse and/or heavy particles and becomes increasingly untenable for solids smaller than 1-2 mm, especially if the particle densities do not exceed 3000... 

Since the liquid divides itself between the solids-free wake and the particulate region of the liquid-fluidized sohds. 

Eq. (12) assumes that the liquid divides itself between the solids-free wakes and the particulate region of the fluidized bed. On the other hand, Eq. (13) considers that the interstitial velocity of the liquid can be represented by an equation similar to the one proposed by Richardson and Zaki [14] ... 

Darton and Harrison (1975) derived a criterion for the point of transition to predict whether a solid-liquid fluidized bed will expand or contract when the gas is first introduced. The definition of Pa used by Darton and Harrison was the ratio of upper clear (particle-free) wake volume to the bubble volume. But since they did not consider the circulation of sohds associated with the lower nonclear portion of the wake, their Pa was effectively the same as that of Bhatia and Epstein (1974). The use of the Wallis drift flux approach by Darton and Harrison (1975) also represents no real difference from the relative velocity approach taken by Bhatia and Epstein (1974), since the two methods are rigorously interrelated. It is therefore not surprising that the final criteria of Bhatia and Epstein (1974) and Darton and Harrison (1975) are identical. 

Note that the value of surface free energy appropriate to the Dupre equation is 7s, rather than ysv. As pointed out by Wake [103], if the latter term is used in the Dupre equation then the separation to which the value of Wa refers is the separation of the liquid from a solid which is still covered with a layer of... 

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