Terminal velocity slugs

In the slug flow region, Griffith and Wallis (1961) suggested the terminal velocity,... 

For the special case (a) above where surface tension and viscous effects are negligible, the terminal velocity of a slug in a column of rectangular cross section (D x D2) is given by... 

Detailed consideration of the interaction between particles and fluids is given in Volume 2 to which reference should be made. Briefly, however, if a particle is introduced into a fluid stream flowing vertically upwards it will be transported by the fluid provided that the fluid velocity exceeds the terminal falling velocity m0 of the particle the relative or slip velocity will be approximately o- As the concentration of particles increases this slip velocity will become progressively less and, for a slug of fairly close packed particles, will approximate to the minimum fluidising velocity of the particles. (See Volume 2, Chapter 6.)... 

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