Two-Phase, Co-current, Annular Force Balance, Resolved in the Axial Direction

1 Two-Phase, Co-current, Annular Force Balance, Resolved in the Axial Direction 

We begin by performing a force balance in the axial 2 direction over a cross section of the cyclone of height dz. See Fig. 13.C.1. We shall assume that, for all practical purposes, all of the liquid is spiraling down the inner walls of the cyclone as a wall film with the gas phase comprising the core flow. A force balance on the gas phase gives (note that dp is itself negative), 

if we name the fraction of the total cross-sectional area, A = 7ri5 /4, taken up by gas the void fraction , e, then Ag = eA, Ai = l—e)A. Furthermore, we take the wetted wall perimeter, S u, and the interface perimeter. Si as S-uj = ttD and Si = irDg = ne D, respectively. Substituting this into Eq. (13.C.3) and simplifying gives  

We assume, as is normal, that the pressure in the gas permeates the liquid film 

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