Coalescence Frequency in Turbulent Flow

One of the earliest attempts to quantify coalescence frequencies was the work of Howarth (1967). A procedure was used that is similar to the one described in Section 12-3.1.5. A steady dispersion was established at a high agitation rate. The stirrer speed was then lowered so that only coalescence occurred, at least initially. Howarth defined a global or macroscopic coalescence frequency as the initial slope of a plot of interfacial area (related to d32 versus time and demonstrated that systematic experiments could be conducted to determine the effect of various system variables on coalescence rate. Since the coalescence frequency depends strongly on drop diameter, most models are based on the approach discussed below. 

Collision Frequerx y, (d.cf) Contact Force, F Contact Time, t ----- 

EXTERNAL FLOW - Kolmogoroff Inertial Sub Range, Laminar Flow, etc. INTERNAL FLOW - Deformable or Rigid Sphere, Parallel Interface, etc. 

The model developed by Coulaloglou and Tavlarides (1977) for turbulent stirred tanks applies to drops whose collision rates are determined by interaction with eddies that fall within the inertial subrange of isotropic turbulence (Lt d T ). For equal-sized drops, assuming uniform energy distribution throughout the vessel, the collision frequency is given by eq. (12-36). For unequal-size drops, these authors obtained 

For drops having immobile interfaces, Coulaloglou and Tavlarides (1977) show the drainage time for unequal size drops to be 

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