Abstract Summary (Max 250 words)
Liquid–liquid mixing in mechanically agitated tanks produces drop size distributions governed by the interplay of turbulent stresses, interfacial tension, and viscosity. This work presents a simplified population balance framework for predicting drop size distributions under turbulent agitation. The reactor hydrodynamics is decoupled from drop scale dynamics by deriving a 0D population balance, with the distribution of turbulent dissipation rates obtained from validated single-phase CFD. The averaged breakup frequency is evaluated by integrating the breakup kernel over the full dissipation distribution using a cumulative distribution formulation, which avoids sensitivity to histogram binning. Numerical tests show that the cumulative distribution formulation reduces integration error by about two orders of magnitude relative to a probability density-based discretization and provides stable results with fewer Gauss–Legendre nodes. In addition, a flexible daughter distribution function is introduced as a weighted sum of two-beta functions, preserving mass and enabling asymmetric or multimodal fragmentation outcomes. Model assessment is performed using a dedicated experimental dataset spanning nine operating conditions obtained by combining three dispersed phase viscosities with three impeller speeds, in terms of both drop size distributions and mean diameters. Conventional kernel/daughter distribution combinations provide the closest agreement at low viscosity, whereas higher viscosity conditions exhibit pronounced small diameter tails associated with satellite drops. The two-beta daughter distribution improves the representation of the small diameter region, but remaining discrepancies indicate that further refinement of the breakup frequency model is required.
