A volume-averaged population balance model is presented for predicting drop breakup in turbulent liquid-liquid dispersions with varying dispersed-phase viscosity. The approach is based on a zero-dimensional population balance equation and incorporates hydrodynamic information through the cumulative distribution function of the turbulent dissipation rate over the vessel volume, extracted from validated single-phase CFD simulations. Using the cumulative distribution of turbulent dissipation rate, instead of reconstructing its probability density function through histogram binning, yields numerically stable solutions, faster quadrature convergence, and substantially fewer discretization nodes. The model is evaluated against a dedicated experimental dataset covering nine operating conditions, obtained by combining three dispersed-phase viscosities with three impeller rotation speeds. Drop size distributions were measured, enabling assessment of both moment-based metrics and distribution-level features. Analysis of these data motivated a novel, flexible daughter distribution function based on a weighted sum of two beta distributions. The formulation captures asymmetric and multimodal fragment patterns at high viscosity and improves the representation of the small-diameter region, especially the number-weighted mean size and the left-hand tail, while classical shapes remain adequate at low viscosity. Across all conditions, the model predicts the Sauter mean diameter with deviations ranging from approximately 5% at low viscosity to about 50% at high viscosity. The increasing discrepancies with viscosity highlight the need for more accurate breakup rate descriptions and for experiments resolving daughter size statistics at high viscosity ratios. Overall, the framework provides a practical route for screening breakup models and for analysing viscosity effects in turbulent dispersions while retaining the full drop size distribution.
Maluta, F., D'Avino, G., Marchioli, C., Paglianti, A., Buffo, A. (2026). Improving volume-averaged population balance models for turbulent breakup in liquid–liquid dispersions. INTERNATIONAL JOURNAL OF MULTIPHASE FLOW, 203, 1-13 [10.1016/j.ijmultiphaseflow.2026.105854].
Improving volume-averaged population balance models for turbulent breakup in liquid–liquid dispersions
Maluta F.Primo
;Paglianti A.;
2026
Abstract
A volume-averaged population balance model is presented for predicting drop breakup in turbulent liquid-liquid dispersions with varying dispersed-phase viscosity. The approach is based on a zero-dimensional population balance equation and incorporates hydrodynamic information through the cumulative distribution function of the turbulent dissipation rate over the vessel volume, extracted from validated single-phase CFD simulations. Using the cumulative distribution of turbulent dissipation rate, instead of reconstructing its probability density function through histogram binning, yields numerically stable solutions, faster quadrature convergence, and substantially fewer discretization nodes. The model is evaluated against a dedicated experimental dataset covering nine operating conditions, obtained by combining three dispersed-phase viscosities with three impeller rotation speeds. Drop size distributions were measured, enabling assessment of both moment-based metrics and distribution-level features. Analysis of these data motivated a novel, flexible daughter distribution function based on a weighted sum of two beta distributions. The formulation captures asymmetric and multimodal fragment patterns at high viscosity and improves the representation of the small-diameter region, especially the number-weighted mean size and the left-hand tail, while classical shapes remain adequate at low viscosity. Across all conditions, the model predicts the Sauter mean diameter with deviations ranging from approximately 5% at low viscosity to about 50% at high viscosity. The increasing discrepancies with viscosity highlight the need for more accurate breakup rate descriptions and for experiments resolving daughter size statistics at high viscosity ratios. Overall, the framework provides a practical route for screening breakup models and for analysing viscosity effects in turbulent dispersions while retaining the full drop size distribution.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
