Analyzing the impact of surfactant on dispersion DSD, with a focus on Isotherm

This thesis develops and validates a novel MATLAB population-balance model of continuous gravity liquid–liquid separation that combines multi-cell spatial discretization with surfactant adsorption isotherms to predict droplet coalescence dynamics, dispersion height, and outlet droplet size distributions. The model enables a priori prediction of separator performance in surfactant- affected systems, a capability not available in current design practices, which rely on surfactant- free correlations and frequently fail catastrophically in industrial applications. Pilot-scale data validation indicates an accurate prediction of dispersion height with a 8.7% mean error and a 0.023 m mean absolute error, within the 15 − 25% engineering tolerance for gravity settlers. Studies show that in conditions relevant to industry (with inlet flow rates of 10 − 30 L/s, dispersed phase fractions of 0.15 − 0.30, and inlet droplet sizes of 100 − 150 µm), increasing the inlet droplet size from 100 micrometers to 150 micrometers boosts separation efficiency from about 60% to 83% in a 1 m separator length when no surfactants are used. Outlet droplet diameters range from 470 µm to 1300 µm as the flow rate decreases (30 - 10 L/s), thereby providing quantitative design correlations for equipment sizing. The model determines optimum phase fraction ranges that maximize separation efficiency while avoiding phase inversion, providing engineers with helpful design charts for equipment specification. Adding surfactant improves separation performance by lowering interfacial tension from about 30 mN/m to around 5 mN/m. This helps prevent droplet coalescence and maintains the size of outlet droplets between 145 and 175 µm, regardless of the operating conditions. This stabilizing action requires four times longer separators to achieve a similar separation. A critical design threshold emerges for inlet droplet sizes less than 125 µm, gravity separation becomes impractical under surfactant-stabilized conditions, and the allowable throughputs are 2–3 times more restrictive than for surfactant-free separators. The validated model gives clear recommendations for designing and improving surfactant-affected separators in petrochemical, pharmaceutical, and environmental industries. It connects process parameters to the size and performance needs of the equipment used for separation. Economic analysis indicates that the presence of surfactant can increase capital costs due to extended separator lengths, resulting in significantly reduced operational flexibility. The predictive capability of the model enables process engineers to make quantitative trade-offs between throughput, separation quality, and equipment size early in the design phase.