Optimisation of the Design and Operation of Mixing Processes using Computational Fluid Dynamics and High Performance Computing

  • Ioannis Bagkeris

Student thesis: Phd


Immiscible liquid-liquid systems are commonly encountered in chemical, petroleum, fast-moving consumer goods and pharmaceutical industries. Process design and scale-up typically rely on time-consuming experiments, motivating the evaluation of emulsification processes via simulation techniques. CFD coupled with population balance modelling (PBM) can improve understanding of the process mechanics in emulsifying devices and has the potential to provide predictions of key features of the final product. The accuracy of CFD-PBM is predicated by the fidelity of sub-models describing discrete events (e.g. droplet breakage). The present work aims to use CFD-PBM to explore the physics of the formulation of dilute emulsions in Sonolator high-pressure homogenisers, and to develop and validate simulation techniques for studying such problems in industry. Firstly, the flow field in a Sonolator is analysed via LES. The predicted distribution of the turbulence energy dissipation rate suggests that most of droplet breakage in the device occurs close to the Sonolator nozzle. Energy spectra and second-order structure functions obtained in this region highlight finite Reynolds number effects and deviations from models based on isotropic turbulence. Most droplet breakage models assume isotropic turbulence of infinite Reynolds number and, therefore, appear to be unsuitable for modelling turbulent emulsification in a Sonolator. Average droplet size results from CFD-PBM simulations show that a droplet breakage model of empirical form (model of Alopaeus et al.) outperforms a model based on isotropic turbulence. The breakage time terms in these two models are interpreted as variations of the underlying turbulence structure, embodied in the structure function assumed by each model. The model of Alopaeus et al. is found to correspond to strongly anisotropic turbulence of finite Reynolds number. A new anisotropic drop breakage model is developed, aiming to characterise the underlying turbulence structure. The anisotropy is introduced via a perturbation of the turbulence energy spectrum, assuming that the anisotropic part of the Reynolds stresses is confined to the energy-containing range. The structure function arising from the perturbed spectrum provides a physically plausible mechanism which allows its scaling exponent to vary as a function of the underlying turbulence structure. The two breakage models tested previously are limiting responses of the new model to the underlying turbulence anisotropy. Finally, the new model is tested on a CFD-PBM simulation of turbulent emulsification in a Sonolator. Validation is carried out using the exponent of the average drop size - pressure drop correlation; this exponent is thought to be closely linked with the drop fragmentation mechanism in an emulsification device. Kolmogorov-Hinze emulsification theory predicts a value of -0.6, while exponents of smaller magnitude are observed in experiments. The new model, as well as the model of Alopaeus et al., capture the decrease in magnitude of the exponent as compared to breakage models based on isotropic turbulence. It is shown that the reduced magnitude of the exponent obtained with these two models is related with the effect of anisotropy on the mathematical behaviour of the droplet breakage frequency.
Date of Award1 Aug 2020
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorRobert Prosser (Supervisor) & Paola Carbone (Supervisor)


  • Emulsion
  • Population balance modelling
  • Turbulence
  • Droplet breakage
  • High-pressure homogeniser

Cite this