Multi-scale interface-capturing methods for thin-film coalescence
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2016
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Melbourne Authors
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Chemical and Biomolecular Engineering
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PhD thesis
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© 2016 Dr. Lachlan Robert Mason
Abstract
Solvent extraction units are core separation systems in the metals, pharmaceutical and nuclear reprocessing industries. In Australia, extraction units are widely used for the separation of base metals and rare-earth elements from their leached ores. A throughput-limiting process is the efficient separation of raffinate and loaded organic phases via coalescence of dispersed droplets. New research findings are needed in order to quantify the physical and chemical regimes that favour coalescence, which will aid in the design and optimisation of hydrometallurgical processing equipment; with both economic and environmental benefits.
Coalescence remains difficult to model due to the disparate length scales involved: a successful model must capture both droplet and film-scale dynamics. While multiphase flows have been well simulated by interface-capturing methods, the detail of thin-film drainage is difficult to simultaneously resolve using these techniques alone. Conversely, existing planar-interface drainage models are not accurate when applied in emulsion settings. This thesis demonstrates the predictive power of multi-scale simulation methodologies, whereby droplet-scale interface-capturing techniques are coupled to a lubrication analysis of thin-film drainage. The developed multi-scale interface-capturing (MSIC) method is applied to droplet/wall and droplet/droplet interactions in emulsion systems.
The thesis details the implementation of appropriate interface-capturing methods, together with coupled film equations, using an open-source finite-volume solver. Level-set, volume-of-fluid (VOF) and high-order VOF techniques are detailed for droplet-scale interface motion; while a new method is presented for the automated discretisation of the required finite-difference drainage relations. The approach is modular, in that alternative interface-capturing techniques can be coupled to the same base film equations.
For validation purposes, MSIC model results were compared with existing Stokes–Reynolds–Young–Laplace theory in the low-inertia limit. Quantitative agreement was achieved for both static and dynamic response scenarios. The model was then used to simulate free-droplet collisions in emulsion systems under moderate-inertia conditions. Results are consistent with existing experimental data for droplet/wall interactions, while outcome predictions for binary droplet collisions agree with existing high-speed video sequences in the presence of continuous-phase electrolytes. Modelling of emulsion interactions requires an accurate description of repulsive electrical-double-layer (EDL) forces; as such, a multiphase ion-transport model was used to confirm the validity of existing disjoining pressure treatments under low-inertia conditions. In the studied case, however, it is the action of interface immobilisation which promotes a bouncing outcome, and not the presence of EDL repulsion.
The techniques presented are important for the development of coalescence kernels in macro-scale population balance equation models. Physically accurate coalescence models can be used to generate comprehensive outcome regime maps, with accompanying quantitative drainage-time data. The MSIC model can be used to discern the influence of continuous-phase chemistry on outcome regime boundaries, which is yet to be studied experimentally. Though the present implementation is restricted to axisymmetric collisions, the model can be generalised for the future study of three-dimensional interactions.
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Keywords
coalescence, multiphase flow, computational fluid dynamics, volume of fluid, level set, emulsion, solvent extraction