Application of Queueing Theory and Foam Drainage Model to Enhance Understanding of Droplet Layer in Emulsion-flow Column Extractor

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<p>“Emulsion-flow” is an innovative technique of liquid-liquid extraction, utilizing the counter-current flow of both aqueous and organic phases in the form of droplets. It maintains a broad operational range across various phase velocities, primarily attributed to the steady droplet layer due to rapid drop coalescence in the layer. This study sheds a light on the importance of the droplet size and liquid flow in the droplet layer in the column. To simplify the analysis of droplet coalescence, no mass transfer was considered in the experiment, but the interaction was focused on between n-heptane and deionized water droplets. With the assumption of uniformed droplet size D32, queueing theory has been applied to predict the average droplet coalescence time, τ and the droplet layer height, H with D32 as well as a fitting parameter, n. The physical meaning of n was elucidated as the product between droplet distance and space time. Due to the similarity with the structure of a foam layer, the foam drainage model was analogically used to describe the speed of liquid flow among droplets, and to predict the organic phase hold-up, φorg within the droplet layer. The result revealed observed values of φorg aligned well with the shape coefficient, f, in a narrow deviation range.</p>

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