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The dispersion of an immiscible fluid in a turbulent liquid flow is a frequent occurrence in various natural and technical processes, with particular importance in the chemical, pharmaceutical, mining, petroleum, and food industries. Understanding the dynamics and breakup of liquid droplets is crucial in many scientific and engineering applications, as poor control and optimization of droplet systems results in significant financial losses annually. Although a theoretical background for describing droplet breakup exists, many assumptions still require experimental verification. Numerous mathematical models have been proposed to describe the rate coefficient of droplet breakup and child distribution functions. However, the validation and discrimination between models have been hindered by the lack of experimental data gathered under well-controlled and well characterized conditions. Thus, to validate the current models, novel equipment and methodology for optical droplet breakage research are required. In this work, a von K´arm´an swirling flow apparatus was designed and constructed to carry out optical based droplet breakage experiments under low-intensity, homogeneous turbulent flow. The methodology presented here describes the procedure for generating and controlling the size of the droplets being injected into the homogeneous turbulent flow field. The experiments involved introducing single droplets into the test section, using peanut oil to be the droplet phase and the continuous phase is water. Automated image analysis algorithms were utilized to determine breakage time, breakage probability, and child droplet size distribution for different turbulence intensities. 

Chemical process engineering unit operations such as solvent extraction, liquid–liquid chemical reactions, and emulsion processing are all dependent on turbulent liquid–liquid droplet flow dynamics. The design and operation of equipment used in these applications is often guided by theoretical models for droplet breakup. Although several models for droplet breakage in agitated liquid emulsions have been developed, their utility is limited because they incorporate fitting factors that must be determined empirically by performing experiments using a specific fluid pairing and relevant flow configuration. The need to acquire experimental data to determine model constants is a significant drawback that hinders widespread use of breakage models to design and optimize process equipment. In this work, analytical expressions are formulated to predict the value of a fitting parameter associated with droplet breakage time for two commonly used breakage rate models without having to perform empirical studies. These equations were derived by using the underlying assumptions within each of the two breakage models considered, namely, that droplet breakage is a result of the competition between relevant deformation and restorative stresses. Data from experiments conducted in a homogeneous turbulent von Kármán box as well as from previously published investigations of droplet breakage in heterogeneous flow devices were utilized to validate the derived equations for the breakage time parameters. In general, good agreement was observed between predictions obtained using the derived equations for fitting parameters and those obtained from experiments. 

Droplet dispersion in liquid–liquid systems is a crucial step in many unit operations throughout the chemical, food, and pharmaceutic industries, where improper operation causes billions of dollars of loss annually. A theoretical background for the description of droplet breakup has been established, but many assumptions are still unconfirmed by experimental observations. In this investigation, a von Kármán swirling flow device was used to produce homogeneous, low-intensity turbulence suitable for carrying out droplet breakage experiments using optical image analysis. Individual droplets of known, adjustable, and repeatable sizes were introduced into an isotropic turbulent flow field providing novel control over two of the most important factors impacting droplet breakage: turbulence dissipation rate and parent droplet size. Introducing droplets one at a time, large data sets were gathered using canola, safflower, and sesame oils for the droplet phase and water as the continuous phase. Automated image analysis was used to determine breakage time, breakage probability, and child droplet size distribution for various turbulence intensities. Breakage time and breakage probability were observed to increase with increasing parent droplet size, consistent with the classic and widely used Coulaloglou–Tavlarides breakage model (C–T model). The shape of the child drop size distribution function was found to depend upon the size of the parent droplet.