(550b) Determination and Validation of Equations for Fitting Parameters for Two Common Droplet Breakage Models

Engineering operations frequently involve the dispersion of one immiscible liquid in another. Examples of these processes include liquid-liquid extraction and dispersed phase reactions. Mechanical agitation of liquid-liquid systems is widely used to create these dispersions. The size distribution of the droplets and their dynamics in dispersions have a significant impact in the overall behavior of these systems. Applications that feature dispersed phases in multiphase flows include channel or pipe flow, biological and chemical reactor flows, and phase separation equipment such as gravity separators. The size distribution of the dispersed phase is critical for determining the possible separation of a dispersed phase or the interfacial mass or heat transfer of a system. Predictive simulation of such systems requires a thorough understanding of transient breaking events. The design and operation of equipment and processes used in these applications are often optimized using validated 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. This, along with large variability in the collected experimental data among researchers due to the importance of quantities such as turbulence dissipation rate, ε, that can be difficult to accurately determine ,because of the inherent heterogeneity of droplet breakage experimental apparatuses and process equipment such as stirred tanks makes it difficult to develop easily applied predictive models

In this work, analytical expressions are hypothesized to predict the value of a fitting parameter associated with droplet breakage time for two commonly used breakage models without having to perform empirical studies. These equations were determined 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 Karman 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.