Fitting Parameter Estimations for Droplet Breakage Rate Models

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 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.