| Droplet formation is a common phenomenon that occurs in liquid-liquid or liquid-gas two-phase flows where turbulent mixing is present. This study considers only liquid-liquid systems and presents the theoretical background and validation of a droplet formation and entrainment (DFE) model with application to stratified shear layer flows of diesel fuel and water. A parallel experimental study by Wu and Katz (1999) of the same flow is used as a guide in our analysis. The new Droplet Formation and Entrainment Model, DFE, is based on a previous DFE model [Wilson, W. (1999)] which used the gradient Richardson number, Ri g, as the local flow parameter, however, singularities arose in the calculations. Thus, a turbulent Richardson number definition is derived and used in the characteristic length scale expression. The predicted variation of average droplet size with axial distance using the new formulation agrees with that derived from experiments surprisingly well. The present DFE model not only predicts the slope of the droplet-size profile, but it also predicts a larger average droplet size with increased overall Richardson number, Ri*, consistent with the observed experimental trend. |
