Development of a Droplet Formation and Entrainment Model for Simulations of Immiscible Liquid-Liquid Flows

摘要

Droplet formation is a common phenomenon in turbulent mixing and has many practical applications. The ability to predict the relative sizes and distributions of fluid droplets formed from mixing events is a complex problem which is dependent on many different parameters including geometric considerations, the nature and physical properties of the fluids in question, turbulence parameters, buoyancy and body forces, and flow history. While there have been many researchers who have analyzed this problem for both liquid- liquid and gas-liquid systems, the present study will focus only on droplet formation in immiscible liquid-liquid systems. A review of the literature has shown that previous attempts at describing fluid droplet sizes essentially fall into two categories: (1) phenomenological models, and (2) statistical models. The use of phenomenological models usually involves semi-empirical analyses of a particular liquid-liquid or gas-liquid system, and typically employs a force balance to determine the conditions under which droplet formation or breakage occurs. Statistical models, on the other hand, utilize flow history and probability density functions to determine the size and number distribution of daughter droplets formed from the splitting of larger droplets or the coalescence of smaller ones. In the present study we will adopt many of the methods of the former set of models, resulting in expressions which determine the sizes of the dispersed phase droplets based on local flow parameters including turbulence quantities, appropriate characteristic length scales, and dimensionless parameters such as the gradient Richardson number. While much of the development of the droplet formation/entrainment (DFE) model comes from results from the literature concerning stratified shear flows, the model can be calibrated through the adjustment of certain constants to conform to a wide variety of flow scenarios.