Keywords: Droplet-based microfluidics; Lattice Boltzmann method; Color-gradient model
Double emulsion, known as a small droplet completely engulfed by another emulsion, has a huge potential to be applied in a variety of fields, such as drug delivery, functional material, food science. Especially, it has many advantages for precisely implementing mixing or reaction processes taken double emulsion as a micro-reactor. Thus it is important to develop devices to fabricate the highly monodispersed and uniform core-shell structure of double emulsion. Many researchers have provided valuable empirical knowledge of the double emulsion formation in their extensive studies. For example, two distinctive flow mechanisms of double emulsion formation are illustrated as dripping and jetting modes, and the corresponding flow behaviors are accordant to the flow conditions. Several empirical equations summarized from experiments have been put forward to predict the size of double emulsions, where Capillary number (Ca = viscosity force/ interface tension) and Weber number (We = inertia force/interface tension) are mostly important to help determine the size of encapsulated emulsion products. These dimensionless criterions further demonstrate that viscoelastic shear deforms the double emulsion growth, characterized by a competition between viscous force and interface tension at the local flow field. However, the influencing factors, such as micro-channel material and geometry, flow conditions, and physical properties of fluids, have complex impacts on the emulsion formation in different ways. Parametric studies of such processes play a key role in distinguishing the flow condition and adjust the double emulsion system.
Lattice Boltzmann method (LBM) has experienced rapid development and attracted increasing interests during the past two decades in simulating multiphase/multicomponent flows owing to its excellent numerical stability and constitutive versatility, especially on solving the challenge of moving and deformable interfaces. Several model frameworks have been established for immiscible multiphase flows, which can be classified as color-gradient method, pseudo-potential method and free energy model. As for the color-gradient method, a great effort has been made to model two-phase flows by the pioneers, where it can be easily expanded to N-phase condition with theoretical analysis and the computation load is greatly reduced. In addition, the model can be adopted for describing multiphase systems with large density and/or viscosity ratio, low interface tension, etc.
In the present work, a ternary LBM model was successfully established to numerically investigate the double emulsion formation process in a microfluidic flow-focusing device [1,2]. The model was validated by comparing the simulated interfacial phenomena in three-phase systems with the theoretical solutions, where physical properties of each fluid can be independently defined in the newly established LB model. Meanwhile, the numerical simulations of the double emulsion formation in different flow regimes showed good agreement with the experimental data in the literature. Especially for the three representative flow regimes, i.e., dripping and jetting and middle jet containing monodispersed inner drop regimes, the model predictions can well disclose the interplay of viscous force and interface tension during the emulsion formation in microchannels. Effect of the viscosities of middle and inner fluids on the occurrence of flow regimes was further discussed, indicating that smaller viscosity of either middle or inner fluid should be beneficial to the double emulsion production.
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