Abstract
Double emulsion formation in a hierarchical flow-focusing channel is systematically investigated using a free energy ternary lattice Boltzmann model. A three dimensional formation regime diagram is constructed based on the capillary numbers of the inner ($Ca_i$), middle ($Ca_m$) and outer ($Ca_o$) phase fluids. The results show that the formation diagram can be classified into periodic two-step region, periodic one-step region, and non-periodic region. By varying $Ca_i$ and $Ca_m$ in the two-step formation region, different morphologies are obtained, including the regular double emulsions, decussate regimes with one or two alternate empty droplets, and structures with multiple inner droplets contained in the continuous middle phase thread. Bidisperse behaviors are also frequently encountered in the two-step formation region. In the periodic one-step formation region, scaling laws are proposed for the double emulsion size and for the size ratio between the inner droplet and the overall double emulsion. Furthermore, we show that the interfacial tension ratio can greatly change the morphologies of the obtained emulsion droplets, and the channel geometry plays an important role in changing the formation regimes and the double emulsion sizes. In particular, narrowing the side inlets or the distance between the two side inlets promotes the conversion from the two-step formation regime to the one-step formation regime.
Highlights
Double emulsions are droplets with one other droplet inside
We have learned the effects of Cao on two-step formation regimes in figure 7(c): the inner droplet size is almost independent of Cao, but the breakup frequency of the middle phase increases with increasing Cao, which could further lead to the decussate regime
A two-dimensional ternary free-energy lattice Boltzmann model is developed and used to systematically study the double emulsion formation behaviours in a planar hierarchical flow-focusing channel under variations of the flow rate, interfacial tension ratio and geometrical settings
Summary
Double emulsions are droplets with one other droplet inside. Their core–shell structure has attracted wide attention in various fields (Vladisavljevic, Nuumani & Nabavi 2017). In contrast to other microfluidic geometries, systematic parametric study is rarely reported on planar flow-focusing devices Several works, such as Abate et al (2011) and Azarmanesh et al (2016), briefly discussed the possible conversion between the two-step and one-step formation regimes and the variation of shell thickness. It remains unclear in which flow rate regions monodisperse double emulsions are produced, and correspondingly, how the droplet sizes can be varied in those regions. Coupling the free-energy model with the advantages of the lattice Boltzmann method, we conduct a systematic study on the dynamics of double emulsion formation behaviours in planar hierarchical flow-focusing junctions.
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