(522d) Lattice Boltzmann Simulation of Mixing-Induced Dynamic Interfacial Tension during Droplet Formation

Microdroplets have emerged as microreactors for the controllable preparation of functional materials. Multiple streams containing different reactants or active ingredients are injected into the microchannel and interact at the crossing forming droplets with a uniform size. During the formation process, the internal components get mixed and reacted, and the reaction efficiency depends on the degree of mixing. Suppose there is an initial interfacial tension difference between the continuous phase and the two miscible dispersed phases. In that case, the interfacial tension will dynamically change with the reactant concentration during the mixing process, which can be expected to affect the mixing inside droplets and the formation process. Meanwhile, the interfacial tension between fluids has a dominant impact on the droplet formation process. It is essential to study the mechanism of microdroplet formation with mixing-induced dynamic interfacial tension.

We propose a ternary color-gradient lattice Boltzmann model to study the droplet formation process accompanied by the mixing-induced dynamic interfacial tension. An isothermal collision operator is introduced to the color-gradient LB model for describing the mixing interaction between two miscible components, where the mutual diffusion coefficient of binary mixtures could be independently adjusted by the relaxation time. Moreover, the model can flexibly couple the correlation between component concentration and interfacial tension to simulate the linear and non-linear variation of interfacial tension. Several numerical cases involving phase decomposition, Laplace law, diffusion coefficient, and wettability of solid boundary have been taken to validate the model performance of simulating mixing-induced dynamic interfacial tension. Through LB simulations, the evolution of the interface deformation caused by the dynamic interfacial tensions between binary components at interfaces with ambient phase is well demonstrated. Then, the effects of the continuous phase flow rate and the initial interfacial tension difference on the droplet formation are investigated by using this model.

The simulation results showed that when there is no initial interfacial tension difference between components, a symmetrical internal vortex field is formed inside the dispersed phase under the shearing of the continuous phase. The mixing of components mainly depends on mutual diffusion. Increasing the flow rate of the continuous phase can improve the mixing efficiency of the whole process. Nevertheless, the increase in flow rate will reduce the droplet formation time, making the droplet disperse without being thoroughly mixed. Furthermore, when there is an initial interfacial tension difference between the two dispersed phases, the dynamic interfacial tension redistributes the components and breaks the original symmetric internal vortex field leading to the promotion of mixing. The greater the difference in initial interfacial tension, the more pronounced the effect on the promotion of mixing and droplet size becomes.

The proposed model has demonstrated strong potential for quantitative investigations on mixing inside droplet microreactors with dynamic interfacial tension phenomenon in microfluidics.