(490i) Ternary Fluid Lattice Boltzmann Simulation of Dynamic Interfacial Tension Induced By Mixing inside Micro-Droplets

Droplet-based microfluidics has been popularly applied in material synthesis, pharmaceutics, analytical and biological chemistry, electro-optic display, and so on, owing to the larger surface area to volume ratio and extra inner vortex for mixing intensification. Among practical applications of droplet-based microfluidics, a general process is observed: usually two or more active ingredients dissolved in different solvents are served as dispersed phases injected into a microdevice. After an inert continuous flow shears the multicomponent flow into the dispersed droplets at the orifice of a microchannel, mixing of miscible solutes is triggered inside microdroplets containing different reagents for further extraction or reaction. Therefore, studies on the mixing inside these soft ‘droplet microreactors’ are highly necessary for the control, intensification and optimization of the related process.

However, it is still challenging for experimental techniques to accurately characterize mixing details in a broad range of physical systems in microfluidics without any limited requirement on systems and channel geometries. Thus, appropriate numerical methods are expected to provide a deep understanding of the mechanism of multiphase/multicomponent mixing involving the interface rupturing and merging at microscale with detailed information. The mesoscopic lattice Boltzmann method (LBM) based on Boltzmann equation and kinetic theory possesses inherent advantages on describing complex interfacial interactions with high numerical stability, constitutive versatility and parallel efficiency. In our previous works, a three-dimensional pseudopotential LB model was established to investigate the effect of channel geometries and the initial distribution of dispersed liquids on mixing inside microdroplets during droplet formation process¹, and later it was applied to reveal the mixing intensification inside a droplet passing through a winding microchannel². Then, we expanded a new collision operator to describe dilute solute transport in ternary fluid color-gradient LB model for simulations of interphase mass transfer and reaction of dilute species inside a moving Janus droplet in microchannel³. It should be noted that the fundamental assumption was made in the dilute solute model, i.e., the dynamic distribution of these solutes would not affect the motion of bulk phase.

However, the mass transfer accompanied with the concentration change of components gives rise to the variation of interfacial tension in many practical chemical processes. It is well known that the interfacial tension always plays a key role in the droplet formation and its motion in microfluidics, which affects the droplet size and flow pattern. The non-uniform distribution of dynamic interfacial tension would affect the hydrodynamic behavior of droplet flows. Most existing studies are focused on the effect of dynamic interfacial tension induced by surfactant adsorption and interphase mass transfer on droplet formation process. But for a more common process having practical relevance, investigation on the mixing of two miscible fluids inside moving droplet microreactors accompanied with the dynamic interfacial tension phenomenon in three-phase flows is rarely reported.

In this work, a ternary fluid color-gradient LB model is proposed to investigate the effect of mixing-induced dynamic interfacial tension on the diffusive mixing of two fluids inside micro-droplets moving in a third continuous phase through a baffled channel. The diffusion coefficient of binary mixtures and mixing-controlled dynamic interfacial tension in this model can be directly defined and independently adjusted. The simulation results show that the large interfacial tension gradient between binary components at the interfaces with the continuous flow promotes the mixing efficiency. The interfacial tension difference leads to the redistribution of components rather than the common toroidal flow inside the droplet in systems without dynamic interfacial tension phenomenon at the early stage of mixing. The present model can be easily applied to characterize the mixing behavior inside droplets in the practical processes involving the dynamic interfacial tension phenomenon and helpful for the prediction, design and optimization of the relevant practical process.

References:

1. 1. Zhao SF, Wang WT, Zhang MX, Shao T, Jin Y, Cheng Y. Three-dimensional simulation of mixing performance inside droplets in micro-channels by Lattice Boltzmann method. Chem. Eng. J. 2012;207:267-277.
2. 2. Wang WT, Shao T, Zhao SF, Jin Y, Cheng Y. Experimental and Numerical Study of Mixing Behavior inside Droplets in Microchannels. AlChE J. 2013;59(5):1801-1813.
3. 3. Fu YH, Bai L, Luo KH, Jin Y, Cheng Y. Modeling mass transfer and reaction of dilute solutes in a ternary phase system by the lattice Boltzmann method. Phys. Rev. E. 2017;95(4).