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A ternary fluid color-gradient lattice Boltzmann model is proposed to investigate the effect of mixing-induced dynamic interfacial tension on the diffusive mixing of two fluids inside microdroplets moving in a third continuous phase through a baffled channel. The diffusion coefficient of binary mixtures and dynamic interfacial tension in this model can be directly defined and independently adjusted. The simulation results show that the dynamic interfacial tension between miscible binary fluids at interfaces with ambient phase would lead to the motion of the interface and redistribution of solutes inside the droplet during mixing. The larger initial interfacial tension gradient would improve mixing efficiency at early stages by promoting faster solute flow. The present model can be easily applied to quantitatively characterize the mixing behavior inside droplets in the practical processes involving the dynamic interfacial tension phenomenon and inspire new designs for mixing intensification.

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The mixing process between miscible fluids in a splitting-and-recombination microreactor is analyzed numerically by solving the Navier–Stokes equation and species transfer equation. The commercial microreactor combines rectangular channels with comb-shaped inserts to achieve the splitting-and-recombination effect. The results show that the microreactor with three-layer standard inserts have the highest mixing rate as well as good mixing efficiency within a wide range of Reynolds numbers from 0.1 to 160. The size parameters of the inserts, both the ratio of the width of comb tooth (marked as l) and the spacing distance (marked as s) between two comb teeth, and the ratio of the vertical distance (marked as V) of comb teeth and the horizontal distance (marked as H) are essential for influencing the liquid–liquid mixing process at low Reynolds numbers (e.g., Re ≤ 2). With the increase of s/l from 1 to 4, the mixing efficiency drops from 0.99 to 0.45 at Re = 0.2. Similarly, the increase in V/H is not beneficial to promote the mixing between fluids. When the ratio of V/H changes from 10:10 to 10:4, the splitting and recombination cycles reduce so that the uniform mixing between different fluids can be hardly achieved. The width of comb tooth (marked as l) is 1 mm and the spacing distance (marked as s) between two comb teeth is 2 mm. The vertical distance (marked as V) of comb teeth and the horizontal distance (marked as H) are both 10 mm.