Optimized design of droplet micro-mixer with sinusoidal structure based on Pareto genetic algorithm

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Mixing is one of the important steps in biological and chemical reactions and assays. In this paper, we numerically simulate the droplet generation and dynamic mixing in a double T-junction microchannel and optimize the geometry of the sinusoidal microchannel using a Pareto multi-objective genetic algorithm to provide important reference values for the design of efficient and integrated microfluidic chips. We choose two parameters related to the geometry of the sinusoidal microchannel as design variables, and use the average concentration difference within the droplet and the average pressure drop within the microchannel as two objective functions to explore the effects of design variables on the objective functions. The Latin hypercube sampling approach is used as an experimental design tool for parametric studies in design space, and it is used to choose design points in the design space. We employ proxy modeling of response surface functions to approximate the objective function. The Pareto optimal frontier of the micro-mixer is obtained using the Pareto genetic algorithm and the optimal solution set is classified using K-means clustering, from which representative design variables are chosen. The optimal set of solutions optimized with the Pareto genetic algorithm ensures the mixing quality while taking into account the pressure drop inside the microchannel. We also found two important factors affecting the mixing quality. (1) The contraction of the channel cross-section leads to alternating deformation of the droplets and enhances the mixing inside the droplets. When the droplet moves inside the microchannel, the channel cross-section alternately contracts and expands, changing the droplet to undergo alternate deformation, which changes the original internal circulation within the droplet and enhances the mixing inside the droplet. (2) Under the action of centrifugal force, the Dean vortex is generated, which enhances the mixing inside the droplet. The Dean vortex is generated when droplets move inside the curved channel. The Dean vortex causes asymmetric circulating flow inside the droplet, which increases the contact area of the fluid and thus significantly improves the mixing efficiency.