Finding the optimal design of a Cantor fractal-based AC electric micromixer with film heating sheet by a three-objective optimization approach

In this paper, we present a three-objective optimization process for an Alternating Current (AC) electrothermal theory-based micromixer. For the first time, we propose to combine the three-objective optimization of the AC electric heating micromixer with the fractal principle. We chose the width-to-length ratio (a/b) of the AC electrode based on the Cantor fractal, the inlet velocity (U), the voltage amplitude (V) and the heat of the film heating sheet (Q) as design variables. The mixing index, the temperature rise and the mixing energy cost are used as the objective functions. The Latin Hypercube Sampling method is used to select design points within the design range. The response surface function method is used to build the surrogate model. We use Multi-objective genetic algorithm to optimize the surrogate model to obtain the Pareto optimal surface. Finally, we use K-means clustering method to classify the optimal solution set, and select a representative design point from each class for numerical analysis. What is more, the relationship between the three objective functions in the Pareto optimal solution set can be weighed, which means that we can choose a micromixer with better overall performance. The results show that the mixing index of the optimized micromixer is increased by a maximum of 19.81% compared with the reference design, and the mixing energy cost is 73.16% lower than the reference design. The safety and reliability of the micromixer are greatly improved by multi-objective optimization.