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In this paper, a series of novel passive micromixers, called topological micromixers with reversed flow (TMRFX), are proposed. The reversed flow in the microchannels can enhance chaotic advection and produce better mixing performance. Therefore the maximum of reversed flow is chosen as the objective function of the topology optimization problem. Because the square-wave unit is easier to fabricate and have better mixing performance than many other serpentine micromixers, square-wave structure becomes the original geometry structure. By simulating analysis, the series of TMRFX, namely TMRF, TMRF0.75, TMRF0.5, TMRF0.25, mix better than the square-wave micromixer at various Reynolds numbers (Re), but pressure drops of TMRFX are much higher. Lots of intensive numerical simulations are conducted to prove that TMRF and TMRF0.75 have remarkable advantages on mixing over other micromixers at various Re. The mixing performance of TMRF0.75 is similar to TMRF's. What's more, TMRF have a larger pressure drop than TMRF0.75, which means that TMRF have taken more energy than TMRF0.75. For a wide range of Re (Re ≤ 0.1 and Re ≥ 10), TMRF0.75 delivers a great performance and the mixing efficiency is greater than 95 %. Even in the range of 0.1-10 for the Re, the mixing efficiency of TMRF0.75 is higher than 85 %.

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