In this work, a serpentine mixing unit model based on topology optimization is proposed to enhance the reverse flow in both horizontal and vertical directions. The increase in reverse flow in both directions can enhance the chaotic advection phenomenon, leading to a rapid increase in the mixing index. The proposed mixing unit model is applied in a T-shaped micromixer to create a new micromixer design, named TOD. Numerical simulations of TOD are performed using Comsol Multiphysics software to analyze the characteristics of the liquid flow, mixing surface, and pressure drop. The simulation results confirm that TOD has an outstanding mixing performance. By widening the surface area of contact and enhancing the chaotic advection phenomenon, TOD shows an excellent mixing performance at both a high and low Reynolds number, making it a promising micromixer design. For Re > 5, the mixing indexes of TOD are all beyond 90%.