Shape optimization of a micromixer with staggered-herringbone grooves patterned on opposite walls

The shape optimization of a micromixer with staggered-herringbone grooves at both the top and bottom walls has been performed through three-dimensional Navier-Stokes analysis. The mixing of two working fluids, viz., water and ethanol, is considered at Re = 1. The mixing index at the exit of the micromixer is selected as the objective function and four design variables, viz., the number of grooves per half cycle, angle of grooves, ratio of the groove depth to channel height, and ratio of the groove width to pitch are chosen out of the various geometric parameters that affect the performance of a micromixer with regard to shape optimization. The variance of the mass-fraction at various nodes on a plane is used to quantify the mixing performance in the micromixer. The design space is explored through some preliminary calculations and a Latin hypercube sampling method is used as the design of experiments to select design points in the design space. The objective function values are obtained at these design points by Navier-Stokes analysis, and a surrogate model, namely, the response surface approximation method, is used to construct a response surface for the objective function. Sequential quadratic programming is used to find out an optimal solution on the constructed response space. The optimization results show that the mixing is highly sensitive to the shape of the groove as well as the number of grooves per cycle, which can be used to control mixing in microfluidics. Through the optimization, the mixing index at the exit of the micromixer is enhanced by about 9% in comparison with the reference design.