A double MRT-LBM for simulation of mixing in an active micromixer with rotationally oscillating stirrer in high Peclet number flows

In the present study, a double multiple relaxation time lattice Boltzmann method (MRT-LBM) simulation is performed to analyze the performance of an active micromixer with rotationally oscillating stirrer in high Peclet number flows. Almost all previous LBM studies consider the stirrer as a zero-thickness flat plate, while in the present problem, the stirrer has been considered as a rectangular cylinder with different aspect ratios. Calculations are performed for the important dimensionless parameters of the problem including the oscillation amplitude (K) and aspect ratio (AR) in the range of 0.1-1, while the Strouhal number (St) varies in the range of 0.5-2 for Re=1 and Pe = 10,000. The aim was to evaluate the effects of these parameters on the mixing efficiency in search for the optimal micromixer design. Results indicated that the dimensionless mixing efficiency at the microchannel outlet (εout) increases smoothly with the increase of K at relatively large aspect ratios. Furthermore, at a given amplitude, the εout is slightly influenced by the aspect ratio variations, especially at lower values of K, while it is strongly affected by the Strouhal number (St). Moreover, the costs associated with the mixing process is evaluated with the parameter mixing energy cost (mec) defined as the required cyclic average input power to the obtained averaged mixing at the channel exit. It was found that mec is much higher at the St = 2 as compared to its lower values for all AR and K values. Also, increasing the AR increases the mec for almost all K and St. In general, it can be concluded that 0.1, 1.1, 1 for the εout and 0.1, 0.5, 1 for mec are determined as the optimum values of AR, St and K, respectively.