Numerical Study of the Mixing Characteristics for Rotating and Oscillating Stirrers in a Microchannel

Abstract

The mixing effect was studied numerically by calculating the flows driven by rotating and oscillating stirrers in a microchannel. The D2Q9 lattice Boltzmann method was used due to the merits of the calculation for an unsteady flow with a moving boundary. Within the range of Reynolds numbers from 10 to 80, the concentration distributions for different stirring speeds of the stirrer were investigated and the physical mixing characteristics were illustrated for both the rotating and oscillating stirrers. In this paper, a new time-averaged mixing index formula, D-I = 1/T Sigma(T)(t=1) root 1/N Sigma(N)(i-1) (C-mean/Ci-C-mean)(2), is presented for use in evaluating the mixing rate for periodic, unsteady flows, instead of the conventional one for steady flows. From the variation of the calculated D-I critical values for the stirring speed, which have a maximum mixing efficiency, were found to exist. In addition, the oscillating stirrer was found to have a better mixing efficiency than the rotating stirrer at the critical stirring speed for each Reynolds number.