Transient micromixing: Examples of laminar and chaotic stirring

The efficiency of a micromixing device may be quantified by the time taken for a given initial state of separated fluids to reach a desired level of homogenization. In the physically relevant case of high Peclet number the accurate prediction of the mixing time is a challenging problem, even in simple two-dimensional flows within bounded domains. In this paper a closed-form solution for the time dependence of mixing in an annular micromixer is derived and verified by numerical simulation. The mixing time is found to scale with Peclet number as a power law, but the power-law exponent depends on the level of homogeneity desired in the final state. Numerical simulation of a recent model of chaotic mixing reveals a vortexlike stirring effect in quasiperiodic islands of the Poincaré map of the flow, which strongly influences the mixing time. This stirring effect is identified with an exponential decrease in solute variance on an intermediate time scale, being subdominant to the asymptotic long-time decay, but sensitive to the initial loading of fluids in the mixer. The subdominant decay rate is calculated to scale with Peclet number as the square root of the dominant decay rate.