Lagrangian Scalar Tracking for Laminar Micromixing at High Schmidt Numbers

Abstract

In many mixing processes the Schmidt number can easily reach very high values. In such cases the computation of the scalar field by Eulerian methods causes extremely high memory requirements. In the present study we circumvent this problem by adopting a Lagrangian particle tracking method to compute the scalar field in a laminar T-mixer configuration. The flow field is computed by direct numerical simulation (DNS). The movements of representative molecules are determined by the Langevin equation, describing convection by the flow-field and diffusion due to Brownian motion. The scalar field is computed by evaluation of the particle distribution. The particle density required for calculation of resolved concentration fields increases with increasing Schmidt number. For stationary flow regimes, the effective particle density could be increased via sampling in time. In the unsteady case, the effective density can be augmented by parallelization over the particles. No model is required in this approach, and concentration fields for very high Schmidt numbers can be computed. With this method is was possible to compute the fully resolved concentration field in a T-shaped micromixer at Schmidt number 3571 and Reynolds numbers 186 (steady) and 240 (unsteady). Schlu¨ter et. al. [CIT, 76(11), 2004] examined the stationary configuration experimentally. The agreement between numerical and experimental results is excellent. The developed method provides a possibility to compute the fully resolved scalar field in laminar flow regimes at a wide range of Schmidt numbers. It seems that in the cases under consideration Euler methods cannot provide such results. Therefore the proposed method represents a new basis for the prediction of mixing and the development of mixing models for high Schmidt number flows.