Computational study of convective–diffusive mixing in a microchannel mixer

Scalar mixing due to convection and diffusion in a microchannel mixer is studied using CFD. A method is developed to quantitatively measure the effect of false diffusion on scalar decay rate. This method computes an average false diffusivity from a given numerical solution and it is not limited to any particular numerical scheme. It is found that a range of molecular diffusivity exist in which average false diffusion is smaller than molecular diffusion and scalar decay rates can be computed accurately with CFD in the mixer. This range of molecular diffusivity covers most of the liquid solutions encountered in chemical and biochemical engineering. When effective diffusivity is used, this range can be further expanded. The predicted mixing structures agree well with experimental results in literature. The classical lamellar structures of the baker's transformation are strongly affected by diffusion. The striation doubling process is destroyed by diffusion broadening at very early stage in the mixer. The optimal mixing is achieved at low Re when the mixing mechanism in the mixer is the baker's transformation. At higher Re, secondary flow is generated and the mixing mechanism is the competition of the kinematics of the baker's transformation and the dynamics of the cross sectional flow. Results show that the secondary flow hinders mixing and the scalar decays at lower exponential rates than when the mixing is due to the baker's transformation alone.