Thorough computational analysis of the staggered herringbone micromixer reveals transport mechanisms and enables mixing efficiency-based improved design

Abstract

The problem of mixing of solutions of biomolecules in the famous staggered herringbone micromixer (SHM) is revisited through a computational study with the focus on two overlooked aspects, namely the accuracy of the numerical solution and the thorough analysis of the mixing process. The study is based on the numerical solution of the continuity and Navier-Stokes equations and the mass balance of the solute. The numerical instabilities, induced by the high Péclet number (extremely low diffusion coefficient of biomolecules), are handled with stabilization methods and the accuracy is ensured by a) dense adaptive meshes constructed by an error criterion and b) systematic studies of the mesh independence of the numerical solution. The importance of the accuracy on the calculated mixing efficiency (ME) and the design of the SHM is demonstrated through a comparison with the results for non-adaptive and coarse meshes. The ME versus the length of the SHM is compared with experimental data for the first time, with the mesh independent solution in good agreement with them. The thorough analysis brings to light symmetries and periodicities in the velocity field and explains the inflection point of the ME versus the length of the SHM, observed in experimental and computational studies. Without an optimization algorithm, designs which increase the ME up to 100% and reduce the mixing length are proposed. In particular, the mixing length is reduced a) by 8% through the introduction of symmetric grooves in the SHM, b) up to 39%, if the bottom of the SHM is made slippery, and c) up to 49% by adding symmetric grooves in case (b). The effect of the designs on the chaotic advection is demonstrated.