On the estimate of mixing length in interdigital micromixers

The multilamination process that characterizes interdigital micromixers is an efficient and technologically feasible method for maximizing and controlling mass and/or heat transfer between two or more segregated fluid streams. We analyze the dynamics of mixing that takes place in the mixing channel downstream the interdigital apparatus. Specifically, we investigate, for different flow profiles, how the channel length necessary to achieve a prescribed level of mixedness depends on the degree of lamination (number and thickness of lamellae) of the feed stream. As a case study, we consider plug, shear and Poiseuille flow, and compare steady-state profiles resulting from the numerical simulation of the full advection–diffusion problem with the analytical solution stemming from the one-dimensional Sturm–Liouville eigenvalue problem along the spanwise coordinate, obtained neglecting streamwise diffusion. We find that (i) the mixing length can be significantly affected by the flow profile, especially at high degree of lamination of the feed stream, and (ii) in general, no obvious scaling between mixing length and lamellar thickness can be assumed. A rigorous way to approach the design of these micromixers is proposed.