On the modelling of time-interleaved sequential lamination micromixers

We develop a novel and simple theoretical model of time-interleaved sequential lamination micromixers that improves the model proposed by Nguyen and coworkers (Microfluid Nanofluid 1:373–375, 2005a, Lab Chip 5:1320–1326, b, J Phys Conf Ser 34:136–141, 2006) based on the Taylor–Aris dispersion theory. The Nguyen model takes into account the non uniform structure of the velocity profile through an effective dispersion coefficient. However, it is essentially a one-dimensional model that is not suitable to describe (i) neither the behavior of mixing occurring at short length-scales, and characterized by the growth of a mixing boundary layer near the channel walls, (ii) nor the exponential decay of the concentration field occurring at larger length-scales. The model we propose, which is based upon the theory of imaginary potential developed by Giona et al. (J Fluid Mech 513:221–237, 2004, Europhys Lett 83:34001, 2008, J Fluid Mech 639:291–341, 2009a), is able to provide quantitative predictions on the evolution of the L2-norm of the concentration fields as function of the axial coordinate ξ, both for short and asymptotic lengthscales. The quantitative comparison with respect to the Nguyen model is illustrated and discussed. Finally, the coupling between parallel lamination and sequential segmentation is analyzed, and leads to unexpected and apparently counter-intuitive findings.