Staggered passive micromixers with fractal surface patterning

We present a procedure for inducing chaotic mixing based on a non-periodic patterning of the walls making use of the Weierstrass fractal function to generate the locations for the grooves. We show the numerical analysis of flow in three different geometries generated with the Weierstrass function and compare the results with a fourth geometry, quite similar to the staggered herringbone mixer (SHM) of Stroock et al (2002 Science 295 647), for which the patterning is periodic. We evaluate the Lyapunov exponents for massless and non-interacting particles advected by the flow and traced along the channels. We also compute the entropy of mixing for binary mixtures. Finally, we compute generalized (fractal) dimensions associated with the interface of the two fluids. The results show consistently substantial enhancement in mixing efficiency for two of the Weierstrass channels compared to the SHM.