Residence time distributions for in-line chaotic mixers.

We investigate the distributions of residence time for in-line chaotic mixers; in particular, we consider the Kenics, the F-mixer, and the multilevel laminating mixer and also a synthetic model that mimics their behavior and allows exact mathematical calculations. We show that whatever the number of elements of mixer involved, the distribution possesses a t^{-3} tail, so that its shape is always far from Gaussian. This t^{-3} tail also invalidates the use of second-order moment and variance. As a measure for the width of the distribution, we consider the mean absolute deviation and show that, unlike the standard deviation, it converges in the limit of large sample size. Finally, we analyze the performances of the different in-line mixers from the residence-time point of view when varying the number of elements and the shape of the cross section.

Two-dimensional numerical model of Marangoni surfers: From single swimmer to crystallization.

We numerically study the dynamics of an ensemble of Marangoni surfers in a two-dimensional and unconfined space. The swimmers are modeled as Gaussian sources of surfactant generating surface tension gradients and are shown to follow the Marangoni flow filtered at their spatial scale in the lubrication regime, an unstable situation leading to spontaneous motion as soon as the Marangoni effect is intense enough. As the system is fully unconstrained, it is possible to study the various dynamical regimes from single swimmer, two-body interaction, to the many-particles case characterized by an efficient particle dispersion. We show that, although the present model is very simple, it reproduces the experimentally observed transition between a regime of dispersion by random agitation when the number of swimmers is moderate to the regime of crystallization with imperfect hexagonal lattice at high density.

Numerical modeling of DNA-chip hybridization with chaotic advection.

We present numerical simulations of DNA-chip hybridization, both in the "static" and "dynamical" cases. In the static case, transport of free targets is limited by molecular diffusion; in the dynamical case, an efficient mixing is achieved by chaotic advection, with a periodic protocol using pumps in a rectangular chamber. This protocol has been shown to achieve rapid and homogeneous mixing. We suppose in our model that all free targets are identical; the chip has different spots on which the probes are fixed, also all identical, and complementary to the targets. The reaction model is an infinite sink potential of width dh , i.e., a target is captured as soon as it comes close enough to a probe, at a distance lower than dh . Our results prove that mixing with chaotic advection enables much more rapid hybridization than the static case. We show and explain why the potential width dh does not play an important role in the final results, and we discuss the role of molecular diffusion. We also recover realistic reaction rates in the static case.